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

Low-Rankness Guided Group Sparse Representation for Image Restoration

As a spotlighted nonlocal image representation model, group sparse representation (GSR) has demonstrated a great potential in diverse image restoration tasks. Most of the existing GSR-based image restoration approaches exploit the nonlocal self-similarity (NSS) prior by clustering similar patches into groups and imposing sparsity to each group coefficient, which can effectively preserve image texture information. However, these methods have imposed only plain sparsity over each individual patch of the group, while neglecting other beneficial image properties, e.g., low-rankness (LR), leads to degraded image restoration results. In this article, we propose a novel low-rankness guided group sparse representation (LGSR) model for highly effective image restoration applications. The proposed LGSR jointly utilizes the sparsity and LR priors of each group of similar patches under a unified framework. The two priors serve as the complementary priors in LGSR for effectively preserving the texture and structure information of natural images. Moreover, we apply an alternating minimization algorithm with an adaptively adjusted parameter scheme to solve the proposed LGSR-based image restoration problem. Extensive experiments are conducted to demonstrate that the proposed LGSR achieves superior results compared with many popular or state-of-the-art algorithms in various image restoration tasks, including denoising, inpainting, and compressive sensing (CS).

A Hybrid Structural Sparsification Error Model for Image Restoration

Recent works on structural sparse representation (SSR), which exploit image nonlocal self-similarity (NSS) prior by grouping similar patches for processing, have demonstrated promising performance in various image restoration applications. However, conventional SSR-based image restoration methods directly fit the dictionaries or transforms to the internal (corrupted) image data. The trained internal models inevitably suffer from overfitting to data corruption, thus generating the degraded restoration results. In this article, we propose a novel hybrid structural sparsification error (HSSE) model for image restoration, which jointly exploits image NSS prior using both the internal and external image data that provide complementary information. Furthermore, we propose a general image restoration scheme based on the HSSE model, and an alternating minimization algorithm for a range of image restoration applications, including image inpainting, image compressive sensing and image deblocking. Extensive experiments are conducted to demonstrate that the proposed HSSE-based scheme outperforms many popular or state-of-the-art image restoration methods in terms of both objective metrics and visual perception.

Compressed Feature Vector-based Effective Object Recognition Model in Detection of COVID-19

To better understand the structure of the COVID-19, and to improve the recognition speed, an effective recognition model based on compressed feature vector is proposed. Object recognition plays an important role in computer vison aera. To improve the recognition accuracy, most recent approaches always adopt a set of complicated hand-craft feature vectors and build the complex classifiers. Although such approaches achieve the favourable performance on recognition accuracy, they are inefficient. To raise the recognition speed without decreasing the accuracy loss, this paper proposed an efficient recognition modeltrained witha kind of compressed feature vectors. Firstly, we propose a kind of compressed feature vector based on the theory of compressive sensing. A sparse matrix is adopted to compress feature vector from very high dimensions to very low dimensions, which reduces the computation complexity and saves enough information for model training and predicting. Moreover, to improve the inference efficiency during the classification stage, an efficient recognition model is built by a novel optimization approach, which reduces the support vectors of kernel-support vector machine (kernel SVM). The SVM model is established with whether the subject is infected with the COVID-19 as the dependent variable, and the age, gender, nationality, and other factors as independent variables. The proposed approach iteratively builds a compact set of the support vectors from the original kernel SVM, and then the new generated model achieves approximate recognition accuracy with the original kernel SVM. Additionally, with the reduction of support vectors, the recognition time of new generated is greatly improved. Finally, the COVID-19 patients have specific epidemiological characteristics, and the SVM recognition model has strong fitting ability. From the extensive experimental results conducted on two datasets, the proposed object recognition model achieves favourable performance not only on recognition accuracy but also on recognition speed.

Deep Learning-Enabled Resolution-Enhancement in Mini- and Regular Microscopy for Biomedical Imaging

Artificial intelligence algorithms that aid mini-microscope imaging are attractive for numerous applications. In this paper, we optimize artificial intelligence techniques to provide clear, and natural biomedical imaging. We demonstrate that a deep learning-enabled super-resolution method can significantly enhance the spatial resolution of mini-microscopy and regular-microscopy. This data-driven approach trains a generative adversarial network to transform low-resolution images into super-resolved ones. Mini-microscopic images and regular-microscopic images acquired with different optical microscopes under various magnifications are collected as our experimental benchmark datasets. The only input to this generative-adversarial-network-based method are images from the datasets down-sampled by the Bicubic interpolation. We use independent test set to evaluate this deep learning approach with other deep learning-based algorithms through qualitative and quantitative comparisons. To clearly present the improvements achieved by this generative-adversarial-network-based method, we zoom into the local features to explore and highlight the qualitative differences. We also employ the peak signal-to-noise ratio and the structural similarity, to quantitatively compare alternative super-resolution methods. The quantitative results illustrate that super-resolution images obtained from our approach with interpolation parameter α=0.25 more closely match those of the original high-resolution images than to those obtained by any of the alternative state-of-the-art method. These results are significant for fields that use microscopy tools, such as biomedical imaging of engineered living systems. We also utilize this generative adversarial network-based algorithm to optimize the resolution of biomedical specimen images and then generate three-dimensional reconstruction, so as to enhance the ability of three-dimensional imaging throughout the entire volumes for spatial-temporal analyses of specimen structures.

Art Image Processing and Color Objective Evaluation Based on Multicolor Space Convolutional Neural Network

A convolutional neural network's weight sharing feature can significantly reduce the cumbersome degree of the network structure and reduce the number of weights that need to be trained. The model can directly input the original image, without the process of feature extraction and data reconstruction in common classification algorithms. This kind of network structure has got a good performance in image processing and recognition. Based on the color objective evaluation method of the convolutional neural network, this paper proposes a convolutional neural network model based on multicolor space and builds a convolutional neural network based on VGGNet (Visual Geometry Group Net) in three different color spaces, namely, RGB (Red Green Blue), LAB (Luminosity a b), and HSV (Hue Saturation Value) color spaces. We carry out research on data input processing and model output selection and perform feature extraction and prediction of color images. After a model output selection judger, the prediction results of different color spaces are merged and the final prediction category is output. This article starts with the multidimensional correlation for visual art image processing and color objective evaluation. Considering the relationship between the evolution of artistic painting style and the color of artistic images, this article explores the characteristics of artistic image dimensions. In view of different factors, corresponding knowledge extraction strategies are designed to generate color label distribution, provide supplementary information of art history for input images, and train the model on a multitask learning framework. In this paper, experiments on multiple art painting data sets prove that this method is superior to single-color label classification methods.

Triply Complementary Priors for Image Restoration

Recent works that utilized deep models have achieved superior results in various image restoration (IR) applications. Such approach is typically supervised, which requires a corpus of training images with distributions similar to the images to be recovered. On the other hand, the shallow methods, which are usually unsupervised remain promising performance in many inverse problems, e.g., image deblurring and image compressive sensing (CS), as they can effectively leverage nonlocal self-similarity priors of natural images. However, most of such methods are patch-based leading to the restored images with various artifacts due to naive patch aggregation in addition to the slow speed. Using either approach alone usually limits performance and generalizability in IR tasks. In this paper, we propose a joint low-rank and deep (LRD) image model, which contains a pair of triply complementary priors, namely, internal and external, shallow and deep, and non-local and local priors. We then propose a novel hybrid plug-and-play (H-PnP) framework based on the LRD model for IR. Following this, a simple yet effective algorithm is developed to solve the proposed H-PnP based IR problems. Extensive experimental results on several representative IR tasks, including image deblurring, image CS and image deblocking, demonstrate that the proposed H-PnP algorithm achieves favorable performance compared to many popular or state-of-the-art IR methods in terms of both objective and visual perception.

Image Restoration via Reconciliation of Group Sparsity and Low-Rank Models

Image nonlocal self-similarity (NSS) property has been widely exploited via various sparsity models such as joint sparsity (JS) and group sparse coding (GSC). However, the existing NSS-based sparsity models are either too restrictive, e.g., JS enforces the sparse codes to share the same support, or too general, e.g., GSC imposes only plain sparsity on the group coefficients, which limit their effectiveness for modeling real images. In this paper, we propose a novel NSS-based sparsity model, namely, low-rank regularized group sparse coding (LR-GSC), to bridge the gap between the popular GSC and JS. The proposed LR-GSC model simultaneously exploits the sparsity and low-rankness of the dictionary-domain coefficients for each group of similar patches. An alternating minimization with an adaptive adjusted parameter strategy is developed to solve the proposed optimization problem for different image restoration tasks, including image denoising, image deblocking, image inpainting, and image compressive sensing. Extensive experimental results demonstrate that the proposed LR-GSC algorithm outperforms many popular or state-of-the-art methods in terms of objective and perceptual metrics.

Image Compressive Sensing via Hybrid Nonlocal Sparsity Regularization

This paper focuses on image compressive sensing (CS). As the intrinsic properties of natural images, nonlocal self-similarity and sparse representation have been widely used in various image processing tasks. Most existing image CS methods apply either self-adaptive dictionary (e.g., principle component analysis (PCA) dictionary and singular value decomposition (SVD) dictionary) or fixed dictionary (e.g., discrete cosine transform (DCT), discrete wavelet transform (DWT), and Curvelet) as the sparse basis, while single dictionary could not fully explore the sparsity of images. In this paper, a Hybrid NonLocal Sparsity Regularization (HNLSR) is developed and applied to image compressive sensing. The proposed HNLSR measures nonlocal sparsity in 2D and 3D transform domain simultaneously, and both self-adaptive singular value decomposition (SVD) dictionary and fixed 3D transform are utilized. We use an efficient alternating minimization method to solve the optimization problem. Experimental results demonstrate that the proposed method outperforms existing methods in both objective evaluation and visual quality.

Group Sparsity Residual Constraint with Non-Local Priors for Image Restoration

Group sparse representation (GSR) has made great strides in image restoration producing superior performance, realized through employing a powerful mechanism to integrate the local sparsity and nonlocal self-similarity of images. However, due to some form of degradation (e.g., noise, down-sampling or pixels missing), traditional GSR models may fail to faithfully estimate sparsity of each group in an image, thus resulting in a distorted reconstruction of the original image. This motivates us to design a simple yet effective model that aims to address the above mentioned problem. Specifically, we propose group sparsity residual constraint with nonlocal priors (GSRC-NLP) for image restoration. Through introducing the group sparsity residual constraint, the problem of image restoration is further defined and simplified through attempts at reducing the group sparsity residual. Towards this end, we first obtain a good estimation of the group sparse coefficient of each original image group by exploiting the image nonlocal self-similarity (NSS) prior along with self-supervised learning scheme, and then the group sparse coefficient of the corresponding degraded image group is enforced to approximate the estimation. To make the proposed scheme tractable and robust, two algorithms, i.e., iterative shrinkage/thresholding (IST) and alternating direction method of multipliers (ADMM), are employed to solve the proposed optimization problems for different image restoration tasks. Experimental results on image denoising, image inpainting and image compressive sensing (CS) recovery, demonstrate that the proposed GSRC-NLP based image restoration algorithm is comparable to state-of-the-art denoising methods and outperforms several state-of-the-art image inpainting and image CS recovery methods in terms of both objective and perceptual quality metrics.

A Benchmark for Sparse Coding: When Group Sparsity Meets Rank Minimization

Sparse coding has achieved a great success in various image processing tasks. However, a benchmark to measure the sparsity of image patch/group is missing since sparse coding is essentially an NP-hard problem. This work attempts to fill the gap from the perspective of rank minimization. We firstly design an adaptive dictionary to bridge the gap between group-based sparse coding (GSC) and rank minimization. Then, we show that under the designed dictionary, GSC and the rank minimization problems are equivalent, and therefore the sparse coefficients of each patch group can be measured by estimating the singular values of each patch group. We thus earn a benchmark to measure the sparsity of each patch group because the singular values of the original image patch groups can be easily computed by the singular value decomposition (SVD). This benchmark can be used to evaluate performance of any kind of norm minimization methods in sparse coding through analyzing their corresponding rank minimization counterparts. Towards this end, we exploit four well-known rank minimization methods to study the sparsity of each patch group and the weighted Schatten p-norm minimization (WSNM) is found to be the closest one to the real singular values of each patch group. Inspired by the aforementioned equivalence regime of rank minimization and GSC, WSNM can be translated into a non-convex weighted ℓp-norm minimization problem in GSC. By using the earned benchmark in sparse coding, the weighted ℓp-norm minimization is expected to obtain better performance than the three other norm minimization methods, i.e., ℓ1-norm, ℓp-norm and weighted ℓ1-norm. To verify the feasibility of the proposed benchmark, we compare the weighted ℓp-norm minimization against the three aforementioned norm minimization methods in sparse coding. Experimental results on image restoration applications, namely image inpainting and image compressive sensing recovery, demonstrate that the proposed scheme is feasible and outperforms many state-of-the-art methods.

A Sound Source Identification Algorithm Based on Bayesian Compressive Sensing and Equivalent Source Method

Near-field acoustic holography (NAH) based on equivalent source method (ESM) is an effective method for identifying sound sources. Conventional ESM focuses on relatively low frequencies and cannot provide a satisfactory solution at high frequencies. So its improved method called wideband acoustic holography (WBH) has been proposed, which has high reconstruction accuracy at medium-to-high frequencies. However, it is less accurate for coherent sound sources at low frequencies. To improve the reconstruction accuracy of conventional ESM and WBH, a sound source identification algorithm based on Bayesian compressive sensing (BCS) and ESM is proposed. This method uses a hierarchical Laplace sparse prior probability distribution, and adaptively adjusts the regularization parameter, so that the energy is concentrated near the correct equivalent source. Referring to the function beamforming idea, the original algorithm with order v can improve its dynamic range, and then more accurate position information is obtained. Based on the simulation of irregular microphone array, comparisons with conventional ESM and WBH show that the proposed method is more accurate, suitable for a wider range of frequencies, and has better reconstruction performance for coherent sources. By increasing the order v, the coherent sources can be located accurately. Finally, the stability and reliability of the proposed method are verified by experiments.

Robustly reconstructing magnetic resonance images via structure decomposition

In magnetic resonance (MR) imaging, for highly under-sampled k-space data, it is typically difficult to reconstruct images and preserve their original texture simultaneously. The high-degree total variation (HDTV) regularization handles staircase effects but still blurs textures. On the other hand, the non-local TV (NLTV) regularization can preserve textures, but will introduce additional artifacts for highly-noised images. In this paper, we propose a reconstruction model derived from HDTV and NLTV for robust MRI reconstruction. First, an MR image is decomposed into a smooth component and a texture component. Second, for the smooth component with sharp edges, isotropic second-order TV is used to reduce staircase effects. For the texture component with piecewise constant background, NLTV and contourlet-based sparsity regularizations are employed to recover textures. The piecewise constant background in the texture component contributes to accurately detect non-local similar image patches and avoid artifacts introduced by NLTV. Finally, the proposed reconstruction model is solved through an alternating minimization scheme. The experimental results demonstrate that the proposed reconstruction model can effectively achieve satisfied quality of reconstruction for highly under-sampled k-space data.