Image denoising via adaptive soft-thresholding based on non-local samples

Liu, Hangfan; Xiong, Ruiqin; Zhang, Jian; Gao, Wen

doi:10.1109/cvpr.2015.7298646

Cited by 70 publications

(39 citation statements)

References 26 publications

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“…Based on this designed dictionary, we bridge the gap between the proposed RRC model and GSR model. More specifically, we prove that the proposed RRC model is equivalent to a GSR model, i.e., group sparsity residual constraint (GSRC) model [35,46,39,47].…”

Section: Analyzing the Rrc Model Using Group Sparse Representationmentioning

confidence: 90%

From Rank Estimation to Rank Approximation: Rank Residual Constraint for Image Restoration

Zha

Yuan

Wen

et al. 2020

IEEE Trans. on Image Process.

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In this paper, we propose a novel approach for the rank minimization problem, termed rank residual constraint (RRC). Different from existing low-rank based approaches, such as the well-known weighted nuclear norm minimization (WNNM) and nuclear norm minimization (NNM), which aim to estimate the underlying lowrank matrix directly from the corrupted observation, we progressively approximate or approach the underlying low-rank matrix via minimizing the rank residual. By integrating the image nonlocal self-similarity (NSS) prior with the proposed RRC model, we develop an iterative algorithm for image denoising. To this end, we first present a recursive based nonlocal means method to obtain a good reference of the original image patch groups, and then the rank residual of the image patch groups between this reference and the noisy image is minimized to achieve a better estimate of the desired image. In this manner, both the reference and the estimated image in each iteration are improved gradually and jointly. Based on the groupbased sparse representation model, we further provide a theoretical analysis on the feasibility of the proposed RRC model. Experimental results demonstrate that the proposed RRC model outperforms many state-of-the-art denoising methods in both the objective and perceptual qualities.

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Section: Analyzing the Rrc Model Using Group Sparse Representationmentioning

confidence: 90%

From Rank Estimation to Rank Approximation: Rank Residual Constraint for Image Restoration

Zha

Yuan

Wen

et al. 2020

IEEE Trans. on Image Process.

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“…In adaptive MBIR (e.g., [2], [6], [8]), one may apply adaptive image denoising [53], [67]- [71] to optimize thresholding parameters. However, if CAOL (P0) and testing the learned 6 Their double-precision MATLAB implementations were tested on 3.3 GHz Intel Core i5 CPU with 32 GB RAM.…”

Section: B Caol With Bpeg-mmentioning

confidence: 99%

Convolutional Analysis Operator Learning: Acceleration and Convergence

Chun

Fessler

2020

IEEE Trans. on Image Process.

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Convolutional operator learning is gaining attention in many signal processing and computer vision applications. Learning kernels has mostly relied on so-called patch-domain approaches that extract and store many overlapping patches across training signals. Due to memory demands, patch-domain methods have limitations when learning kernels from large datasetsparticularly with multi-layered structures, e.g., convolutional neural networks -or when applying the learned kernels to highdimensional signal recovery problems. The so-called convolution approach does not store many overlapping patches, and thus overcomes the memory problems particularly with careful algorithmic designs; it has been studied within the "synthesis" signal model, e.g., convolutional dictionary learning. This paper proposes a new convolutional analysis operator learning (CAOL) framework that learns an analysis sparsifying regularizer with the convolution perspective, and develops a new convergent Block Proximal Extrapolated Gradient method using a Majorizer (BPEG-M) to solve the corresponding block multi-nonconvex problems. To learn diverse filters within the CAOL framework, this paper introduces an orthogonality constraint that enforces a tight-frame filter condition, and a regularizer that promotes diversity between filters. Numerical experiments show that, with sharp majorizers, BPEG-M significantly accelerates the CAOL convergence rate compared to the state-of-the-art block proximal gradient (BPG) method. Numerical experiments for sparse-view computational tomography show that a convolutional sparsifying regularizer learned via CAOL significantly improves reconstruction quality compared to a conventional edge-preserving regularizer. Using more and wider kernels in a learned regularizer better preserves edges in reconstructed images.

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“…Then the similarities between these 3D blocks are measured and "similar" blocks are grouped together. After this, group-sparsity principles [54], [55] are used to encode such groups of blocks, which shares the same spirit with vBM4D [52].…”

Section: Mpeg Video Compression Involves Performing Two Key Steps: Jpmentioning

confidence: 99%

Snapshot Compressed Sensing: Performance Bounds and Algorithms

Jalali

Yuan

2019

IEEE Trans. Inform. Theory

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Snapshot compressed sensing (CS) refers to compressive imaging systems in which multiple frames are mapped into a single measurement frame. Each pixel in the acquired frame is a noisy linear mapping of the corresponding pixels in the frames that are combined together. While the problem can be cast as a CS problem, due to the very special structure of the sensing matrix, standard CS theory cannot be employed to study such systems. In this paper, a compression-based framework is employed for theoretical analysis of snapshot CS systems. It is shown that this framework leads to two novel, computationally-efficient and theoretically-analyzable compression-based recovery algorithms. The proposed methods are iterative and employ compression codes to define and impose the structure of the desired signal. Theoretical convergence guarantees are derived for both algorithms. In the simulations, it is shown that, in the cases of both noise-free and noisy measurements, combining the proposed algorithms with a customized video compression code, designed to exploit nonlocal structures of video frames, significantly improves the state-of-the-art performance.

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Image denoising via adaptive soft-thresholding based on non-local samples

Cited by 70 publications

References 26 publications

From Rank Estimation to Rank Approximation: Rank Residual Constraint for Image Restoration

From Rank Estimation to Rank Approximation: Rank Residual Constraint for Image Restoration

Convolutional Analysis Operator Learning: Acceleration and Convergence

Snapshot Compressed Sensing: Performance Bounds and Algorithms

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