Iterative Singular-value Thresholding Research Articles

2D Compressed Sensing Using Nonlocal Low-Rank Prior Reconstruction for Cipher-Image Coding

In recent years, cipher-image coding by using compressed sensing (CS) has became a hot topic. However, the ratio-distortion (R-D) performance of the previous methods are barely satisfactory. In order to address this concern, a 2D CS (2DCS) scheme by using nonlocal low-rank prior (NLP) reconstruction is proposed in this letter. Firstly, the scrambling encryption is applied to mask the plaintext image. Secondly, the cipher image is compressed by 2DCS. Lastly, an iterative singular value thresholding (ISVT) algorithm is developed, which can reconstruct the image effectively by exploring the NLP information of the image. Simulation results show that the proposed method outperforms the previous CS-based methods in terms of R-D performance.

An Enhanced Low Rank Approximation SVD-Based Method for Image Denoising

Nonlocal self-similarity of images has attracted considerable interest in the field of image processing and has led to several state-of-the-art image denoising algorithms, such as block matching and 3-D, principal component analysis with local pixel grouping, patch-based locally optimal wiener, and spatially adaptive iterative singular-value thresholding. In this paper, we propose a computationally simple denoising algorithm using the nonlocal self-similarity and the low-rank approximation (LRA). The proposed method consists of three basic steps. First, our method classifies similar image patches by the block-matching technique to form the similar patch groups, which results in the similar patch groups to be low rank. Next, each group of similar patches is factorized by singular value decomposition (SVD) and estimated by taking only a few largest singular values and corresponding singular vectors. Finally, an initial de-noised image is generated by aggregating all processed patches. For low-rank matrices, SVD can provide the optimal energy compaction in the least square sense. The proposed method exploits the optimal energy compaction property of SVD to lead an LRA of similar patch groups. Unlike other SVD based methods, the LRA in SVD domain avoids learning the local basis for representing image patches, which usually is computationally expensive. The experimental results demonstrate that the proposed method can effectively reduce noise and be competitive with the current state-of-the-art denoising algorithms in terms of both quantitative metrics and subjective visual quality.

Gradient-Based Low Rank Method for Highly Undersampled Magnetic Resonance Imaging Reconstruction

Recently, exploiting low rank property of the data accomplished by the non-convex optimization has shown great potential to decrease measurements for compressed sensing. In this paper, the low rank regularization is adopted to gradient similarity minimization, and applied for highly undersampled magnetic resonance imaging (MRI) reconstruction, termed gradient-based low rank MRI reconstruction (GLRMRI). In the proposed method, by incorporating the spatially adaptive iterative singular-value thresholding (SAIST) to optimize our gradient scheme, the deterministic annealing iterates the procedure efficiently and superior reconstruction performance is achieved. Extensive experimental results have consistently demonstrated that GLRMRI recovers both realvalued MR images and complex-valued MR data accurately, especially in the edge preserving perspective, and outperforms the current state-of-the-art approaches in terms of higher peak signal to noise ratio (PSNR) and lower high-frequency error norm (HFEN) values.

Gradient-based low rank method and its application in image inpainting

Conventional inpainting methods generally apply textures that are most similar to the areas around the missing region or use large image database. Recently, low rank property of data shows that the non-convex optimization decreases measurements. In this paper, we propose a new image prior, which implies the low rank prior knowledge of image gradients. The proposed detail-preserving image inpainting algorithm adopts the low rank regularization to gradient similarity minimization, termed gradient-based low rank approximation (Grad-LR), namely that we employ the low rank constraints in the horizontal and vertical gradients of the image and then reconstruct the desired image using the adaptive iterative singular-value thresholding of both derivatives. In the method, by incorporating the spatially adaptive iterative singular-value thresholding (SAIST) to optimize our gradient scheme, the deterministic annealing iterates the procedure efficiently. As a result, the strength of the algorithm is obvious when filling large missing region. Experimental results consistently demonstrate that the proposed algorithm works well for both structural and texture images and outperforms other techniques, in terms of both objective and subjective performance measures.

An Efficient SVD-Based Method for Image Denoising

Nonlocal self-similarity of images has attracted considerable interest in the field of image processing and has led to several state-of-the-art image denoising algorithms, such as block matching and 3-D, principal component analysis with local pixel grouping, patch-based locally optimal wiener, and spatially adaptive iterative singular-value thresholding. In this paper, we propose a computationally simple denoising algorithm using the nonlocal self-similarity and the low-rank approximation (LRA). The proposed method consists of three basic steps. First, our method classifies similar image patches by the block-matching technique to form the similar patch groups, which results in the similar patch groups to be low rank. Next, each group of similar patches is factorized by singular value decomposition (SVD) and estimated by taking only a few largest singular values and corresponding singular vectors. Finally, an initial denoised image is generated by aggregating all processed patches. For low-rank matrices, SVD can provide the optimal energy compaction in the least square sense. The proposed method exploits the optimal energy compaction property of SVD to lead an LRA of similar patch groups. Unlike other SVD-based methods, the LRA in SVD domain avoids learning the local basis for representing image patches, which usually is computationally expensive. The experimental results demonstrate that the proposed method can effectively reduce noise and be competitive with the current state-of-the-art denoising algorithms in terms of both quantitative metrics and subjective visual quality.

Nonlocal sparse and low-rank regularization for optical flow estimation.

Designing an appropriate regularizer is of great importance for accurate optical flow estimation. Recent works exploiting the nonlocal similarity and the sparsity of the motion field have led to promising flow estimation results. In this paper, we propose to unify these two powerful priors. To this end, we propose an effective flow regularization technique based on joint low-rank and sparse matrix recovery. By grouping similar flow patches into clusters, we effectively regularize the motion field by decomposing each set of similar flow patches into a low-rank component and a sparse component. For better enforcing the low-rank property, instead of using the convex nuclear norm, we use the log det(·) function as the surrogate of rank, which can also be efficiently minimized by iterative singular value thresholding. Experimental results on the Middlebury benchmark show that the performance of the proposed nonlocal sparse and low-rank regularization method is higher than (or comparable to) those of previous approaches that harness these same priors, and is competitive to current state-of-the-art methods.

Nonlocal Image Restoration With Bilateral Variance Estimation: A Low-Rank Approach

Simultaneous sparse coding (SSC) or nonlocal image representation has shown great potential in various low-level vision tasks, leading to several state-of-the-art image restoration techniques, including BM3D and LSSC. However, it still lacks a physically plausible explanation about why SSC is a better model than conventional sparse coding for the class of natural images. Meanwhile, the problem of sparsity optimization, especially when tangled with dictionary learning, is computationally difficult to solve. In this paper, we take a low-rank approach toward SSC and provide a conceptually simple interpretation from a bilateral variance estimation perspective, namely that singular-value decomposition of similar packed patches can be viewed as pooling both local and nonlocal information for estimating signal variances. Such perspective inspires us to develop a new class of image restoration algorithms called spatially adaptive iterative singular-value thresholding (SAIST). For noise data, SAIST generalizes the celebrated BayesShrink from local to nonlocal models; for incomplete data, SAIST extends previous deterministic annealing-based solution to sparsity optimization through incorporating the idea of dictionary learning. In addition to conceptual simplicity and computational efficiency, SAIST has achieved highly competent (often better) objective performance compared to several state-of-the-art methods in image denoising and completion experiments. Our subjective quality results compare favorably with those obtained by existing techniques, especially at high noise levels and with a large amount of missing data.