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Journal articles on the topic 'Interpolation Filters'

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Author: Grafiati

Published: 14 March 2023

Last updated: 1 June 2024

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1

Zhou, Xiao, Chengyou Wang, Zhi Zhang, and Qiming Fu. "Interpolation Filter Design Based on All-Phase DST and Its Application to Image Demosaicking." Information 9, no. 9 (August 21, 2018): 206. http://dx.doi.org/10.3390/info9090206.

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Based on a deep understanding of all-phase digital filter (APDF) design and all-phase biorthogonal transform (APBT), this paper will further study the windowed all-phase digital filter (WAPDF) and windowed all-phase biorthogonal transform (WAPBT), discuss the principle of the WAPBT, and provide a unified construction method of the all-phase transform (APT). Based on a type of orthogonal transform, i.e., discrete sine transform (DST), an interpolation filter called an all-phase DST (APDST) filter is constructed and used for image demosaicking; it is compared with bilinear interpolation and all-phase inverse discrete cosine transform (APIDCT) interpolation filters, to test its performance in image interpolation and provide analysis and discussion. The experimental results show that APIDCT and APDST filters with a size of 7 × 7 are similar in interpolation performance, but better than the bilinear interpolation method. In addition to its use in image interpolation demosaicking, the low-pass filter designed in this paper can also be widely used in image interpolation, image denoising, image resizing, and other fields of image processing.

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2

Lim, SuYeon, MinKyeong Choi, and Yunglyul Lee. "Frequency-Based Adaptive Interpolation Filter in Intra Prediction." Applied Sciences 13, no. 3 (January 22, 2023): 1475. http://dx.doi.org/10.3390/app13031475.

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This paper proposes a method to improve the fractional interpolation of reference samples in the Versatile Video Coding (VVC) intra prediction. The proposed method uses additional interpolation filters which use more integer-positioned reference samples for prediction according to the frequency information of the reference samples. In VVC, a 4-tap Discrete Cosine Transform-based interpolation filter (DCT-IF) and 4-tap Smoothing interpolation filter (SIF) are alternatively performed on the block size and block directional prediction mode for reference sample interpolation. This paper uses four alternative interpolation filters such as 8-tap/4-tap DCT-IFs, and 4-tap/8-tap SIFs and an interpolation filter selection method using a high-frequency ratio calculated from one-dimensional (1D) transform of the reference samples are proposed. The proposed frequency-based Adaptive Filter allows to achieve the overall Bjøntegaard Delta (BD) rate gains of −0.16%, −0.13%, and −0.09% for Y, Cb, and Cr components, respectively, compared with VVC.

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3

Savinykh, I. S., and D. A. Chemasov. "Computing efficiency of the three-stage interpolated low pass filters." Radio industry 28, no. 4 (November 27, 2018): 21–27. http://dx.doi.org/10.21778/2413-9599-2018-28-4-21-27.

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Undoubted advantages of finite impulse response filters are their unconditional stability, the absence of limit cycles and the possibility of implementing a filter that does not introduce phase distortion. The disadvantage of such filters is the large cost required to compute the response. This paper considers three-stage interpolated finite impulse response low-pass filters. The maximum values of the interpolation factors are determined. Dependences of the coefficient of computational efficiency and the coefficient of increase in the registers of the three-stage interpolated low-pass filter on the values of the interpolation factors, the widths of the passband and the transition band are obtained. Relations for determining the optimal values of interpolation factors corresponding to the maximal value of computational efficiency coefficient are obtained. In addition, the dependencies of the maximum coefficient of computational efficiency and the optimal coefficient of increase in the registers of the three-stage interpolated low-pass filter on the widths of the passband and the transition band at the optimum values of the interpolation factors are obtained. Considered three-stage interpolated low-pass filters should be used in the case when the required stopband is significantly less than the sampling rate. In this case, three- stage interpolated filters require less computational resources for calculating the response than the two-stage interpolated filters or filter implemented by the transversal structure.

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4

Naghizadeh, Mostafa, and Mauricio D. Sacchi. "f-x adaptive seismic-trace interpolation." GEOPHYSICS 74, no. 1 (January 2009): V9—V16. http://dx.doi.org/10.1190/1.3008547.

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We use exponentially weighted recursive least squares to estimate adaptive prediction filters for frequency-space [Formula: see text] seismic interpolation. Adaptive prediction filters can model signals where the dominant wavenumbers vary in space. This concept leads to an [Formula: see text] interpolation method that does not require windowing strategies for optimal results. In other words, adaptive prediction filters can be used to interpolate waveforms that have spatially variant dips. The interpolation method’s performance depends on two parameters: filter length and forgetting factor. We pay particular attention to selection of the forgetting factor because it controls the algorithm’s adaptability to changes in local dip. Finally, we use synthetic- and real-data examples to illustrate the performance of the proposed adaptive [Formula: see text] interpolation method.

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Dilip, Pawar Ashwini, K. Rameshbabu, Kanase Prajakta Ashok, and Shital Arjun Shivdas. "Bilinear Interpolation Image Scaling Processor for VLSI Architecure." International Journal of Reconfigurable and Embedded Systems (IJRES) 3, no. 3 (November 1, 2014): 104. http://dx.doi.org/10.11591/ijres.v3.i3.pp104-113.

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We introduce image scaling processor using VLSI technique. It consist of Bilinear interpolation, clamp filter and a sharpening spatial filter. Bilinear interpolation algorithm is popular due to its computational efficiency and image quality. But resultant image consist of blurring edges and aliasing artifacts after scaling. To reduce the blurring and aliasing artifacts sharpening spatial filter and clamp filters are used as pre-filter. These filters are realized by using T-model and inversed T-model convolution kernels. To reduce the memory buffer and computing resources for proposed image processor design two T-model or inversed T-model filters are combined into combined filter which requires only one line buffer memory. Also, to reduce hardware cost Reconfigurable calculation unit (RCU)is invented. The VLSI architecture in this work can achieve 280 MHz with 6.08-K gate counts, and its core area is 30 378 <em>μ</em>m2 synthesized by a 0.13-<em>μ</em>m CMOS process.

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6

Shan, Bao Tang, and Fa Nian Wang. "Design and Application of a Multi-Phase Interpolation Filter." Applied Mechanics and Materials 556-562 (May 2014): 4518–21. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.4518.

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Multi-phase Interpolation Filters are used widely in wireless communication. Based on the requirements of a high data rate satellite modem, this paper analyses the basic design principle of a multi-phase interpolation filter. A new design scheme of multi-phase interpolation filter is presented and implemented with VHDL TOP-DOWN method on FPGA. Finally, part simulation and application test results are given.

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7

Begon, Mickaël, and Patrick Lacouture. "Accuracy of 3-D Reconstruction with Occlusions." Journal of Applied Biomechanics 26, no. 1 (February 2010): 104–8. http://dx.doi.org/10.1123/jab.26.1.104.

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A marker has to be seen by at least two cameras for its three-dimensional (3-D) reconstruction, and the accuracy can be improved with more cameras. However, a change in the set of cameras used in the reconstruction can alter the kinematics. The purpose of this study was to quantify the harmful effect of occlusions on two-dimensional (2-D) images and to make recommendations about the signal processing. A reference kinematics data set was collected for a three degree-of-freedom linkage with three cameras of a commercial motion analysis system without any occlusion on the 2-D images. In the 2-D images, some occlusions were artificially created based on trials of real cyclic motions. An interpolation of 2-D trajectories before the 3-D reconstruction and two filters (Savitsky–Golay and Butterworth filters) after reconstruction were successively applied to minimize the effect of the 2-D occlusions. The filter parameters were optimized by minimizing the root mean square error between the reference and the filtered data. The optimal parameters of the filters were marker dependent, whereas no filter was necessary after a 2-D interpolation. As the occlusions cause systematic error in the 3-D reconstruction, the interpolation of the 2-D trajectories is more appropriate than filtering the 3-D trajectories.

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8

Won, Chee Sun. "Grid adaptive interpolation filters." Electronics Letters 49, no. 3 (January 2013): 181–82. http://dx.doi.org/10.1049/el.2012.2481.

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9

Vesma, Jussi, and Tapio Saramaki. "Polynomial-Based Interpolation Filters—Part I: Filter Synthesis." Circuits, Systems & Signal Processing 26, no. 2 (April 2007): 115–46. http://dx.doi.org/10.1007/s00034-005-0704-8.

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10

Preatto, Stefania, Andrea Giannini, Luca Valente, Guido Masera, and Maurizio Martina. "Optimized VLSI Architecture of HEVC Fractional Pixel Interpolators with Approximate Computing." Journal of Low Power Electronics and Applications 10, no. 3 (August 17, 2020): 24. http://dx.doi.org/10.3390/jlpea10030024.

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High Efficiency Video Coding (HEVC) is the latest video standard developed by the Joint Video Exploration Team. HEVC is able to offer better compression results than preceding standards but it suffers from a high computational complexity. In particular, one of the most time consuming blocks in HEVC is the fractional-sample interpolation filter, which is used in both the encoding and the decoding processes. Integrating different state-of-the-art techniques, this paper presents an architecture for interpolation filters, able to trade quality for energy and power efficiency by exploiting approximate interpolation filters and by halving the amount of required memory with respect to state-of-the-art implementations.

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11

Wang, Gang, Hexin Chen, Mianshu Chen, Qiang Zhao, and Yingjie Song. "Fractional-pel Interpolation Algorithm Based on Adaptive Filter." International Journal of Pattern Recognition and Artificial Intelligence 34, no. 08 (November 18, 2019): 2054022. http://dx.doi.org/10.1142/s0218001420540221.

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In order to further improve fractional-pel interpolation image quality of video sequence with different resolutions and reduce algorithm complexity, the fractional-pel interpolation algorithm based on adaptive filter (AF_FIA) is proposed. This algorithm adaptively selects the interpolation filters with different orders according to the three video sequence regions with different resolutions; in the three video sequence regions with different resolutions, the high-order interpolation filter is replaced by low-order interpolation filter according to the correlation between pixels to realize the adaptive selection of filter. The complexity analysis results show that compared with other algorithms, this algorithm reduces space complexity and computation complexity, thus reducing the storage access and coding time. The simulation results indicate that compared with other algorithms, this algorithm has good coding performance and robustness for video sequences with different resolutions.

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12

Jeon, Gwang Gil. "Designing and Performance Assessment for Sensor Color Interpolation." Advanced Materials Research 705 (June 2013): 307–12. http://dx.doi.org/10.4028/www.scientific.net/amr.705.307.

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This paper addresses the problem of color restoration on Lukac color filter array (CFA) pattern [. Digital camera acquires the continuous color spectrum using three filters. However, each pixel indicates only a sample out of three channels. This order is called a mosaicking and the opposite process is called demosaicking. This article designs filters for Lukac CFA, and apply it to generate demosaicked images. The objective (CPSNR and S-CIELAB) and visual quality comparison are provided in simulation results section.

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13

Balster, Eric J., Francis D. Fradette, Frank A. Scarpino, and Kerry L. Hill. "Time-Domain Matrix Analysis of Polyphase FIR Filters." International Journal of Electrical Engineering & Education 49, no. 3 (July 2012): 275–90. http://dx.doi.org/10.7227/ijeee.49.3.7.

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Polyphase filter design is a common subject studied in discrete systems analysis and digital signal processing (DSP) courses. However, the classic z-domain analysis, utilizing the noble identities, gives a conclusion to the true physical structures of polyphase filters which may not be obvious to many students. The proposed time-domain analysis provides a more straightforward development of polyphase implementation of interpolation and decimation functions, and hopes to provide students with a more visual representation of the polyphase interpolation and decimation processes. Results from a student survey show that over 73% of students believe that the proposed polyphase analysis strengthened their understanding of polyphase filters, and over 71% would prefer to use the proposed method over the traditional z-domain analysis when explaining polyphase filters to others.

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14

RAMACHANDRAN, V., and V. NINOV. "2D ZERO-PHASE FIR FILTER DESIGN WITH NONUNIFORM FREQUENCY SAMPLING." Journal of Circuits, Systems and Computers 10, no. 05n06 (October 2000): 239–77. http://dx.doi.org/10.1142/s0218126600000172.

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In this paper, nonuniform frequency sampling techniques used in the design of two-dimensional zero-phase FIR filters are proposed and investigated. The design problem is treated as a bivariate interpolation problem with unevenly spaced data. The main idea is to select (find) sampling locations in the (ω1, ω2) frequency plane and corresponding sample values Hd(ω1k, ω2k) of the desired filter frequency response such that the designed filter performance is high. Although the filters designed with the proposed techniques are not optimal, the methods are conceptually simple and produce filters with high degree of shape regularity and approximation error comparable and sometimes even smaller than the "conventional" 2D FIR filter design methods.

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15

Çetin, A. Enis, and Rashid Ansari. "Digital interpolation beamforming using recursive filters." Journal of the Acoustical Society of America 85, no. 1 (January 1989): 493–95. http://dx.doi.org/10.1121/1.397701.

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16

Liu, Yang, Geng Wu, and Zhisheng Zheng. "Seismic data interpolation without iteration using a t-x-y streaming prediction filter with varying smoothness." GEOPHYSICS 87, no. 1 (November 19, 2021): V29—V38. http://dx.doi.org/10.1190/geo2021-0052.1.

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Although there is an increase in the amount of seismic data acquired with wide-azimuth geometry, it is difficult to achieve regular data distributions in spatial directions owing to limitations imposed by the surface environment and economic factors. To address this issue, interpolation is an economical solution. The current state-of-the-art methods for seismic data interpolation are iterative methods. However, iterative methods tend to incur high computational costs, which restricts their application in cases of large, high-dimensional data sets. Hence, we have developed a two-step noniterative method to interpolate nonstationary seismic data based on streaming prediction filters (SPFs) with varying smoothness in the time-space domain and we extend these filters to two spatial dimensions. Streaming computation, which is the kernel of the method, directly calculates the coefficients of nonstationary SPF in the overdetermined equation with local smoothness constraints. In addition to the traditional streaming prediction-error filter, we adopt a similarity matrix to improve the constraint condition in which the smoothness characteristics of the adjacent filter coefficient change with the varying data. We also design noncausal-in-space filters for interpolation by using several neighboring traces around the target traces to predict the signal; this is performed to obtain more accurate interpolated results than those from the causal-in-space version. Compared to the Fourier projection onto a convex sets interpolation method, our method has the advantages of fast computational speed and nonstationary event reconstruction. Application of our method on synthetic and nonstationary field data finds that it can successfully interpolate high-dimensional data with low computational cost and reasonable accuracy even in the presence of aliased and conflicting events.

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17

Dumitrescu and Boiangiu. "A Study of Image Upsampling and Downsampling Filters." Computers 8, no. 2 (April 23, 2019): 30. http://dx.doi.org/10.3390/computers8020030.

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In this paper, a set of techniques used for downsampling and upsampling of 2D images is analyzed on various image datasets. The comparison takes into account a significant number of interpolation kernels, their parameters, and their algebraical form, focusing mostly on linear interpolation methods with symmetric kernels. The most suitable metrics for measuring the performance of upsampling and downsampling filters’ combinations are presented, discussing their strengths and weaknesses. A test benchmark is proposed, and the obtained results are analyzed with respect to the presented metrics, offering explanations about specific filter behaviors in general, or just in certain circumstances. In the end, a set of filters and parameters recommendations is offered based on extensive testing on carefully selected image datasets. The entire research is based on the study of a large set of research papers and on a solid discussion of the underlying signal processing theory.

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18

Aldababseh, Mahmoud, and Ali Jamoos. "Estimation of FBMC/OQAM Fading Channels Using Dual Kalman Filters." Scientific World Journal 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/586403.

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We address the problem of estimating time-varying fading channels in filter bank multicarrier (FBMC/OQAM) wireless systems based on pilot symbols. The standard solution to this problem is the least square (LS) estimator or the minimum mean square error (MMSE) estimator with possible adaptive implementation using recursive least square (RLS) algorithm or least mean square (LMS) algorithm. However, these adaptive filters cannot well-exploit fading channel statistics. To take advantage of fading channel statistics, the time evolution of the fading channel is modeled by an autoregressive process and tracked by Kalman filter. Nevertheless, this requires the autoregressive parameters which are usually unknown. Thus, we propose to jointly estimate the FBMC/OQAM fading channels and their autoregressive parameters based on dual optimal Kalman filters. Once the fading channel coefficients at pilot symbol positions are estimated by the proposed method, the fading channel coefficients at data symbol positions are then estimated by using some interpolation methods such as linear, spline, or low-pass interpolation. The comparative simulation study we carried out with existing techniques confirms the effectiveness of the proposed method.

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19

Fang, Wenqian, Lihua Fu, Shaoyong Liu, and Hongwei Li. "Dealiased seismic data interpolation using a deep-learning-based prediction-error filter." GEOPHYSICS 86, no. 4 (June 30, 2021): V317—V328. http://dx.doi.org/10.1190/geo2020-0487.1.

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Deep-learning (DL) technology has emerged as a new approach for seismic data interpolation. DL-based methods can automatically learn the mapping between regularly subsampled and complete data from a large training data set. Subsequently, the trained network can be used to directly interpolate new data. Therefore, compared with traditional methods, DL-based methods reduce the manual workload and render the interpolation process efficient and automatic by avoiding the selection of hyperparameters. However, two limitations of DL-based approaches exist. First, the generalization performance of the neural network is inadequate when processing new data with a different structure compared to the training data. Second, the interpretation of the trained networks is very difficult. To overcome these limitations, we have combined the deep neural network and classic prediction-error filter (PEF) methods, proposing a novel seismic data dealiased interpolation framework called prediction-error filters network (PEFNet). The PEFNet designs convolutional neural networks to learn the relationship between the subsampled data and the PEFs. Thus, the filters estimated by the trained network are used for the recovery of missing traces. The learning of filters enables the network to better extract the local dip of seismic data and has a good generalization ability. In addition, PEFNet has the same interpretability as traditional PEF-based methods. The applicability and the effectiveness of our method are demonstrated here by synthetic and field data examples.

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20

Raiche, A. P. "Transient electromagnetic field computations for polygonal loops on layered earths." GEOPHYSICS 52, no. 6 (June 1987): 785–93. http://dx.doi.org/10.1190/1.1442345.

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The transient electromagnetic response (vertical and horizontal components of dB/dt) of a large polygonal transmitting loop on a layered earth is calculated using a nested interpolation scheme based on the dipole‐dipole response function. The frequency‐domain field of a vertical magnetic dipole is inverse Laplace transformed into the time domain, for selected values of the Hankel transform variable, using the Gaver‐Stehfest method. After interpolation, the result is inverse Hankel transformed (for selected values of distance) using digital filters. Interpolating over distance allows integration of the dipole response over the area of one or more transmitting loops. An interpolation over time gives the step‐current response, which in turn is convolved with the transmitter‐receiver characteristics to yield the system response. This method allows robust calculation of several transmitting loops (with different signal parameters) and several receiver positions in little more time than that required for one loop with one receiver. The computation time for the single transmitter‐receiver response can be decreased by analytical integration of the Bessel function over the transmitter loop area before performing the inverse Hankel transform. Since this procedure precludes the use of standard digital filters for the inverse Hankel transform, it is not efficient for multireceiver computations.

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21

Yang, Jie, Weiqi Jin, Su Qiu, Fuduo Xue, and Meishu Wang. "Residual Interpolation Integrated Pixel-by-Pixel Adaptive Iterative Process for Division of Focal Plane Polarimeters." Sensors 22, no. 4 (February 16, 2022): 1529. http://dx.doi.org/10.3390/s22041529.

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Residual interpolations are effective methods to reduce the instantaneous field-of-view error of division of focal plane (DoFP) polarimeters. However, their guide-image selection strategies are improper, and do not consider the DoFP polarimeters’ spatial sampling modes. Thus, we propose a residual interpolation method with a new guide-image selection strategy based on the spatial layout of the pixeled polarizer array to improve the sampling rate of the guide image. The interpolation performance is also improved by the proposed pixel-by-pixel, adaptive iterative process and the weighted average fusion of the results of the minimized residual and minimized Laplacian energy guide filters. Visual and objective evaluations demonstrate the proposed method’s superiority to the existing state-of-the-art methods. The proposed method proves that considering the spatial layout of the pixeled polarizer array on the physical level is vital to improving the performance of interpolation methods for DoFP polarimeters.

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22

Vol'pyan, O. D., P. P. Yakovlev, and B. B. Meshkov. "Synthesizing chromatic interference filters using trigonometric interpolation." Journal of Optical Technology 71, no. 7 (July 1, 2004): 491. http://dx.doi.org/10.1364/jot.71.000491.

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23

Venetsanopoulos, Anastasios N. "Image interpolation based on median-type filters." Optical Engineering 37, no. 9 (September 1, 1998): 2472. http://dx.doi.org/10.1117/1.601771.

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24

Cuyt, Annie, Oliver Salazar Celis, and Maryna Lukach. "Multidimensional IIR filters and robust rational interpolation." Multidimensional Systems and Signal Processing 25, no. 3 (November 11, 2012): 447–71. http://dx.doi.org/10.1007/s11045-012-0208-1.

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Yu, Bo, Hui Zhou, Wenling Liu, Lingqian Wang, and Hanming Chen. "Interpolation method based on pattern-feature correlation." GEOPHYSICS 86, no. 3 (March 11, 2021): R253—R264. http://dx.doi.org/10.1190/geo2019-0773.1.

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Reasonable low-wavenumber initial models are essential for reducing the nonuniqueness of seismic inversion. A traditional approach to estimate the low-wavenumber models of elastic parameters is well-log interpolation. However, complex geologic structures decrease the accuracy of this method. To overcome these challenges in building prior models, we have developed an interpolation method based on pattern-feature correlation (PFC) inspired by multiple-point geostatistics (MPG). In our interpolation method, we scan a stacked seismic profile using a predefined data template to obtain a geologic pattern around each node in the seismic profile. Each pattern is then converted into several filter scores with the filters defined in the MPG algorithm of the filter-based simulation. We calculate the correlation coefficients of the filter scores among different patterns for the various nodes and define them as PFCs. We construct the initial models from well-log data based on the weighted interpolation method, in which the weighting factors are precisely determined by the PFCs. We build the initial models using our method for synthetic and field data to demonstrate its effectiveness. To verify the validity of the initial models, we apply them to Bayesian linearized inversion. The accuracy of the interpolation and inversion results verifies the excellent performance of our interpolation method. Our method provides a novel and convenient approach that combines seismic and well-log data, which contributes to seismic exploration and geologic modeling.

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Porsani, Milton J. "Seismic trace interpolation using half‐step prediction filters." GEOPHYSICS 64, no. 5 (September 1999): 1461–67. http://dx.doi.org/10.1190/1.1444650.

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A method to perform seismic trace interpolation known as the Spitz method handles spatially aliased events. The Spitz method uses the unit‐step prediction filter to estimate data spaced at Δx/2. The missing data are obtained by solving a complex linear system of equations whose unknowns are the coefficients at the interpolated location. We attack this problem by introducing a half‐step prediction filter that makes trace interpolation significantly more efficient and easier for implementation. A complex half‐step prediction filter at frequency f/2 is computed in the least‐squares sense to predict odd data components from even ones. At the frequency f, the prediction operator is shrunk and convolved with the input data spaced at Δx to predict data at Δx/2 directly. Instead of solving two systems of linear equations, as proposed by Spitz, only a system for the half‐step prediction filter has to be solved. Numerical examples using a marine seismic common‐midpoint (CMP) gather and a poststack seismic section were used to illustrate the new interpolation method.

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27

Jeon, Gwang Gil. "Image Reconstruction on Quincunx Patterned Green Channel." Advanced Materials Research 717 (July 2013): 493–96. http://dx.doi.org/10.4028/www.scientific.net/amr.717.493.

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This paper addresses the issue of the quincunx patterned green channel interpolation method that is obtained by single sensor cameras. Our goal is to reconstruct the green channel in Bayer color filter array (CFA) data. We present a new filter-based method for the reduction of image artifacts in green channel. To reconstruct green channel, we trained a filter using least squares method. Experimental results confirm the effectiveness of the proposed method. Compared to other bilinear and bicubic filters, the improvement in quality has been achieved.

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28

Zheng, Zhisheng, Yang Liu, and Cai Liu. "Seismic data interpolation using streaming prediction filter in the frequency domain." Geophysical Journal International 229, no. 1 (November 23, 2021): 370–89. http://dx.doi.org/10.1093/gji/ggab474.

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SUMMARY Surface conditions and economic factors restrict field geometries, so seismic data acquisition typically obtains field data with irregular spatial distribution, which can adversely affect the subsequent data processing and interpretation. Therefore, data interpolation techniques are used to convert field data into regularly distributed data and reconstruct the missing traces. Recently, the mainstream methods have implemented iterative algorithms to solve data interpolation problems, which require substantial computational resources and restrict their application in high dimensions. In this study, we proposed the f–x and f–x–y streaming prediction filters (SPFs) to reconstruct missing seismic traces without iterations. According to the streaming computation framework, we directly derived an analytic solution to the overdetermined least-squares problem with local smoothness constraints for estimating SPFs in the frequency domain. We introduced different processing paths and filter forms to reduce the interference of missing traces, which can improve the accuracy of filter coefficients. Meanwhile, we utilized a two-step interpolation strategy to guarantee the effective interpolation of the irregularly missing traces. Numerical examples show that the proposed methods effectively recover the missing traces in seismic data when compared with the traditional Fourier Projection Onto Convex Sets method. In particular, the frequency domain SPFs are suitable for high-dimensional seismic data interpolation with the advantages of low computational cost and reasonable non-stationary signal reconstruction.

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Li, Haolin, Joris Van Kerrebrouck, Johan Bauwelinck, Piet Demeester, and Guy Torfs. "Maximally Flat and Least-Square Co-Design of Variable Fractional Delay Filters for Wideband Software-Defined Radio." Journal of Circuits, Systems and Computers 28, no. 01 (October 15, 2018): 1950006. http://dx.doi.org/10.1142/s0218126619500063.

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This paper describes improvements in a Farrow-structured variable fractional delay (FD) Lagrange filter for all-pass FD interpolation. The main idea is to integrate the truncated sinc into the Farrow structure of a Lagrange filter, in order that a superior FD approximation in the least-square sense can be achieved. Its primary advantages are the lower level of mean-square-error (MSE) over the whole FD range and the reduced implementation cost. Extra design parameters are introduced for making the trade-off between MSE and maximal flatness under different design requirements. Design examples are included, illustrating an MSE reduction of [Formula: see text] compared to a classical Farrow-structured Lagrange interpolator while the implementation cost is reduced. This improved variable FD interpolation system is suitable for many applications, such as sample rate conversion, digital beamforming and timing synchronization in wideband software-defined radio (SDR) communications.

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Taejin, Hwang, Yongjo Ahn, Jiwoo Ryu, and Donggyu Sim. "Optimized Implementation of Interpolation Filters for HEVC Encoder." Journal of the Institute of Electronics and Information Engineers 50, no. 10 (October 25, 2013): 199–203. http://dx.doi.org/10.5573/ieek.2013.50.10.199.

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31

Hung, Barry, and Carl Notfors. "3D seismic trace interpolation using noncausal spatial filters." ASEG Extended Abstracts 2004, no. 1 (December 2004): 1–5. http://dx.doi.org/10.1071/aseg2004ab073.

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Putnam, William L., and Julius O. Smith. "Optimal Chebychev interpolation filters for accurate beam steering." Journal of the Acoustical Society of America 100, no. 4 (October 1996): 2831. http://dx.doi.org/10.1121/1.416676.

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Kulberg, N. S., T. V. Yakovleva, and I. I. Litvinov. "Method of construction of two-dimensional interpolation filters." Pattern Recognition and Image Analysis 21, no. 2 (June 2011): 292–96. http://dx.doi.org/10.1134/s1054661811020659.

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Liu, Xiaojie, Wenpeng Ding, Yunhui Shi, and Baocai Yin. "Content adaptive interpolation filters based on HEVC framework." Journal of Visual Communication and Image Representation 56 (October 2018): 131–38. http://dx.doi.org/10.1016/j.jvcir.2018.09.006.

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Jain, Alok, Rajiv Saxena, and S. C. Saxena. "Anti-image FIR filters for large interpolation factors." Signal Processing 86, no. 11 (November 2006): 3240–45. http://dx.doi.org/10.1016/j.sigpro.2006.01.003.

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Liu, Zujun, and Kechu Yi. "Symbol Timing Synchronization Using Interpolation-Based Matched-Filters." Wireless Personal Communications 50, no. 4 (November 7, 2008): 457–67. http://dx.doi.org/10.1007/s11277-008-9617-8.

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Zhou, Yatong, and Song Li. "Simultaneous deblending and interpolation using structure-oriented filters." Journal of Applied Geophysics 150 (March 2018): 230–43. http://dx.doi.org/10.1016/j.jappgeo.2018.01.015.

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Babic, Djordje. "Windowing Design Method for Polynomial-Based Interpolation Filters." Circuits, Systems, and Signal Processing 32, no. 2 (September 19, 2012): 759–80. http://dx.doi.org/10.1007/s00034-012-9486-y.

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Habuka, Kensuke, and Yoshihisa Shinagawa. "Image Interpolation Using Enhanced Multiresolution Critical-Point Filters." International Journal of Computer Vision 58, no. 1 (June 2004): 19–35. http://dx.doi.org/10.1023/b:visi.0000016145.44583.5f.

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Wu, Zhongmou, and Yun He. "Combined adaptive-fixed interpolation with multi-directional filters." Signal Processing: Image Communication 24, no. 4 (April 2009): 277–86. http://dx.doi.org/10.1016/j.image.2009.03.005.

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Li, Wenzhe, and Alfred Fettweis. "Interpolation filters for 2-D hexagonally sampled signals." International Journal of Circuit Theory and Applications 25, no. 4 (July 1997): 259–77. http://dx.doi.org/10.1002/(sici)1097-007x(199707/08)25:4<259::aid-cta962>3.0.co;2-9.

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Chao, Chen, Wei Zhang Xu, and Si Lu. "The Application of the Sub-Filters of the Polyphase Filter in Multi-Path Delay." Applied Mechanics and Materials 303-306 (February 2013): 1864–68. http://dx.doi.org/10.4028/www.scientific.net/amm.303-306.1864.

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This paper first reviews the polyphase filter in the decimation and interpolation application, and simply introduces the multi-rate system. And then through the simulation experiments, the characteristics of the sub-filter of the polyphase filter were analyzed. Finally, according to the characteristics of the sub-filter, this paper presents an application in multipath delay.

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Ouala, Said, Ronan Fablet, Cédric Herzet, Bertrand Chapron, Ananda Pascual, Fabrice Collard, and Lucile Gaultier. "Neural Network Based Kalman Filters for the Spatio-Temporal Interpolation of Satellite-Derived Sea Surface Temperature." Remote Sensing 10, no. 12 (November 22, 2018): 1864. http://dx.doi.org/10.3390/rs10121864.

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The forecasting and reconstruction of oceanic dynamics is a crucial challenge. While model driven strategies are still the state-of-the-art approaches in the reconstruction of spatio-temporal dynamics. The ever increasing availability of data collections in oceanography raised the relevance of data-driven approaches as computationally efficient representations of spatio-temporal fields reconstruction. This tools proved to outperform classical state-of-the-art interpolation techniques such as optimal interpolation and DINEOF in the retrievement of fine scale structures while still been computationally efficient comparing to model based data assimilation schemes. However, coupling this data-driven priors to classical filtering schemes limits their potential representativity. From this point of view, the recent advances in machine learning and especially neural networks and deep learning can provide a new infrastructure for dynamical modeling and interpolation within a data-driven framework. In this work we adress this challenge and develop a novel Neural-Network-based (NN-based) Kalman filter for spatio-temporal interpolation of sea surface dynamics. Based on a data-driven probabilistic representation of spatio-temporal fields, our approach can be regarded as an alternative to classical filtering schemes such as the ensemble Kalman filters (EnKF) in data assimilation. Overall, the key features of the proposed approach are two-fold: (i) we propose a novel architecture for the stochastic representation of two dimensional (2D) geophysical dynamics based on a neural networks, (ii) we derive the associated parametric Kalman-like filtering scheme for a computationally-efficient spatio-temporal interpolation of Sea Surface Temperature (SST) fields. We illustrate the relevance of our contribution for an OSSE (Observing System Simulation Experiment) in a case-study region off South Africa. Our numerical experiments report significant improvements in terms of reconstruction performance compared with operational and state-of-the-art schemes (e.g., optimal interpolation, Empirical Orthogonal Function (EOF) based interpolation and analog data assimilation).

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Fomel, Sergey. "Applications of plane‐wave destruction filters." GEOPHYSICS 67, no. 6 (November 2002): 1946–60. http://dx.doi.org/10.1190/1.1527095.

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Plane‐wave destruction filters originate from a local plane‐wave model for characterizing seismic data. These filters can be thought of as a time–distance (T‐X) analog of frequency‐distance (F‐X) prediction‐error filters and as an alternative to T‐X prediction‐error filters. The filters are constructed with the help of an implicit finite‐difference scheme for the local plane‐wave equation. Several synthetic and real data examples show that finite‐difference plane‐wave destruction filters perform well in applications such as fault detection, data interpolation, and noise attenuation.

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Skulina, E. G., and I. S. Savinykh. "Computational efficiency of interpolated band stop filters for odd spectral bands." Proceedings of the Russian higher school Academy of sciences, no. 1 (March 29, 2023): 56–66. http://dx.doi.org/10.17212/1727-2769-2023-1-56-66.

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Interpolated band stop FIR filters are excluded. A block diagram of an interpolated band stop FIR filter for odd spectral regions is proposed. The use of the proposed maximum allowable value of the filter coefficient in comparison with the reference filter calculated by the classical method, namely the maximum allowable value of the quantitative limitation to the computing resource. For the proposed structure, relations are obtained to determine the coefficient of computational efficiency and the coefficient of increase in the number of registers. In the proposed work, the following values were determined: the optimal interpolation coefficient, the maximum coefficient of computational efficiency and the coefficient of increase in the number of registers at the optimal interpolation coefficient. In the obtained relations for the synthesis of the interpolated band-stop FIR filter, the values of the stop band and the central frequency of the rejection are used. We also compared the interpolated band stop filter for odd spectral zones, synthesized according to the proposed structure, and the reference band stop filter calculated by the classical method. As a result of the study, it was found that the proposed nature is used under specific conditions. The obtained structure of the interpolated band stop FIR filter is optimal from a computational point of view, however, the calculated structure is not universal. The main limitation for the application of the resulting structure is the discreteness of switching between spectral zones and the need for fine tuning of the center rejection frequency.

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Lyakhov, Pavel, Maria Valueva, Georgii Valuev, and Nikolai Nagornov. "A Method of Increasing Digital Filter Performance Based on Truncated Multiply-Accumulate Units." Applied Sciences 10, no. 24 (December 18, 2020): 9052. http://dx.doi.org/10.3390/app10249052.

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This paper proposes new digital filter architecture based on a modified multiply-accumulate (MAC) unit architecture called truncated MAC (TMAC), with the aim of increasing the performance of digital filtering. This paper provides a theoretical analysis of the proposed TMAC units and their hardware simulation. Theoretical analysis demonstrated that replacing conventional MAC units with modified TMAC units, as the basis for the implementation of digital filters, can theoretically reduce the filtering time by 29.86%. Hardware simulation showed that TMAC units increased the performance of digital filters by up to 10.89% compared to digital filters using conventional MAC units, but were associated with increased hardware costs. The results of this research can be used in the theory of digital signal processing to solve practical problems such as noise reduction, amplification and suppression of the frequency spectrum, interpolation, decimation, equalization and many others.

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Ganguly, Poulami Somanya, Daniël M. Pelt, Doga Gürsoy, Francesco de Carlo, and K. Joost Batenburg. "Improving reproducibility in synchrotron tomography using implementation-adapted filters." Journal of Synchrotron Radiation 28, no. 5 (August 12, 2021): 1583–97. http://dx.doi.org/10.1107/s1600577521007153.

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For reconstructing large tomographic datasets fast, filtered backprojection-type or Fourier-based algorithms are still the method of choice, as they have been for decades. These robust and computationally efficient algorithms have been integrated in a broad range of software packages. The continuous mathematical formulas used for image reconstruction in such algorithms are unambiguous. However, variations in discretization and interpolation result in quantitative differences between reconstructed images, and corresponding segmentations, obtained from different software. This hinders reproducibility of experimental results, making it difficult to ensure that results and conclusions from experiments can be reproduced at different facilities or using different software. In this paper, a way to reduce such differences by optimizing the filter used in analytical algorithms is proposed. These filters can be computed using a wrapper routine around a black-box implementation of a reconstruction algorithm, and lead to quantitatively similar reconstructions. Use cases for this approach are demonstrated by computing implementation-adapted filters for several open-source implementations and applying them to simulated phantoms and real-world data acquired at the synchrotron. Our contribution to a reproducible reconstruction step forms a building block towards a fully reproducible synchrotron tomography data processing pipeline.

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KIM, WONKOO, and CHING-CHUNG LI. "ON PRECONDITIONING MULTIWAVELET SYSTEMS FOR IMAGE COMPRESSION." International Journal of Wavelets, Multiresolution and Information Processing 01, no. 01 (March 2003): 51–74. http://dx.doi.org/10.1142/s0219691303000049.

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This paper presents a study on applications of multiwavelet analysis to image compression. The biorthogonality and perfect reconstruction conditions are applied to multiwavelet filters. As a multiwavelet filter bank has multiple channels of inputs, the data structure of inputs to the multiwavelet system should be taken into consideration in multiwavelet decomposition and reconstruction algorithms. We investigate the data initialization problem by considering prefilters and postfilters that may give more efficient representations of the decomposed data. The interpolation postfilter and prefilter are formulated, which are capable to provide a better approximate image at each coarser resolution level. A design process is given to obtain both filters having compact supports, if exist. Image compression performances of three multiwavelet systems are studied in comparison to those of single wavelet systems.

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Stordal, Andreas S., and Hans A. Karlsen. "Large Sample Properties of the Adaptive Gaussian Mixture Filter." Monthly Weather Review 145, no. 7 (July 2017): 2533–53. http://dx.doi.org/10.1175/mwr-d-15-0372.1.

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In high-dimensional dynamic systems, standard Monte Carlo techniques that asymptotically reproduce the posterior distribution are computationally too expensive. Alternative sampling strategies are usually applied and among these the ensemble Kalman filter (EnKF) is perhaps the most popular. However, the EnKF suffers from severe bias if the model under consideration is far from linear. Another class of sequential Monte Carlo methods is kernel-based Gaussian mixture filters, which reduce the bias but maintain the robustness of the EnKF. Although many hybrid methods have been introduced in recent years, not many have been analyzed theoretically. Here it is shown that the recently proposed adaptive Gaussian mixture filter can be formulated in a rigorous Bayesian framework and that the algorithm can be generalized to a broader class of interpolated kernel filters. Two parameters—the bandwidth of the kernel and a weight interpolation factor—determine the filter performance. The new formulation of the filter includes particle filters, EnKF, and kernel-based Gaussian mixture filters as special cases. Techniques from particle filter literature are used to calculate the asymptotic bias of the filter as a function of the parameters and to derive a central limit theorem. The asymptotic theory is then used to determine the parameters as a function of the sample size in a robust way such that the error norm vanishes asymptotically, whereas the normalized error is sample independent and bounded. The parameter choice is tested on the Lorenz 63 model, where it is shown that the error is smaller or equal to the EnKF and the optimal particle filter for a varying sample size.

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Rusanovskyy, D., K. Ugur, A. Hallapuro, J. Lainema, and M. Gabbouj. "Video Coding With Low-Complexity Directional Adaptive Interpolation Filters." IEEE Transactions on Circuits and Systems for Video Technology 19, no. 8 (August 2009): 1239–43. http://dx.doi.org/10.1109/tcsvt.2009.2022708.

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