Restricted Threshold Based Compressive Sensing Using Group Sparse Representation Rt-Gsr

Compressed sensing (CS) is a sparse signal sampling methodology for efficiently acquiring and reconstructing a signal from relatively few measurements. Recent work shows that CS is well-suited to be applied to problems in genomics, including probe design in microarrays, RNA interference (RNAi), and taxonomic assignment in metagenomics. The principle of using different CS recovery methods in these applications has thus been established, but a comprehensive study of using a wide range of CS methods has not been done. For each of these applications, we apply three hitherto unused CS methods, namely, l1-magic, CoSaMP, and l1-homotopy, in conjunction with CS measurement matrices such as randomly generated CS m matrix, Hamming matrix, and projective geometry-based matrix. We find that, in RNAi, the l1-magic (the standard package for l1 minimization) and l1-homotopy methods show significant reduction in reconstruction error compared to the baseline. In metagenomics, we find that l1-homotopy as well as CoSaMP estimate concentration with significantly reduced time when compared to the GPSR and WGSQuikr methods.

Denoising is a fundamental task in image processing, aimed at estimating an unknown image from its noisy observation. In this paper, we develop a computationally simple paradigm for image denoising using superpixel grouping and principal component analysis (PCA) of similar patches within the superpixels. Our method comprises three steps. First, we perform a superpixel segmentation on the noisy images. Next, similar patches within the superpixels are grouped in order to preserve the local image structures. Finally, each group of similar patches is factorized by PCA transform and estimated by performing coefficient shrinkage in the PCA domain to remove the noise. The proposed method exploits the optimal energy compaction property of PCA on groups of similar patches in the least squares sense. The performance of our approach is experimentally verified on a variety of synthetic images at various noise levels, and on real world noisy images. Our proposed method achieves very competitive denoising performance, especially in preserving the fine image structures, compared with many existing denoising algorithms with respect to both objective measurement and visual evaluation. We also show that our proposed method is computationally more efficient than other local PCA based methods.

Compressive sensing (CS) can reduce the number of data transmissions and balance the traffic load throughout networks. However, the total number of data transmissions required in CS method is still large. It is observed that there are many zero elements in the measurement matrix. In each round of data transmission in CS method, the sensor nodes corresponding to the zero elements in the measurement matrix do not have their own data to transmit. To further reduce the number of data transmissions in the network, we aim to compute a data gathering tree by taking advantages of these zero elements in the measurement matrix, such that the total number of data transmissions is minimized. We formulate the problem as linear programming with boolean variables. The problem is NP-hard. We propose heuristic algorithm to compute the Minimum Transmission Tree (MTT) for data gathering in CS methods. The MTT algorithm constructs a spanning tree by iteratively including the edge whose average incremental transmission cost is minimum. The simulation results demonstrate that our algorithm can reduce the number of transmissions significantly, compared with the methods using minimum spanning tree (MST), shortest path tree and the CS method with nonzero measurement coefficient using MST.

Towards practical implementation of the compressed sensing framework for multi-element synthetic transmit aperture imaging

Compressive sensing (CS) is a promising technology for realizing energy-efficient wireless sensors for long-term health monitoring. However, conventional model-driven CS frameworks suffer from limited compression ratio and reconstruction quality when dealing with physiological signals due to inaccurate models and the overlook of individual variability. In this paper, we propose a data-driven CS framework that can learn signal characteristics and personalized features from any individual recording of physiologic signals to enhance CS performance with a minimized number of measurements. Such improvements are accomplished by a co-training approach that optimizes the sensing matrix and the dictionary towards improved restricted isometry property and signal sparsity, respectively. Experimental results upon ECG signals show that the proposed method, at a compression ratio of 10x, successfully reduces the isometry constant of the trained sensing matrices by 86% against random matrices and improves the overall reconstructed signal-to-noise ratio by 15dB over conventional model-driven approaches.

MRI currently is the most powerful medical diagnostic tomography system. It provides high resolution with high detail medical image. Its magnetization sensing is also free from radiation impact hence safe for the patient. However, the data acquisition process takes quite a long time with high-rate sampling. The sensing patient should stay still in the MRI sensing device for 20 to 40 minutes. It can affect claustrophobia for some patients. The high-rate sampling will also linearly affect the cost, which is considerably high. Hence, the research on enabling under-sampling MRI imaging has been raised. The main objective of under-sampling MRI Imaging is reducing the scanning time by under-sampling the data acquisition while at the same time the resulting qualified reconstructed image can be maintained. Compressive Sensing (CS) framework is one of the approaches that can be utilized on solving projection with less measurement. It can recover signals which have sparsity property. The signal is sparse if the signal being sensed has low information rate. Thus, the framework of Compressive Sensing matches under-sampling MRI Imaging. The sparsity requirement is closely related to the design of sensing matrix and dictionary on the Compressive Sensing framework. This paper presents analysis of two proposed sensing matrix designs for Under-sampling MRI Imaging: square sensing matrix and sorting-based sensing matrix designs. The proposed sensing matrix design is intended to appropriately sample the data measurement on certain sampling rate in frequency domain to maintain the quality of the reconstructed MRI image closely to the ground truth (full sampling MRI Imaging). The simulations show that both proposed sensing matrix designs are able to conduct under-sampling MRI Imaging for at least at 40% sampling rate with average of PSNR 27.72 and 33.07 respectively subject to the ground truth.

We demonstrate a method to build signal dependent sparse representation dictionary for neural action potentials using K-SVD algorithm and Discrete Wavelets Transform. We also show a method to utilize this dictionary to recover the neural signal in the Compressive Sensing (CS) framework. Comparing against the non-signal dependent CS recovery algorithms, this new recovery algorithm can achieve same reconstruction quality with 2.5 times less compressed sensing measurements. For the same compression ratio, the purposed approach can increase recovery signal's signal to noise and distortion ratio (SNDR) by around 6 dB compare to non-signal dependent recovery method. We also evaluated the recovered signal using spike sorting techniques. The results have shown that the spikes clusters still maintain clear separation even when the compression ratio is at 15-20% of the Nyquist rate. This work also implies that any hardware implementation of compressed sensing could be scaled down in term of power and chip area by the same order if this signal dependent framework is used to recover the signal.

We present an algorithm for denoising of videos corrupted by additive i.i.d. zero mean Gaussian noise with a fixed and known standard deviation. Our algorithm is patch-based. Given a patch from a frame in the video, the algorithm collects similar patches from the same and adjacent frames. All the patches in this group are denoised using a transform-based approach that involves hard thresholding of insignificant coefficients. In this paper, the transform chosen is the higher order singular value decomposition of the group of similar patches. This procedure is repeated across the entire video in sliding window fashion. We present results on a well-known database of eight video sequences. The results demonstrate the ability of our method to preserve fine textures. Moreover we demonstrate that our algorithm, which is entirely driven by patch-similarity, can produce mean-squared error results which are comparable to those produced by state of the art techniques such as [1], as also methods such as [2] that explicitly use motion estimation before denoising.

Functional near- infrared spectroscopy (fNIRS) as an emerging optical neuroimaging technique has attracted the interest and attention of many investigators. With the growth of fNIRS data volume, effective data compression methods are urgent. Compressive sensing (CS) has been demonstrated a promising tool to deal with biomedical data. However, whether the compressibility of fNIRS data can discriminate different brain states is unclear. In this study, the fNIRS signals from fifteen attention-deficit/hyperactivity disorder (ADHD) children and fifteen typically developing (TD) children were recorded during an N-back task and a Go/NoGo task respectively. A block sparse Bayesian learning-based CS method was used to reconstruct the compressed fNIRS data. To assess the performance of the CS method, we adopted two metrics, structural similarity index (SSIM) and mean squared error (MSE), both of them effective in evaluating the compressibility of fNIRS data. Then, the two metrics were analyzed to discriminate the brain states of ADHD children and TD children during the two tasks using the multivariate pattern analysis (MVPA) method. As indicated by the results, the CS method could reconstruct the compressed fNIRS data with a high reconstruction quality at different compression ratio ([Formula: see text] and [Formula: see text]). Furthermore, the MVPA method could distinguish different brain states with high accuracy, and identify that the prefrontal cortex is a key brain region for distinguishing ADHD vs. TD or N-back vs. Go/NoGo. These findings indicated that CS is very promising for the storage and transmission of massive fNIRS data, and the compressibility of fNIRS data is a potential biomarker for the diagnosis of ADHD.

Recently, multimedia has developed and become very important for transferring images securely through public networks. This paper uses the COOT optimization algorithm with compressive sensing (CS) for image encryption. A good method was proposed for encryption using compressive sensing with COOT optimization and chaos to encrypt images and obtain optimal encryption with the least correlation between pixels. This method will strengthen the encryption against various types of attacks. The natural image was sparsed using discreet wavelet transform (DWT) and the FAN transform. The image is divided into several blocks, and CS is applied to each block. The best measurement matrix was obtained using a COOT-optimized algorithm. All blocks are masked to get the compressed image, and the pixels are quantified. Next, the COOT optimization is used to Shuffle the image pixels to achieve the minimum correlation between the pixels. Then, a logistic map will be used to uniform the image pixel values by diffusion to get the final encrypted image. Chen’s chaotic and logistic map initial values are obtained from the input image after its division into four parts by taking a value from each part. The evaluation results obtained for this algorithm showed that it performs highly compared to other conventional methods. The average PSNR for the reconstructed images was 35.244, the average NPCR and UACI were 90.53 and 29.54, respectively, and the average correlation was (D = 0.0018, V = 0.0031, H = 0.0039). The results proved that the method is strong enough and very efficient to withstand attacks.

With the aim of developing a fast yet accurate algorithm for compressive sensing (CS) reconstruction of natural images, we combine in this paper the merits of two existing categories of CS methods: the structure insights of traditional optimization-based methods and the speed of recent network-based ones. Specifically, we propose a novel structured deep network, dubbed ISTA-Net, which is inspired by the Iterative Shrinkage-Thresholding Algorithm (ISTA) for optimizing a general $$ norm CS reconstruction model. To cast ISTA into deep network form, we develop an effective strategy to solve the proximal mapping associated with the sparsity-inducing regularizer using nonlinear transforms. All the parameters in ISTA-Net (e.g. nonlinear transforms, shrinkage thresholds, step sizes, etc.) are learned end-to-end, rather than being hand-crafted. Moreover, considering that the residuals of natural images are more compressible, an enhanced version of ISTA-Net in the residual domain, dubbed ISTA-Net+, is derived to further improve CS reconstruction. Extensive CS experiments demonstrate that the proposed ISTA-Nets outperform existing state-of-the-art optimization-based and network-based CS methods by large margins, while maintaining fast computational speed. Our source codes are available: http://jianzhang.tech/projects/ISTA-Net.

In compressive sensing (CS), a challenge is to find a space in which the signal is sparse and, hence, faithfully recoverable. Since many natural signals such as images have locally varying statistics, the sparse space varies in time/spatial domain. As such, CS recovery should be conducted in locally adaptive signal-dependent spaces to counter the fact that the CS measurements are global and irrespective of signal structures. On the contrary, existing CS reconstruction methods use a fixed set of bases (e.g., wavelets, DCT, and gradient spaces) for the entirety of a signal. To rectify this problem, we propose a new framework for model-guided adaptive recovery of compressive sensing (MARX) and show how a 2-D piecewise autoregressive model can be integrated into the MARX framework to make CS recovery adaptive to spatially varying second order statistics of an image. In addition, MARX offers a mechanism of characterizing and exploiting structured sparsities of natural images, greatly restricting the CS solution space. Simulation results over a wide range of natural images show that the proposed MARX technique can improve the reconstruction quality of existing CS methods by 2-7 dB.

Compressive sensing (CS) theory proves that signals can be recovered from far fewer random measurements than that suggested by Nyquist-Shannon theorem. This advantage of CS is extremely useful in some data processing applications, especially in video processing. Considering that nonlocal patch-based CS methodology has achieved an impressive performance in image CS field, it motivates us to generalize the idea into the video CS filed. In this paper, by taking account of the spatiotemporal information, we propose a novel strategy to reconstruct the non-key frames of a video sequence by introducing the nonlocal similar patch group from some key frames. Experimental results illustrate that our proposed nonlocal patch-based video CS recovery algorithm can extremely exploit the information of the key frames, and achieve a better performance compared with some existing popular video CS recovery algorithms. It is noted that our idea to construct a spatiotemporal comprehensive patch group may be combined with any nonlocal patch-based CS method for video reconstruction, which leads to various of nonlocal patch-based compressive sensing video recovery algorithms.

Compressive sampling (CS) aims at acquiring a signal at a sampling rate below the Nyquist rate by exploiting prior knowledge that a signal is sparse or correlated in some domain. Despite the remarkable progress in the theory of CS, the sampling rate on a single image required by CS is still very high in practice. In this paper, a non-local compressive sampling (NLCS) recovery method is proposed to further reduce the sampling rate by exploiting non-local patch correlation and local piecewise smoothness present in natural images. Two non-local sparsity measures, i.e., non-local wavelet sparsity and non-local joint sparsity, are proposed to exploit the patch correlation in NLCS. An efficient iterative algorithm is developed to solve the NLCS recovery problem, which is shown to have stable convergence behavior in experiments. The experimental results show that our NLCS significantly improves the state-of-the-art of image compressive sampling.

A review of the most recent contributions in the framework of Compressive Sensing (CS) strategies as applied to Electromagnetics is presented in this work. Towards this end, the CS fundamentals are firstly discussed in the light of their impact in Electromagnetics technologies. A set of CS applicative scenarios is then discussed, taking into account problems coming from antenna array design and diagnosis, direction-of-arrival estimation, and microwave imaging. An assessment of the effectiveness and potentialities of CS techniques in Electromagnetics is provided by selected numerical examples.