Journal articles: 'Regularization by Denoising'

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Lin, Huangxing, Yihong Zhuang, Xinghao Ding, Delu Zeng, Yue Huang, Xiaotong Tu, and John Paisley. "Self-Supervised Image Denoising Using Implicit Deep Denoiser Prior." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 2 (June 26, 2023): 1586–94. http://dx.doi.org/10.1609/aaai.v37i2.25245.

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We devise a new regularization for denoising with self-supervised learning. The regularization uses a deep image prior learned by the network, rather than a traditional predefined prior. Specifically, we treat the output of the network as a ``prior'' that we again denoise after ``re-noising.'' The network is updated to minimize the discrepancy between the twice-denoised image and its prior. We demonstrate that this regularization enables the network to learn to denoise even if it has not seen any clean images. The effectiveness of our method is based on the fact that CNNs naturally tend to capture low-level image statistics. Since our method utilizes the image prior implicitly captured by the deep denoising CNN to guide denoising, we refer to this training strategy as an Implicit Deep Denoiser Prior (IDDP). IDDP can be seen as a mixture of learning-based methods and traditional model-based denoising methods, in which regularization is adaptively formulated using the output of the network. We apply IDDP to various denoising tasks using only observed corrupted data and show that it achieves better denoising results than other self-supervised denoising methods.

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Prasath, V. "A well-posed multiscale regularization scheme for digital image denoising." International Journal of Applied Mathematics and Computer Science 21, no. 4 (December 1, 2011): 769–77. http://dx.doi.org/10.2478/v10006-011-0061-7.

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A well-posed multiscale regularization scheme for digital image denoisingWe propose an edge adaptive digital image denoising and restoration scheme based on space dependent regularization. Traditional gradient based schemes use an edge map computed from gradients alone to drive the regularization. This may lead to the oversmoothing of the input image, and noise along edges can be amplified. To avoid these drawbacks, we make use of a multiscale descriptor given by a contextual edge detector obtained from local variances. Using a smooth transition from the computed edges, the proposed scheme removes noise in flat regions and preserves edges without oscillations. By incorporating a space dependent adaptive regularization parameter, image smoothing is driven along probable edges and not across them. The well-posedness of the corresponding minimization problem is proved in the space of functions of bounded variation. The corresponding gradient descent scheme is implemented and further numerical results illustrate the advantages of using the adaptive parameter in the regularization scheme. Compared with similar edge preserving regularization schemes, the proposed adaptive weight based scheme provides a better multiscale edge map, which in turn produces better restoration.

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Tan, Yi, Jin Fan, Dong Sun, Qingwei Gao, and Yixiang Lu. "Multi-scale Image Denoising via a Regularization Method." Journal of Physics: Conference Series 2253, no. 1 (April 1, 2022): 012030. http://dx.doi.org/10.1088/1742-6596/2253/1/012030.

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Abstract Image restoration is a widely studied problem in the field of image processing. Although the existing image restoration methods based on denoising regularization have shown relatively well performance, image restoration methods for different features of unknown images have not been proposed. Since images have different features, it seems necessary to adopt different priori regular terms for different features. In this paper, we propose a multiscale image regularization denoising framework that can simultaneously perform two or more denoising prior regularization terms to better obtain the overall image restoration results. We use the alternating direction multiplier method (ADMM) to optimize the model and combine multiple denoising algorithms for extensive image deblurring and image super-resolution experiments, and our algorithm shows better performance compared to the existing state-of-the-art image restoration methods.

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Li, Ao, Deyun Chen, Kezheng Lin, and Guanglu Sun. "Hyperspectral Image Denoising with Composite Regularization Models." Journal of Sensors 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/6586032.

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Denoising is a fundamental task in hyperspectral image (HSI) processing that can improve the performance of classification, unmixing, and other subsequent applications. In an HSI, there is a large amount of local and global redundancy in its spatial domain that can be used to preserve the details and texture. In addition, the correlation of the spectral domain is another valuable property that can be utilized to obtain good results. Therefore, in this paper, we proposed a novel HSI denoising scheme that exploits composite spatial-spectral information using a nonlocal technique (NLT). First, a specific way to extract patches is employed to mine the spatial-spectral knowledge effectively. Next, a framework with composite regularization models is used to implement the denoising. A number of HSI data sets are used in our evaluation experiments and the results demonstrate that the proposed algorithm outperforms other state-of-the-art HSI denoising methods.

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Li, Shu, Xi Yang, Haonan Liu, Yuwei Cai, and Zhenming Peng. "Seismic Data Denoising Based on Sparse and Low-Rank Regularization." Energies 13, no. 2 (January 13, 2020): 372. http://dx.doi.org/10.3390/en13020372.

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Seismic denoising is a core task of seismic data processing. The quality of a denoising result directly affects data analysis, inversion, imaging and other applications. For the past ten years, there have mainly been two classes of methods for seismic denoising. One is based on the sparsity of seismic data. This kind of method can make use of the sparsity of seismic data in local area. The other is based on nonlocal self-similarity, and it can utilize the spatial information of seismic data. Sparsity and nonlocal self-similarity are important prior information. However, there is no seismic denoising method using both of them. To jointly use the sparsity and nonlocal self-similarity of seismic data, we propose a seismic denoising method using sparsity and low-rank regularization (called SD-SpaLR). Experimental results showed that the SD-SpaLR method has better performance than the conventional wavelet denoising and total variation denoising. This is because both the sparsity and the nonlocal self-similarity of seismic data are utilized in seismic denoising. This study is of significance for designing new seismic data analysis, processing and inversion methods.

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Baloch, Gulsher, Huseyin Ozkaramanli, and Runyi Yu. "Residual Correlation Regularization Based Image Denoising." IEEE Signal Processing Letters 25, no. 2 (February 2018): 298–302. http://dx.doi.org/10.1109/lsp.2017.2789018.

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Chen, Guan Nan, Dan Er Xu, Rong Chen, Zu Fang Huang, and Zhong Jian Teng. "Iterative Regularization Model for Image Denoising Based on Dual Norms." Applied Mechanics and Materials 182-183 (June 2012): 1245–49. http://dx.doi.org/10.4028/www.scientific.net/amm.182-183.1245.

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Image denoising algorithm based on gradient dependent energy functional often compromised the image features like textures or certain details. This paper proposes an iterative regularization model based on Dual Norms for image denoising. By using iterative regularization model, the oscillating patterns of texture and detail are added back to fit and compute the original Dual Norms model, and the iterative behavior avoids overfull smoothing while denoising the features of textures and details to a certain extent. In addition, the iterative procedure is proposed in this paper, and the proposed algorithm also be proved the convergence property. Experimental results show that the proposed method can achieve a batter result in preserving not only the features of textures for image denoising but also the details for image.

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Guo, Li, Weilong Chen, Yu Liao, Honghua Liao, and Jun Li. "An Edge-Preserved Image Denoising Algorithm Based on Local Adaptive Regularization." Journal of Sensors 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/2019569.

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Image denoising methods are often based on the minimization of an appropriately defined energy function. Many gradient dependent energy functions, such as Potts model and total variation denoising, regard image as piecewise constant function. In these methods, some important information such as edge sharpness and location is well preserved, but some detailed image feature like texture is often compromised in the process of denoising. For this reason, an image denoising method based on local adaptive regularization is proposed in this paper, which can adaptively adjust denoising degree of noisy image by adding spatial variable fidelity term, so as to better preserve fine scale features of image. Experimental results show that the proposed denoising method can achieve state-of-the-art subjective visual effect, and the signal-noise-ratio (SNR) is also objectively improved by 0.3–0.6 dB.

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Liu, Kui, Jieqing Tan, and Benyue Su. "An Adaptive Image Denoising Model Based on Tikhonov and TV Regularizations." Advances in Multimedia 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/934834.

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To avoid the staircase artifacts, an adaptive image denoising model is proposed by the weighted combination of Tikhonov regularization and total variation regularization. In our model, Tikhonov regularization and total variation regularization can be adaptively selected based on the gradient information of the image. When the pixels belong to the smooth regions, Tikhonov regularization is adopted, which can eliminate the staircase artifacts. When the pixels locate at the edges, total variation regularization is selected, which can preserve the edges. We employ the split Bregman method to solve our model. Experimental results demonstrate that our model can obtain better performance than those of other models.

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Shen, Lixin, Bruce W. Suter, and Erin E. Tripp. "Algorithmic versatility of SPF-regularization methods." Analysis and Applications 19, no. 01 (July 3, 2020): 43–69. http://dx.doi.org/10.1142/s0219530520400060.

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Sparsity promoting functions (SPFs) are commonly used in optimization problems to find solutions which are sparse in some basis. For example, the [Formula: see text]-regularized wavelet model and the Rudin–Osher–Fatemi total variation (ROF-TV) model are some of the most well-known models for signal and image denoising, respectively. However, recent work demonstrates that convexity is not always desirable in SPFs. In this paper, we replace convex SPFs with their induced nonconvex SPFs and develop algorithms for the resulting model by exploring the intrinsic structures of the nonconvex SPFs. These functions are defined as the difference of the convex SPF and its Moreau envelope. We also present simulations illustrating the performance of a special SPF and the developed algorithms in image denoising.

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Zhu, Shisong, Bibo Lu, and Cuiyun Zhang. "High Order Regularization for Mr Image Denoising." Information Technology Journal 12, no. 21 (October 15, 2013): 6481–86. http://dx.doi.org/10.3923/itj.2013.6481.6486.

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Reehorst, Edward T., and Philip Schniter. "Regularization by Denoising: Clarifications and New Interpretations." IEEE Transactions on Computational Imaging 5, no. 1 (March 2019): 52–67. http://dx.doi.org/10.1109/tci.2018.2880326.

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WU, Di, Tao ZHANG, and Xutao MO. "Group Sparsity Residual Constraint Image Denoising Model with 𝒍₁/𝒍₂ Regularization." Wuhan University Journal of Natural Sciences 28, no. 1 (February 2023): 53–60. http://dx.doi.org/10.1051/wujns/2023281053.

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Group sparse residual constraint with non-local priors (GSRC) has achieved great success in image restoration producing state-of-the-art performance. In the GSRC model, the [see formula in PDF] norm minimization is employed to reduce the group sparse residual. In recent years, non-convex regularization terms have been widely used in image denoising problems, which have achieved better results in denoising than convex regularization terms. In this paper, we use the ratio of the [see formula in PDF] and [see formula in PDF] norm instead of the [see formula in PDF] norm to propose a new image denoising model, i.e., a group sparse residual constraint model with [see formula in PDF] minimization (GSRC-[see formula in PDF]). Due to the computational difficulties arisen from the non-convexity and non-linearity, we focus on a constrained optimization problem that can be solved by alternative direction method of multipliers (ADMM). Experimental results of image denoising show that the pro-posed model outperforms several state-of-the-art image denoising methods both visually and quantitatively.

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Li, Minmin, Guangcheng Cai, Shaojiu Bi, and Xi Zhang. "Improved TV Image Denoising over Inverse Gradient." Symmetry 15, no. 3 (March 8, 2023): 678. http://dx.doi.org/10.3390/sym15030678.

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Noise in an image can affect one’s extraction of image information, therefore, image denoising is an important image pre-processing process. Many of the existing models have a large number of estimated parameters, which increases the time complexity of the model solution and the achieved denoising effect is less than ideal. As a result, in this paper, an improved image-denoising algorithm is proposed based on the TV model, which effectively solves the above problems. The L1 regularization term can make the solution generated by the model sparser, thus facilitating the recovery of high-quality images. Reducing the number of estimated parameters, while using the inverse gradient to estimate the regularization parameters, enables the parameters to achieve global adaption and improves the denoising effect of the model in combination with the TV regularization term. The split Bregman iteration method is used to decouple the model into several related subproblems, and the solutions of the coordinated subproblems are derived as optimal solutions. It is also shown that the solution of the model converges to a Karush–Kuhn–Tucker point. Experimental results show that the algorithm in this paper is more effective in both preserving image texture structure and suppressing image noise.

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Bi, Shaojiu, Minmin Li, and Guangcheng Cai. "Mixed Fractional-Order and High-Order Adaptive Image Denoising Algorithm Based on Weight Selection Function." Fractal and Fractional 7, no. 7 (July 24, 2023): 566. http://dx.doi.org/10.3390/fractalfract7070566.

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In this paper, a mixed-order image denoising algorithm containing fractional-order and high-order regularization terms is proposed, which effectively suppresses the staircase effect generated by the TV model and its variants while better preserving the edges and details of the image. Adding different regularization penalties in different regions is fundamental to improving the denoising performance of the model. Therefore, a weight selection function is designed using the structure tensor to achieve a more effective selection of regularization terms in different regions. In each iteration, the regularization parameters are adaptively adjusted according to the Morozov discrepancy principle to promote the performance of the algorithm. Based on the primal–dual theory, the original algorithm is improved by using the predictor–corrector scheme to obtain a more accurate approximate solution while ensuring the convergence of the algorithm. The effectiveness of the proposed algorithm is demonstrated through simulation experiments.

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Guo, Zhongchen, Xuexiang Yu, Chao Hu, Zhihao Yu, and Chuang Jiang. "Correction Model of BDS-3 Satellite Pseudorange Multipath Delays and Its Impact on Single-Frequency Precise Point Positioning." Mathematical Problems in Engineering 2021 (November 30, 2021): 1–16. http://dx.doi.org/10.1155/2021/9189541.

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Precise point positioning (PPP) is used in many fields. However, pseudorange multipath delay is an important error that restricts its accuracy. Pseudorange multipath delay can be considered as the combination of effective information and observation noise; it can be modeled after removing the observation noise. In this work, elastic nets (EN) regularization denoising method is proposed and compared with L2-norm regularization denoising method. Then, quadratic polynomial (QP) model plus autoregressive (AR) model (QP + AR) are used to model the denoised pseudorange multipath delays. Finally, the modeling results are corrected to the observations to verify the improvement of BDS-3 single-frequency PPP accuracy. Three single-frequency PPP schemes are designed to verify the effectiveness of denoising method and QP + AR model. The experimental results show that the accuracy improvement of B3I and B2a is more obvious than that of B1I and B1C when the modeling values are corrected to the pseudorange observations. The improvement of B3I and B2a in the east (E) and up (U) directions can reach 10.6%∼34.4% and 5.9%∼65.7%, and the improvement of the north (N) direction is mostly less than 10.0%. The accuracy of B1I and B1C in E and U directions can be improved by 0%∼30.7% and 0.4%∼28.6%, respectively, while the accuracy of N direction can be improved slightly or even decreased. Using EN regularization denoising and QP + AR model correction, single-frequency PPP performs better at B3I and B2a, while L2-norm regularization denoising and QP + AR model correction perform better at B1I and B1C. The accuracy improvement of B2a and B3I is more obvious than that of B1I and B1C. The convergence time after MP correction of each frequency is slightly shorter. Overall, the proposed pseudorange multipath delays processing strategy is beneficial in improving the single-frequency PPP of BDS-3 satellite.

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Anagaw, Amsalu, and Mauricio D. Sacchi. "A regularization by denoising (RED) scheme for 3-D FWI model updates in large-contrast media." Geophysical Journal International 229, no. 2 (December 15, 2021): 814–27. http://dx.doi.org/10.1093/gji/ggab505.

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SUMMARY Full waveform inversion (FWI) endeavours to estimate high-resolution physical properties of subsurface structures. The technique minimizes the data misfit between observed and modelled seismograms. Despite its success, the application of FWI in areas with high-velocity contrasts remains a challenging problem. Often, quadratic regularization methods are chosen to stabilize inverse problems. Unfortunately, quadratic regularization does not preserve edges and sharp discontinuities adequately. Conversely, a regularization term that uses the l1 norm of the gradient of model parameters can preserve discontinuities. The latter leads to edge-preserving methods based on total variation regularization. This work adopts the framework named regularization by denoising (RED) to solve the FWI problem in high-contrast media. The RED technique only requires an image denoising engine, which, in our case, is a modified weighted total variation filter. One advantage of adopting the RED algorithm for solving FWI problems is its simplicity in the numerical implementation and selection of trade-off parameters. We have benchmarked our algorithm via the 2-D BP/EAGE model, a model with significant velocity contrasts and complex salt bodies. We have also tested the proposed regularization method with the 3-D SEG/EAGE overthrust P-wave velocity model. We also compare the proposed RED method and FWI with total variation regularization.

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Chen Guannan, 陈冠楠, 陈荣 Chen Rong, 林居强 Lin Juqiang, 黄祖芳 Huang Zufang, 冯尚源 Feng Shangyuan, 李永增 Li Yongzeng, and 杨坤涛 Yang Kuntao. "Iterative Regularization Denoising Method Based on OSV Model for Medical Image Denoising." Chinese Journal of Lasers 36, no. 10 (2009): 2548–51. http://dx.doi.org/10.3788/cjl20093610.2548.

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Guan-nan, Chen, Chen Rong, Huang Zu-fang, Lin Ju-qiang, Feng Shang-yuan, Li Yong-zeng, and Teng Zhong-jian. "Iterative Regularization Denoising Method Based on OSV Model for BioMedical Image Denoising." Journal of Physics: Conference Series 277 (January 1, 2011): 012005. http://dx.doi.org/10.1088/1742-6596/277/1/012005.

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Yuan, Quan, Zhenyun Peng, Zhencheng Chen, Yanke Guo, Bin Yang, and Xiangyan Zeng. "Medical Image Denoising Algorithm Based on Sparse Nonlocal Regularized Weighted Coding and Low Rank Constraint." Scientific Programming 2021 (June 7, 2021): 1–6. http://dx.doi.org/10.1155/2021/7008406.

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Medical image information may be polluted by noise in the process of generation and transmission, which will seriously hinder the follow-up image processing and medical diagnosis. In medical images, there is a typical mixed noise composed of additive white Gaussian noise (AWGN) and impulse noise. In the conventional denoising methods, impulse noise is first removed, followed by the elimination of white Gaussian noise (WGN). However, it is difficult to separate the two kinds of noises completely in practical application. The existing denoising algorithm of weight coding based on sparse nonlocal regularization, which can simultaneously remove AWGN and impulse noise, is plagued by the problems of incomplete noise removal and serious loss of details. The denoising algorithm based on sparse representation and low rank constraint can preserve image details better. Thus, a medical image denoising algorithm based on sparse nonlocal regularization weighted coding and low rank constraint is proposed. The denoising effect of the proposed method and the original algorithm on computed tomography (CT) image and magnetic resonance (MR) image are compared. It is revealed that, under different σ and ρ values, the PSNR and FSIM values of CT and MRI images are evidently superior to those of traditional algorithms, suggesting that the algorithm proposed in this work has better denoising effects on medical images than traditional denoising algorithms.

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Kravchuk, Oleg, and Galyna Kriukova. "Regularization by Denoising for Inverse Problems in Imaging." Mohyla Mathematical Journal 5 (December 28, 2022): 57–61. http://dx.doi.org/10.18523/2617-70805202257-61.

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In this work, a generalized scheme of regularization of inverse problems is considered, where a priori knowledge about the smoothness of the solution is given by means of some self-adjoint operator in the solution space. The formulation of the problem is considered, namely, in addition to the main inverse problem, an additional problem is defined, in which the solution is the right-hand side of the equation. Thus, for the regularization of the main inverse problem, an additional inverse problem is used, which brings information about the smoothness of the solution to the initial problem. This formulation of the problem makes it possible to use operators of high complexity for regularization of inverse problems, which is an urgent need in modern machine learning problems, in particular, in image processing problems. The paper examines the approximation error of the solution of the initial problem using an additional problem.

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Ma, Tian-Hui, Ting-Zhu Huang, and Xi-Le Zhao. "New Regularization Models for Image Denoising with a Spatially Dependent Regularization Parameter." Abstract and Applied Analysis 2013 (2013): 1–15. http://dx.doi.org/10.1155/2013/729151.

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We consider simultaneously estimating the restored image and the spatially dependent regularization parameter which mutually benefit from each other. Based on this idea, we refresh two well-known image denoising models: the LLT model proposed by Lysaker et al. (2003) and the hybrid model proposed by Li et al. (2007). The resulting models have the advantage of better preserving image regions containing textures and fine details while still sufficiently smoothing homogeneous features. To efficiently solve the proposed models, we consider an alternating minimization scheme to resolve the original nonconvex problem into two strictly convex ones. Preliminary convergence properties are also presented. Numerical experiments are reported to demonstrate the effectiveness of the proposed models and the efficiency of our numerical scheme.

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Feng, Yayuan, Yu Shi, and Dianjun Sun. "Blind Poissonian Image Deblurring Regularized by a Denoiser Constraint and Deep Image Prior." Mathematical Problems in Engineering 2020 (August 24, 2020): 1–15. http://dx.doi.org/10.1155/2020/9483521.

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The denoising and deblurring of Poisson images are opposite inverse problems. Single image deblurring methods are sensitive to image noise. A single noise filter can effectively remove noise in advance, but it also damages blurred information. To simultaneously solve the denoising and deblurring of Poissonian images better, we learn the implicit deep image prior from a single degraded image and use the denoiser as a regularization term to constrain the latent clear image. Combined with the explicit L0 regularization prior of the image, the denoising and deblurring model of the Poisson image is established. Then, the split Bregman iteration strategy is used to optimize the point spread function estimation and latent clear image estimation. The experimental results demonstrate that the proposed method achieves good restoration results on a series of simulated and real blurred images with Poisson noise.

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Zhang, Wei, Jiao Jie Li, and Yu Pu Yang. "Maximum a Posteriori Image Denoising with Edge-Preserving Markov Random Field Regularization." Applied Mechanics and Materials 443 (October 2013): 12–17. http://dx.doi.org/10.4028/www.scientific.net/amm.443.12.

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Image denoising is still a challenging problem for researchers. The conventional methods for image denoising often smooth the images and result in blurring the edges. In this paper, however, we consider not only the noise removal ability but also another important requirement for image denoising procedures that is true image structures, such as edges, should be preserved. To this end, we propose a maximum a posterior (MAP) image denoising algorithm using a novel edge-preserving Markov random field (MRF) model. Considering edges tend to be continuous in space, the connectivity of structure tensor is defined to describe edges. And the revised Markov random field model is proposed by using the edge connectivity, which can adaptively control the degree of smoothing. The experiments show that our new method gives superior performance in terms of both objective criteria and subjective human vision when compared with related MRF models.

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Wang, Zhi Ming, and Hong Bao. "A New Regularization Model Based on Non-Local Means for Image Deblurring." Applied Mechanics and Materials 411-414 (September 2013): 1164–69. http://dx.doi.org/10.4028/www.scientific.net/amm.411-414.1164.

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Image deblurring with noise is a typical ill-posed problem needs regularization. Various regularization models were proposed during several decades study, such as Tikhonov and TV. A new regularization model based non-local similarity constrains is proposed in this paper, which used l2 non-local norms and could be easily solved by fast non-local image denoising algorithm. By combining with Bregmanrized operator splitting (BOS) algorithm, a fast and efficient iterative three step image deblurring scheme is given. Experimental results show that proposed regularization model obtained better results on ten common test images than other similar regularization model including newly proposed NLTV regularization, both in deblurring performance (PSNR and MSSIM) and processing speed.

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Phan, Tran Dang Khoa. "A multi-stage algorithm for image denoising based on PCA and adaptive TV-regularization." Cybernetics and Physics, Volume 10, 2021, Number 3 (November 30, 2021): 162–70. http://dx.doi.org/10.35470/2226-4116-2021-10-3-162-170.

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In this paper, we present an image denoising algorithm comprising three stages. In the first stage, Principal Component Analysis (PCA) is used to suppress the noise. PCA is applied to image blocks to characterize localized features and rare image patches. In the second stage, we use the Gaussian curvature to develop an adaptive total-variation-based (TV) denoising model to effectively remove visual artifacts and noise residual generated by the first stage. Finally, the denoised image is sharpened in order to enhance the contrast of the denoising result. Experimental results on natural images and computed tomography (CT) images demonstrated that the proposed algorithm yields denoising results better than competing algorithms in terms of both qualitative and quantitative aspects.

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Dinesh, Chinthaka, Gene Cheung, and Ivan V. Bajic. "Point Cloud Denoising via Feature Graph Laplacian Regularization." IEEE Transactions on Image Processing 29 (2020): 4143–58. http://dx.doi.org/10.1109/tip.2020.2969052.

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Parekh, Ankit, and Ivan W. Selesnick. "Convex Denoising using Non-Convex Tight Frame Regularization." IEEE Signal Processing Letters 22, no. 10 (October 2015): 1786–90. http://dx.doi.org/10.1109/lsp.2015.2432095.

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Allard, William K. "Total Variation Regularization for Image Denoising, II. Examples." SIAM Journal on Imaging Sciences 1, no. 4 (January 2008): 400–417. http://dx.doi.org/10.1137/070698749.

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Allard, William K. "Total Variation Regularization for Image Denoising, III. Examples." SIAM Journal on Imaging Sciences 2, no. 2 (January 2009): 532–68. http://dx.doi.org/10.1137/070711128.

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Yuan, Jianjun. "MRI denoising via sparse tensors with reweighted regularization." Applied Mathematical Modelling 69 (May 2019): 552–62. http://dx.doi.org/10.1016/j.apm.2019.01.011.

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Keren, Daniel, and Anna Gotlib. "Denoising Color Images Using Regularization and “Correlation Terms”." Journal of Visual Communication and Image Representation 9, no. 4 (December 1998): 352–65. http://dx.doi.org/10.1006/jvci.1998.0392.

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Sun, Hao, Lihong Peng, Hongyan Zhang, Yuru He, Shuangliang Cao, and Lijun Lu. "Dynamic PET Image Denoising Using Deep Image Prior Combined With Regularization by Denoising." IEEE Access 9 (2021): 52378–92. http://dx.doi.org/10.1109/access.2021.3069236.

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Skribtsov, Pavel Vyacheslavovich, and Sergey Olegovich Surikov. "Regularization Method for Solving Denoising and Inpainting Task Using Stacked Sparse Denoising Autoencoders." American Journal of Applied Sciences 13, no. 1 (January 1, 2016): 64–72. http://dx.doi.org/10.3844/ajassp.2016.64.72.

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Zhu, Jianguang, Ying Wei, Juan Wei, and Binbin Hao. "A Non-Convex Hybrid Overlapping Group Sparsity Model with Hyper-Laplacian Prior for Multiplicative Noise." Fractal and Fractional 7, no. 4 (April 17, 2023): 336. http://dx.doi.org/10.3390/fractalfract7040336.

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Multiplicative noise removal is a quite challenging problem in image denoising. In recent years, hyper-Laplacian prior information has been successfully introduced in the image denoising problem and significant denoising effects have been achieved. In this paper, we propose a new hybrid regularizer model for removing multiplicative noise. The proposed model consists of the non-convex higher-order total variation and overlapping group sparsity on a hyper-Laplacian prior regularizer. It combines the advantages of the non-convex regularization and the hybrid regularization, which may simultaneously preserve the fine-edge information and reduce the staircase effect at the same time. We develop an effective alternating minimization method for the proposed nonconvex model via an alternating direction method of multipliers framework, where the majorization–minimization algorithm and the iteratively reweighted algorithm are adopted to solve the corresponding subproblems. Numerical experiments show that the proposed model outperforms the most advanced model in terms of visual quality and certain image quality measurements.

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Yuan, Quan, Zhenyun Peng, Zhencheng Chen, Yanke Guo, Bin Yang, and Xiangyan Zeng. "Edge-Preserving Median Filter and Weighted Coding with Sparse Nonlocal Regularization for Low-Dose CT Image Denoising Algorithm." Journal of Healthcare Engineering 2021 (July 26, 2021): 1–7. http://dx.doi.org/10.1155/2021/6095676.

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The impulse noise in CT image was removed based on edge-preserving median filter algorithm. The sparse nonlocal regularization algorithm weighted coding was used to remove the impulse noise and Gaussian noise in the mixed noise, and the peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) were calculated to evaluate the quality of the denoised CT image. It was found that in nine different proportions of Gaussian noise and salt-and-pepper noise in Shepp-Logan image and CT image processing, the PSNR and SSIM values of the proposed denoising algorithm based on edge-preserving median filter (EP median filter) and weighted encoding with sparse nonlocal regularization (WESNR) were significantly higher than those of using EP median filter and WESNR alone. It was shown that the weighted coding algorithm based on edge-preserving median filtering and sparse nonlocal regularization had potential application value in low-dose CT image denoising.

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Frischauf, Leon, Melanie Melching, and Otmar Scherzer. "Diffusion tensor regularization with metric double integrals." Journal of Inverse and Ill-posed Problems 30, no. 2 (January 5, 2022): 163–90. http://dx.doi.org/10.1515/jiip-2021-0041.

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Abstract In this paper, we propose a variational regularization method for denoising and inpainting of diffusion tensor magnetic resonance images. We consider these images as manifold-valued Sobolev functions, i.e. in an infinite dimensional setting, which are defined appropriately. The regularization functionals are defined as double integrals, which are equivalent to Sobolev semi-norms in the Euclidean setting. We extend the analysis of [14] concerning stability and convergence of the variational regularization methods by a uniqueness result, apply them to diffusion tensor processing, and validate our model in numerical examples with synthetic and real data.

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Mahdaoui, Assia El, Abdeldjalil Ouahabi, and Mohamed Said Moulay. "Image Denoising Using a Compressive Sensing Approach Based on Regularization Constraints." Sensors 22, no. 6 (March 11, 2022): 2199. http://dx.doi.org/10.3390/s22062199.

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In remote sensing applications and medical imaging, one of the key points is the acquisition, real-time preprocessing and storage of information. Due to the large amount of information present in the form of images or videos, compression of these data is necessary. Compressed sensing is an efficient technique to meet this challenge. It consists in acquiring a signal, assuming that it can have a sparse representation, by using a minimum number of nonadaptive linear measurements. After this compressed sensing process, a reconstruction of the original signal must be performed at the receiver. Reconstruction techniques are often unable to preserve the texture of the image and tend to smooth out its details. To overcome this problem, we propose, in this work, a compressed sensing reconstruction method that combines the total variation regularization and the non-local self-similarity constraint. The optimization of this method is performed by using an augmented Lagrangian that avoids the difficult problem of nonlinearity and nondifferentiability of the regularization terms. The proposed algorithm, called denoising-compressed sensing by regularization (DCSR) terms, will not only perform image reconstruction but also denoising. To evaluate the performance of the proposed algorithm, we compare its performance with state-of-the-art methods, such as Nesterov’s algorithm, group-based sparse representation and wavelet-based methods, in terms of denoising and preservation of edges, texture and image details, as well as from the point of view of computational complexity. Our approach permits a gain up to 25% in terms of denoising efficiency and visual quality using two metrics: peak signal-to-noise ratio (PSNR) and structural similarity (SSIM).

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Merzlikin, Dmitrii, Sergey Fomel, and Xinming Wu. "Least-squares diffraction imaging using shaping regularization by anisotropic smoothing." GEOPHYSICS 85, no. 5 (September 1, 2020): S313—S325. http://dx.doi.org/10.1190/geo2019-0741.1.

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We have used least-squares migration to emphasize edge diffractions. The inverted forward-modeling operator is the chain of three operators: Kirchhoff modeling, azimuthal plane-wave destruction, and the path-summation integral filter. Azimuthal plane-wave destruction removes reflected energy without damaging edge-diffraction signatures. The path-summation integral guides the inversion toward probable diffraction locations. We combine sparsity constraints and anisotropic smoothing in the form of shaping regularization to highlight edge diffractions. Anisotropic smoothing enforces continuity along edges. Sparsity constraints emphasize diffractions perpendicular to edges and have a denoising effect. Synthetic and field data examples illustrate the effectiveness of the proposed approach in denoising and highlighting edge diffractions, such as channel edges and faults.

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Chen, Tianfei, Qinghua Xiang, Dongliang Zhao, and Lijun Sun. "An Unsupervised Image Denoising Method Using a Nonconvex Low-Rank Model with TV Regularization." Applied Sciences 13, no. 12 (June 15, 2023): 7184. http://dx.doi.org/10.3390/app13127184.

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In real-world scenarios, images may be affected by additional noise during compression and transmission, which interferes with postprocessing such as image segmentation and feature extraction. Image noise can also be induced by environmental variables and imperfections in the imaging equipment. Robust principal component analysis (RPCA), one of the traditional approaches for denoising images, suffers from a failure to efficiently use the background’s low-rank prior information, which lowers its effectiveness under complex noise backgrounds. In this paper, we propose a robust PCA method based on a nonconvex low-rank approximation and total variational regularization (TV) to model the image denoising problem in order to improve the denoising performance. Firstly, we use a nonconvex γ-norm to address the issue that the traditional nuclear norm penalizes large singular values excessively. The rank approximation is more accurate than the nuclear norm thanks to the elimination of matrix elements with substantial approximation errors to reduce the sparsity error. The method’s robustness is improved by utilizing the low sensitivity of the γ-norm to outliers. Secondly, we use the l1-norm to increase the sparsity of the foreground noise. The TV norm is used to improve the smoothness of the graph structure in accordance with the sparsity of the image in the gradient domain. The denoising effectiveness of the model is increased by employing the alternating direction multiplier strategy to locate the global optimal solution. It is important to note that our method does not require any labeled images, and its unsupervised denoising principle enables the generalization of the method to different scenarios for application. Our method can perform denoising experiments on images with different types of noise. Extensive experiments show that our method can fully preserve the edge structure information of the image, preserve important features of the image, and maintain excellent visual effects in terms of brightness smoothing.

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Wei, Tengda, Linshan Wang, Ping Lin, Jialing Chen, Yangfan Wang, and Haiyong Zheng. "Learning Non-Negativity Constrained Variation for Image Denoising and Deblurring." Numerical Mathematics: Theory, Methods and Applications 10, no. 4 (September 12, 2017): 852–71. http://dx.doi.org/10.4208/nmtma.2017.m1653.

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AbstractThis paper presents a heuristic Learning-based Non-Negativity Constrained Variation (L-NNCV) aiming to search the coefficients of variational model automatically and make the variation adapt different images and problems by supervised-learning strategy. The model includes two terms: a problem-based term that is derived from the prior knowledge, and an image-driven regularization which is learned by some training samples. The model can be solved by classicalε-constraint method. Experimental results show that: the experimental effectiveness of each term in the regularization accords with the corresponding theoretical proof; the proposed method outperforms other PDE-based methods on image denoising and deblurring.

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Guo, Juncheng, and Qinghua Chen. "Image denoising based on nonconvex anisotropic total-variation regularization." Signal Processing 186 (September 2021): 108124. http://dx.doi.org/10.1016/j.sigpro.2021.108124.

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Shi, Hao, Ruixia Liu, Changfang Chen, Minglei Shu, and Yinglong Wang. "ECG Baseline Estimation and Denoising With Group Sparse Regularization." IEEE Access 9 (2021): 23595–607. http://dx.doi.org/10.1109/access.2021.3056459.

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Cohen, Regev, Michael Elad, and Peyman Milanfar. "Regularization by Denoising via Fixed-Point Projection (RED-PRO)." SIAM Journal on Imaging Sciences 14, no. 3 (January 2021): 1374–406. http://dx.doi.org/10.1137/20m1337168.

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Romano, Yaniv, Michael Elad, and Peyman Milanfar. "The Little Engine That Could: Regularization by Denoising (RED)." SIAM Journal on Imaging Sciences 10, no. 4 (January 2017): 1804–44. http://dx.doi.org/10.1137/16m1102884.

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Du, Hongchun. "Image Denoising Algorithm Based on Nonlocal Regularization Sparse Representation." IEEE Sensors Journal 20, no. 20 (October 15, 2020): 11943–50. http://dx.doi.org/10.1109/jsen.2019.2960318.

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Wei, Wanhui, Wei Zhou, and Yongjun Wu. "Improved Wavelet Denoising by Penalty Function and Regularization Parameter." Journal of Physics: Conference Series 1345 (November 2019): 022072. http://dx.doi.org/10.1088/1742-6596/1345/2/022072.

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Pang, Zhi-Feng, Hui-Li Zhang, Shousheng Luo, and Tieyong Zeng. "Image denoising based on the adaptive weighted TV regularization." Signal Processing 167 (February 2020): 107325. http://dx.doi.org/10.1016/j.sigpro.2019.107325.

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Hou, Guojia, Jingming Li, Guodong Wang, Zhenkuan Pan, and Xin Zhao. "Underwater image dehazing and denoising via curvature variation regularization." Multimedia Tools and Applications 79, no. 27-28 (April 15, 2020): 20199–219. http://dx.doi.org/10.1007/s11042-020-08759-z.

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Zhao, Yong, Hong Qin, Xueying Zeng, Junli Xu, and Junyu Dong. "Robust and effective mesh denoising using L0 sparse regularization." Computer-Aided Design 101 (August 2018): 82–97. http://dx.doi.org/10.1016/j.cad.2018.04.001.

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Journal articles on the topic 'Regularization by Denoising'

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