Compressed Sensing Image Recovery Research Articles

Single pixel imaging at high pixel resolutions.

The usually reported pixel resolution of single pixel imaging (SPI) varies between 32 × 32 and 256 × 256 pixels falling far below imaging standards with classical methods. Low resolution results from the trade-off between the acceptable compression ratio, the limited DMD modulation frequency, and reasonable reconstruction time, and has not improved significantly during the decade of intensive research on SPI. In this paper we show that image measurement at the full resolution of the DMD, which lasts only a fraction of a second, is possible for sparse images or in a situation when the field of view is limited but is a priori unknown. We propose the sampling and reconstruction strategies that enable us to reconstruct sparse images at the resolution of 1024 × 768 within the time of 0.3s. Non-sparse images are reconstructed with less details. The compression ratio is on the order of 0.4% which corresponds to an acquisition frequency of 7Hz. Sampling is differential, binary, and non-adaptive, and includes information on multiple partitioning of the image which later allows us to determine the actual field of view. Reconstruction is based on the differential Fourier domain regularized inversion (D-FDRI). The proposed SPI framework is an alternative to both adaptive SPI, which is challenging to implement in real time, and to classical compressive sensing image recovery methods, which are very slow at high resolutions.

Low‐Rank Combined Adaptive Sparsifying Transform for Blind Compressed Sensing Image Recovery

Compressed sensing (CS) exploits the sparsity of images or image patches in a transform domain or synthesis dictionary to reconstruct images from undegraded images. Because the synthesis dictionary learning methods involves NP-hard sparse coding and expensive learning steps, sparsifying transform based blind compressed sending (BCS) has been shown to be effective and efficient in applications, while also enjoying good convergence guarantees. By minimizing the rank of an overlapped patch group matrix to efficiently exploit the nonlocal self-similarity features of the image, while the sparsifying transform model imposes the local features of the image. We propose a combined low-rank and adaptive sparsifying transform (LRAST) BCS method to better represent natural images. We utilized the patch coordinate (PCD) descent algorithm to optimize the method, and this enforced the intrinsic local sparsity and nonlocal self-similarity of the images simultaneously in a unified framework. The experimental results indicated a promising performance, even in comparison to state-of-theart methods.

Joint group and residual sparse coding for image compressive sensing

Nonlocal self-similarity and group sparsity have been widely utilized in image compressive sensing (CS). Most existing methods utilize either internal priors or external priors. However, when the sampling rate is low, the internal prior information of degraded images is not enough for accurate restoration, resulting in loss of image edges and details. And external prior, which learned from clean data, may be not adaptive to the images. In this paper, we propose a joint group and residual sparse coding method for CS image recovery (JGRSC-CS). In the proposed JGRSC-CS, patch group is treated as the basic unit of sparse coding. Different from the idea of encoding a group with a single dictionary (e.g. DCT, Curvelet or K-SVD dictionary), two dictionaries (namely internal and external dictionaries) are applied to exploit the sparse representation of each group simultaneously. The internal self-adaptive dictionary is used to remove artifacts, and an external Gaussian Mixture Model (GMM) dictionary, learned from clean training images, is used to enhance details and texture. To make the proposed method effective and robust, the split Bregman method is adopted to reconstruct the whole image. Experimental results manifest that with acceptable computational complexity and good convergence property, the proposed JGRSC-CS algorithm outperforms existing state-of-the-art methods in both peak signal to noise ratio (PSNR) and visual quality.

Formula omitted] norm regularization based group sparse representation for image compressed sensing recovery

One important challenge in image compressed sensing (CS) recovery methods is to develop a sparsity inducing model which can reflect the image priors appropriately and hence yields high quality recovery results. Recent advances have suggested that group sparse representation based models, which exploit nonlocal self-similarity prior, lead to superior results in image CS recovery. In this paper, we propose a CS recovery method via group sparse representation with nonconvex LLp norm regularization (GSR-LLp). In the proposed method, nonconvex LLp norm with (0<p≤1) is introduced as a new sparsity metric to better promote the sparsity of the group coefficients, rather than the l0 norm. Furthermore, the principle component analysis (PCA) is utilized to learn an adaptive orthogonal dictionary for each group. To solve the GSR-driven LLp minimization problem, an efficient algorithm based on split Bregman framework and Majorization–Minimization (MM) algorithm is developed. Moreover, the proposed model is combined with a robust M-estimate to cope with the case where measurements are corrupted by impulsive noise. In this case, we substitute the l2 norm data fidelity with Welch m-estimate which has shown the advantage of robustness against heavy-tailed impulsive noise. We develop an efficient scheme based on split Bregman framework and half-quadratic (HQ) theory to solve the resulting optimization problem (called as RGSR-LLp). Extensive experimental results show effectiveness of the proposed methods compared with the state-of-the-arts methods in CS image recovery.

Image compressed sensing recovery via nonconvex garrote regularization

Sparsity inducing model is one of the most important components of image compressed sensing (CS) recovery methods. These models are built on the image prior knowledge. The model which can reflect the image priors appropriately, yields high quality recovery results. Recent studies have shown that nonlocal low-rank prior based models often lead to superior results in CS recovery. The rank regularization problem resulting from these models is an NP-hard problem and how to solve it has a great impact on the recovery results. In this paper, we propose a new CS recovery method via nonconvex Garrote regularization (NGR) toward better exploiting the nonlocal low-rank prior. In the proposed CS-NGR method, the nonconvex Garrote function is introduced as a suitable surrogate for the rank function. To solve the resulting minimization problem efficiently, we employ the alternating direction method and so-called Garrote singular value shrinkage (GSVS) technique. Extensive experimental results show effectiveness of the proposed method compared with the state-of-the-arts methods in CS image recovery.

Compressed Image Sensing by Jointly Leveraging Multi-Scale Heterogeneous Priors for the Internet of Multimedia Things

As an important branch of the Internet of Things, the Internet of Multimedia Things (IoMT) has complex application scenarios, thus putting forward new challenges to data communication. With the application of compressed sensing (CS)-based image compression and transmission in the field of IoMT, the traditional CS image reconstruction algorithms have been extended to model-based algorithms, which exploit more prior information of multimedia objects other than sparsity/compressibility in the reconstruction process. However, these algorithms mainly exploit just one type of prior information, still leaving room for further improvement. In this paper, we propose a novel CS image reconstruction algorithm by jointly leveraging multi-scale (local and global) heterogeneous (statistical and structural) priors of natural images, named jointly leveraging statistical and structural priors for CS image reconstruction (JLSSP-CS), to enable high-quality CS image recovery for IoMT. Specifically, the proposed JLSSP-CS algorithm is realized under the iterative hard thresholding framework, and the reconstruction process is composed of two phases. In the first phase, the local statistical correction and the global statistical correction are considered sequentially. Then, the global statistical and structural priors are exploited in nested iterations to further refine the recovery result in the second phase. The extensive simulations have been conducted, and the results indicate that the proposed JLSSP-CS algorithm outperforms the current state of the art by realizing high-quality image reconstruction with a small number of measurements for IoMT end devices.

Compressive sensing image recovery using dictionary learning and shape-adaptive DCT thresholding

Compressed sensing (CS) has shown to be a successful technique for image recovery. Designing an effective regularization term reflecting the image sparse prior information plays a critical role in this field. Dictionary learning (DL) strategy alleviates the drawback of fixed bases. But the structure information of the image is easy to be blurred in complex regions due to the absence of sparsity in dictionary learning. This paper proposes a novel joint dictionary learning and Shape-Adaptive DCT (SADCT) thresholding method. We first propose to exploit sparsity of image in shape-adaptive regions, which is beneficial to medical images of complex textures. In this framework, the local sparsity depicts the smoothness redundancies exploited by dictionary learning. Moreover, the sparsity is enhanced especially in detail areas by the newly introduced SADCT thresholding. The attenuated SADCT coefficients are used to reconstruct a local estimation of the signal within the adaptive-shape support. Image is represented sparser in SADCT transform domain and the details of the image information can be kept with a much larger probability. Based on split Bregman iterations, an efficient alternating minimization algorithm is developed to solve the proposed CS medical image recovery problem. The results of various experiments on MR images consistently demonstrate that the proposed algorithm efficiently recovers MR images and shows advantages over the current leading CS reconstruction approaches.

Pulsed-high Intensity Focused Ultrasound Therapy of Rabbit Middle Cerebral Artery Thromboembolism Accompanied by Anticoagulant Nanoparticles Administration

One important challenge in image compressed sensing (CS) recovery methods is to develop a sparsity inducing model which can reflect the image priors appropriately and hence yields high quality recovery results. Recent advances have suggested that group sparse representation based models, which exploit nonlocal self-similarity prior, lead to superior results in image CS recovery. In this paper, we propose a CS recovery method via group sparse representation with nonconvex LLp norm regularization (GSR-LLp). In the proposed method, nonconvex LLp norm with (0<p≤1) is introduced as a new sparsity metric to better promote the sparsity of the group coefficients, rather than the l0 norm. Furthermore, the principle component analysis (PCA) is utilized to learn an adaptive orthogonal dictionary for each group. To solve the GSR-driven LLp minimization problem, an efficient algorithm based on split Bregman framework and Majorization–Minimization (MM) algorithm is developed. Moreover, the proposed model is combined with a robust M-estimate to cope with the case where measurements are corrupted by impulsive noise. In this case, we substitute the l2 norm data fidelity with Welch m-estimate which has shown the advantage of robustness against heavy-tailed impulsive noise. We develop an efficient scheme based on split Bregman framework and half-quadratic (HQ) theory to solve the resulting optimization problem (called as RGSR-LLp). Extensive experimental results show effectiveness of the proposed methods compared with the state-of-the-arts methods in CS image recovery.

No-reference quality assessment of compressive sensing image recovery

Compressive sensing (CS) has been attracting tremendous attention in recent years. Extensive CS image recovery algorithms have been proposed for more effective image reconstruction. However, very little work has been addressed for the quality assessment of CS recovered images, which may hinder further development of CS image recovery techniques. The CS recovered images are typically contaminated by multiple distortions, particularly at low sampling rates. Unfortunately, the existing quality metrics are ineffective for evaluating multiple distortions, so they are limited in predicting the quality of CS recovered images. Motivated by this, this paper presents a no-reference CS Recovered Image Quality (CSRIQ) metric based on the measurement of both local and global distortions in CS recovered images. The local features consist of a local phase coherence based edge sharpness measure and a gray level co-occurrence matrix based texture measure. The global features are extracted based on the natural scene statistics and can be divided into two types. One type is obtained by calculating image naturalness parameters. The other type is computed based on the statistics of singular value decomposition coefficients. Support vector regression is employed to do model training and the subsequent quality prediction. Experimental results conducted on a CS recovered image database demonstrate the advantages of the proposed method. As a application, the proposed metric is used for automatic parameter selection for CS image recovery algorithms.

Practical privacy-preserving compressed sensing image recovery in the cloud

Practical privacy-preserving compressed sensing image recovery in the cloud

Image compressive sensing via Truncated Schatten-p Norm regularization

Low-rank property as a useful image prior has attracted much attention in image processing communities. Recently, a nonlocal low-rank regularization (NLR) approach toward exploiting low-rank property has shown the state-of-the-art performance in Compressive Sensing (CS) image recovery. How to solve the resulting rank regularization problem which is known as an NP-hard problem is critical to the recovery results. NLR takes use of logdet as a smooth nonconvex surrogate function for the rank instead of the convex nuclear norm. However, logdet function cannot well approximate the rank because there exists an irreparable gap between the fixed logdet function and the real rank. In this paper, Truncated Schatten-p Norm regularization, which is used as a surrogate function for the rank to exploit the benefits of both schatten-p norm and truncated nuclear norm, has been proposed toward better exploiting low-rank property in CS image recovery. In addition, we have developed an efficient iterative scheme to solve the resulting nonconvex optimization problem. Experimental results have demonstrated that the proposed algorithm can significantly outperform the existing state-of-the-art image CS methods.

Compressive Sensing Image Restoration Using Adaptive Curvelet Thresholding and Nonlocal Sparse Regularization.

Compressive sensing (CS) is a recently emerging technique and an extensively studied problem in signal and image processing, which suggests a new framework for the simultaneous sampling and compression of sparse or compressible signals at a rate significantly below the Nyquist rate. Maybe, designing an effective regularization term reflecting the image sparse prior information plays a critical role in CS image restoration. Recently, both local smoothness and nonlocal self-similarity have led to superior sparsity prior for CS image restoration. In this paper, first, an adaptive curvelet thresholding criterion is developed, trying to adaptively remove the perturbations appeared in recovered images during CS recovery process, imposing sparsity. Furthermore, a new sparsity measure called joint adaptive sparsity regularization (JASR) is established, which enforces both local sparsity and nonlocal 3-D sparsity in transform domain, simultaneously. Then, a novel technique for high-fidelity CS image recovery via JASR is proposed-CS-JASR. To efficiently solve the proposed corresponding optimization problem, we employ the split Bregman iterations. Extensive experimental results are reported to attest the adequacy and effectiveness of the proposed method comparing with the current state-of-the-art methods in CS image restoration.

Image restoration via patch orientation-based low-rank matrix approximation and nonlocal means

Low-rank matrix approximation and nonlocal means (NLM) are two popular techniques for image restoration. Although the basic principle for applying these two techniques is the same, i.e., similar image patches are abundant in the image, previously published related algorithms use either low-rank matrix approximation or NLM because they manipulate the information of similar patches in different ways. We propose a method for image restoration by jointly using low-rank matrix approximation and NLM in a unified minimization framework. To improve the accuracy of determining similar patches, we also propose a patch similarity measurement based on curvelet transform. Extensive experiments on image deblurring and compressive sensing image recovery validate that the proposed method achieves better results than many state-of-the-art algorithms in terms of both quantitative measures and visual perception.

Compressive multi-spectral imaging using self-correlations of images based on hierarchical joint sparsity models

We propose a novel multi-spectral imaging method based on compressive sensing (CS). In CS theory, the enhancement of signal sparsity is important for accurate signal reconstruction. The main novelty of the proposed method is the employment of a self-correlation of an image, that is a local intensity similarity and multi-spectral correlation, to enhance the sparsity of the multi-spectral image to be recovered. Local intensity similarity, which is based on the concept that spatial changes in intensity are likely to be similar within local regions, contributes to sparsity enhancement. Furthermore, we exploit multi-spectral correlation to improve the sparsity of the multi-spectral components to be recovered. In order to simultaneously exploit different types of characteristics (i.e., local intensity similarity and multi-spectral correlation) for representing a signal as sufficiently sparse, we introduce a hierarchical joint sparsity model in the CS image recovery process. Our experiments show that the use of a self-correlation significantly improves the performance of multi-spectral image reconstruction.

Image/video compressive sensing recovery using joint adaptive sparsity measure

Compressive sensing (CS) is a recently emerging technique and an extensively studied problem in signal and image processing, which enables joint sampling and compression into a unified approach. Recently, local smoothness and nonlocal self-similarity have both led to superior sparsity priors for CS image restoration. In this paper, first, a new sparsity measure called joint adaptive sparsity measure (JASM) is introduced. The proposed JASM enforces both local sparsity and nonlocal 3D sparsity in transform domain, concurrently, providing a powerful mechanism for characterizing the structured sparsities of natural image. More precisely, the local sparsity depicts the local smoothness redundancies exploited by an adaptively learned sparsifying basis, and the nonlocal 3D sparsity corresponds to the nonlocal self-similarity constraint achieved by a new proposed nonlocal statistical sparse modeling. Then, two novel techniques for high-fidelity CS image and video recovery via JASM are proposed. The proposed methods are formulated in the form of minimization functional under regularization-based framework which is solved via an efficient alternating minimization algorithm based on split Bregman framework. Comprehensive experimental results are reported to manifest the effectiveness of the proposed methods compared with the current state-of-the-art methods in CS image/video restoration.

A Douglas-Rachford Splitting Approach to Compressed Sensing Image Recovery Using Low-Rank Regularization.

In this paper, we study the compressed sensing (CS) image recovery problem. The traditional method divides the image into blocks and treats each block as an independent sub-CS recovery task. This often results in losing global structure of an image. In order to improve the CS recovery result, we propose a nonlocal (NL) estimation step after the initial CS recovery for denoising purpose. The NL estimation is based on the well-known NL means filtering that takes an advantage of self-similarity in images. We formulate the NL estimation as the low-rank matrix approximation problem, where the low-rank matrix is formed by the NL similarity patches. An efficient algorithm, nonlocal Douglas-Rachford (NLDR), based on Douglas-Rachford splitting is developed to solve this low-rank optimization problem constrained by the CS measurements. Experimental results demonstrate that the proposed NLDR algorithm achieves significant performance improvements over the state-of-the-art in CS image recovery.

Fast Sparse Image Reconstruction Using Adaptive Nonlinear Filtering

Compressed sensing is a new paradigm for signal recovery and sampling. It states that a relatively small number of linear measurements of a sparse signal can contain most of its salient information and that the signal can be exactly reconstructed from these highly incomplete observations. The major challenge in practical applications of compressed sensing consists in providing efficient, stable and fast recovery algorithms which, in a few seconds, evaluate a good approximation of a compressible image from highly incomplete and noisy samples. In this paper, we propose to approach the compressed sensing image recovery problem using adaptive nonlinear filtering strategies in an iterative framework, and we prove the convergence of the resulting two-steps iterative scheme. The results of several numerical experiments confirm that the corresponding algorithm possesses the required properties of efficiency, stability and low computational cost and that its performance is competitive with those of the state of the art algorithms.