Model-based Compressed Sensing Research Articles

Reconstructing Human Pose From Inertial Measurements: A Generative Model-Based Compressive Sensing Approach

Reconstructing Human Pose From Inertial Measurements: A Generative Model-Based Compressive Sensing Approach

Improved Image Compressive Sensing Recovery with Low-Rank Prior and Deep Image Prior

Compressive sensing (CS) aims to recover images with rich and accurate information from a small amount of sampled data. Due to its ill-posedness, the model-based CS method has been widely used ever. In recent years, with the development of the arisen learning-based method, enormous progress has been made in combining learning-based strategy with traditional methods. However, at a low sampling ratio, most such methods tend to over-suppress image information, making the recovered results less satisfactory. In order to push the limits of image CS recovery, we propose a novel non-convex low-rank(NCLR) prior by utilizing weighted Schatten p-norm as a surrogate function of the rank function in low-rank approximation. We then provide a new NCLR-based CS model for image CS recovery by plugging the deep prior as a modular part. In addition, we present an efficient iterated algorithm to solve the proposed model by using the alternating direction method of multiplier (ADMM). Further, the convergence of the proposed method is also illustrated. Extensive experimental results demonstrate that our method achieves good performance in both quantity evaluation and visual perception compared to the existing image CS recovery methods, especially at a low sampling ratio.

Using Graph Signal Processing in Model-Based Compressive Sensing of MRI Brain Image

Using Graph Signal Processing in Model-Based Compressive Sensing of MRI Brain Image

Learning-Based Split Unfolding Framework for 3-D mmW Radar Sparse Imaging

The application of the compressed sensing (CS) method in the radar field enables the radar imaging system to satisfy both low data cost and high reconstruction quality, however, it is accompanied by enormous iterative operations and difficult adjustments of parameters. In this paper, we propose a learning-based split unfolding framework, dubbed as split iterative sparse reconstruction network (SISR-Net), for near-field 3-D millimeter-wave (mmW) radar sparse imaging. Firstly, a sparse reconstruction algorithm, i.e., SISRA, is proposed to theoretically guide the structure of the imaging framework. Subsequently, by combining the model-based CS method and data-driven deep learning method, SISR-Net is constructed by SISRA to produce 3-D mmW radar images efficiently with excellent explainability and generalization ability. Joint the radar-imaging kernel, echo-generation kernel, and the split Bregman method, the efficiency and stability of SISR-Net are guaranteed, all parameters are layer-varied and learned steadily by end-to-end training to improve the convergence and robustness of the imaging network. Simulated data and the echo from a high-resolution mmW radar dataset 3DRIED, are used to train and test the SISR-Net based on the Adam optimizer. For both simulation and extensive 3-D mmW radar measured experiments, the proposed SISR-Net outperforms other state-of-the-art imaging methods in terms of imaging accuracy and generalization ability.

RMIST-Net: Joint Range Migration and Sparse Reconstruction Network for 3-D mmW Imaging

Compressed sensing (CS) demonstrates significant potential to improve image quality in 3-D millimeter-wave imaging compared with conventional matched filtering (MF). However, existing sparsity-driven 3-D imaging algorithms always suffer from large-scale storage, excessive computational cost, and nontrivial tuning of parameters due to the huge-dimensional matrix–vector multiplication in complicated iterative optimization steps. In this article, we present a novel range migration (RM) kernel-based iterative-shrinkage thresholding network, dubbed as RMIST-Net, by combining the traditional model-based CS method and data-driven deep learning method for near-field 3-D millimeter-wave (mmW) sparse imaging. First, the measurement matrices in ISTA optimization steps are replaced by RM kernels, by which matrix–vector multiplication is converted to the Hadamard product. Then, the modified ISTA optimization is unrolled into a deep hierarchical architecture, in which all parameters are learned automatically instead of manually tuned. Subsequently, 1000 pairs of oracle images with randomly distributed targets and their corresponding echoes are simulated to train the network. A well-trained RMIST-Net produces high-quality 3-D images from range-focused echoes. Finally, we experimentally prove that RMIST-Net is capable process <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$512 \times 512$ </tex-math></inline-formula> large-scale imaging tasks within 1 s. Besides, we compare RMIST-Net with other state-of-the-art methods in near-field 3-D imaging applications. Both simulations and real-measured experiments demonstrate that RMIST-Net produces impressive reconstruction performance while maintaining high computational speed compared with conventional and sparse imaging algorithms.

Proximal-Gen for fast compressed sensing recovery

Compressed sensing (CS) can recover an image from a few random measurements by exploiting the sparsity assumption on the structure of images. Some recent generative model-based CS recovery methods have removed the sparsity constraint, but their recovery process is slow and the recovered signal is constrained to be in the generator range. Here, we propose a new framework, called Proximal-Gen, for CS recovery. Specifically, we first formulate a general domain of the recovered signals, this allows the subsequent recovery algorithms to recover the signals that deviate from the generator range. Then based on the general domain, we develop a fast recovery algorithm, which mainly consists of two sub-algorithms, namely network-based projected gradient descent (NPGD) and denoiser-based proximal gradient descent (DPGD). The NPGD is used to obtain an intermediate signal lying in the generator range, while the DPGD is proposed to recover a deviation signal. Compared with multiple recent generative model-based recovery methods, our method can achieve better reconstruction performance and higher efficiency under most measurements.

Efficient COVID-19 testing via contextual model based compressive sensing

The COVID-19 pandemic is threatening billions of people's life all over the world. As of March 6, 2021, covid-19 has confirmed in 115,653,459 people worldwide. It has also a devastating effect on businesses and social activities. Since there is still no definite cure for this disease, extensive testing is the most critical issue to determine the trend of illness, appropriate medical treatment, and make social distancing policies. Besides, testing more people in a shorter time helps to contain the contagion. The PCR-based methods are the most popular tests which take about an hour to make the output result. Obviously, it makes the number of tests highly limited and consequently, hurts the efficiency of pandemic control. In this paper, we propose a new approach to identify affected individuals with a considerably reduced No. of tests. Intuitively, saving time and resources is the main advantage of our approach. We use contextual information to make a graph-based model to be used in model-based compressive sensing (CS). Our proposed model makes the testing with fewer tests required compared to traditional testing methods and even group testing. We embed contextual information such as age, underlying disease, symptoms (i.e. cough, fever, fatigue, loss of consciousness), and social contacts into a graph-based model. This model is used in model-based CS to minimize the required test. We take advantage of Discrete Graph Signal Processing on Graph (DSPG) to generate the model. Our contextual model makes CS more efficient in both the number of samples and the recovery quality. Moreover, it can be applied in the case that group testing is not applicable due to its severe dependency on sparsity. Experimental results show that the overall testing speed (individuals per test ratio) increases more than 15 times compared to the individual testing with the error of less than 5% which is dramatically lower than that of traditional compressive sensing.

ADMM-CSNet: A Deep Learning Approach for Image Compressive Sensing.

Compressive sensing (CS) is an effective technique for reconstructing image from a small amount of sampled data. It has been widely applied in medical imaging, remote sensing, image compression, etc. In this paper, we propose two versions of a novel deep learning architecture, dubbed as ADMM-CSNet, by combining the traditional model-based CS method and data-driven deep learning method for image reconstruction from sparsely sampled measurements. We first consider a generalized CS model for image reconstruction with undetermined regularizations in undetermined transform domains, and then two efficient solvers using Alternating Direction Method of Multipliers (ADMM) algorithm for optimizing the model are proposed. We further unroll and generalize the ADMM algorithm to be two deep architectures, in which all parameters of the CS model and the ADMM algorithm are discriminatively learned by end-to-end training. For both applications of fast CS complex-valued MR imaging and CS imaging of real-valued natural images, the proposed ADMM-CSNet achieved favorable reconstruction accuracy in fast computational speed compared with the traditional and the other deep learning methods.

Model-Based Compressive Sensing Applied to Landmine Detection by GPR

Model-Based Compressive Sensing Applied to Landmine Detection by GPR

Approximation Algorithms for Model-Based Compressive Sensing

Compressive sensing (CS) states that a sparse signal can be recovered from a small number of linear measurements, and that this recovery can be performed efficiently in polynomial time. The framework of model-based CS (model-CS) leverages additional structure in the signal and provides new recovery schemes that can reduce the number of measurements even further. This idea has led to measurement-efficient recovery schemes for a variety of signal models. However, for any given model, model-CS requires an algorithm that solves the model-projection problem: given a query signal, report the signal in the model that is closest to the query signal. Often, this optimization can be computationally very expensive. Moreover, an approximation algorithm is not sufficient for this optimization to provably succeed. As a result, the model-projection problem poses a fundamental obstacle for extending model-CS to many interesting classes of models. In this paper, we introduce a new framework that we call approximation-tolerant model-CS. This framework includes a range of algorithms for sparse recovery that require only approximate solutions for the model-projection problem. In essence, our work removes the aforementioned obstacle to model-CS, thereby extending model-CS to a much wider class of signal models. Interestingly, all our algorithms involve both the minimization and the maximization variants of the model-projection problem. We instantiate this new framework for a new signal model that we call the constrained earth mover distance (CEMD) model. This model is particularly useful for signal ensembles, where the positions of the nonzero coefficients do not change significantly as a function of spatial (or temporal) location. We develop novel approximation algorithms for both the maximization and the minimization versions of the model-projection problem via graph optimization techniques. Leveraging these algorithms and our framework results in a nearly sample-optimal sparse recovery scheme for the CEMD model.

Quantization Noise on Image Reconstruction Using Model-Based Compressive Sensing

The Compressive Sensing (CS) allows the acquisition of signals already compressed and the posterior reconstruction with much less number of measures than the minimum required by the Nyquist theorem. A subarea of CS which improves the performance at the reconstruction stage is named Model-Based CS. Some works have been developed within this subarea. However, most of them consider only the noise generated by sparse approximation, disregarding the noise generated by the quantization stage and its influence on efficiency and robustness of CS. The objective of this study is to investigate the influence of the noise generated by the quantization stage in Model-Based CS efficiency for images with different levels of sparsity and different distributions of coefficients in the frequency domain. In this work, the image acquisition stage is implemented using the partial Fourier matrix which results in a vector of measures. Then, different steps of uniform scalar quantization are added to this vector and the image reconstruction stage is performed using the Compressive Sampling Matching Pursuit (CoSaMP) on a quadtree model. PSNR and bits rate (BR) are then used to evaluate the efficiency of CoSaMP with quantization noise. The performance of this proposed Model-Based CS using different quantization steps were slightly better than other studies using the same model in terms of PSNR, but with the advantage of obtaining smaller values of bit rate (BR maior que 2 bpp).

Compressed sensing based channel estimation used in non-sample-spaced multipath channels of OFDM system

By virtue of an increase in spectral efficiency by reducing the transmitted pilot tones, the compressed sensing (CS) has been widely applied to pilot-aided sparse channel estimation in orthogonal frequency division multiplexing (OFDM) systems. The researches usually assume that the channel is strictly sparse and formulate the channel estimation as a standard compressed sensing problem. However, such strictly sparse assumption does not hold true in non-sample-spaced multiple channels. The authors in this article proposed a new method of compressed sensing based channel estimation in which an over-complete dictionary with a finer delay grid is applied to construct a sparse representation of the non-sample-spaced multipath channels. With the proposed, the channel estimation was formulated as the model-based CS problem and a modified model-based compressed sampling matching pursuit (CoSaMP) algorithm was applied to reconstruct the discrete-time channel impulse response (CIR). Simulation indicates that the new method proposed here outperforms the traditional standard CS-based methods in terms of mean square error (MSE) and bit error rate (BER).

Generalized Alternating Projection for Weighted-$\ell_{2,1}$ Minimization with Applications to Model-Based Compressive Sensing

We consider the group basis pursuit problem, which extends basis pursuit by replacing the $\ell_{1}$ norm with a weighted-$\ell_{2,1}$ norm. We provide an anytime algorithm, called generalized alternating projection (GAP), to solve this problem. The GAP algorithm extends classical alternating projection to the case in which projections are performed between convex sets that undergo a systematic sequence of changes. We prove that, under a set of group-restricted isometry property (group-RIP) conditions, the reconstruction error of GAP monotonically converges to zero. Thus the algorithm can be interrupted at any time to return a valid solution and can be resumed subsequently to improve the solution. This anytime convergence property saves iterations on retracting and correcting mistakes, which, along with an effective acceleration scheme, makes GAP converge fast. Moreover, the per-iteration computation is inexpensive, consisting of sorting of a linear array followed by groupwise thresholding and linear transform of vectors for which fast algorithms often exist. We evaluate the algorithmic performance through extensive experiments in which GAP is compared to other state-of-the-art algorithms and applied to compressive sensing of natural images and video.

Room Reverberation Reconstruction: Interpolation of the Early Part Using Compressed Sensing

This paper deals with the interpolation of the Room Impulse Responses (RIRs) within a whole volume, from as few measurements as possible, and without the knowledge of the geometry of the room. We focus on the early reflections of the RIRs, that have the key property of being sparse in the time domain: this can be exploited in a framework of model-based Compressed Sensing. Starting from a set of RIRs randomly sampled in the spatial domain of interest by a 3D microphone array, we propose a modified Matching Pursuit algorithm to estimate the position of a small set of virtual sources. Then, the reconstruction of the RIRs at interpolated positions is performed using a projection onto a basis of monopoles, which correspond to the estimated virtual sources. An extension of the proposed algorithm allows the interpolation of the positions of both source and receiver, using the acquisition of four different source positions. This approach is validated both by numerical examples, and by experimental measurements using a 3D array with up to 120 microphones.

Accelerated 3D MERGE carotid imaging using compressed sensing with a hidden markov tree model

To determine the potential for accelerated 3D carotid magnetic resonance imaging (MRI) using wavelet based compressed sensing (CS) with a hidden Markov tree (HMT) model. We retrospectively applied HMT model-based CS and conventional CS to 3D carotid MRI data with 0.7 mm isotropic resolution from six subjects with known carotid stenosis (12 carotids). We applied a wavelet-tree model learned from a training database of carotid images to improve CS reconstruction. Quantitative endpoints such as lumen area, wall area, mean and maximum wall thickness, plaque calcification, and necrotic core area were measured and compared using Bland-Altman analysis along with image quality. Rate-4.5 acceleration with HMT model-based CS provided image quality comparable to that of rate-3 acceleration with conventional CS and fully sampled reference reconstructions. Morphological measurements made on rate-4.5 HMT model-based CS reconstructions were in good agreement with measurements made on fully sampled reference images. There was no significant bias or correlation between mean and difference of measurements when comparing rate 4.5 HMT model-based CS with fully sampled reference images. HMT model-based CS can potentially be used to accelerate clinical carotid MRI by a factor of 4.5 without impacting diagnostic quality or quantitative endpoints.

Wavelet-Based Compressed Sensing Using a Gaussian Scale Mixture Model

While initial compressed sensing (CS) recovery techniques operated under the implicit assumption that the sparse domain coefficients are independently distributed, recent results have indicated that integrating a statistical or structural dependence model of sparse domain coefficients into CS enhances recovery. In this paper, we present a method for exploiting empirical dependences among wavelet coefficients during CS recovery using a Bayes least-square Gaussian-scale-mixture model. The proposed model is successfully incorporated into several recent CS algorithms, including reweighted l(1) minimization (RL1), iteratively reweighted least squares, and iterative hard thresholding. Extensive experiments including comparisons with a state-of-the-art model-based CS method demonstrate that the proposed algorithms are highly effective at reducing reconstruction error and/or the number of measurements required for a desired reconstruction quality.

Model-Based Compressive Sensing

Compressive sensing (CS) is an alternative to Shannon/Nyquist sampling for the acquisition of sparse or compressible signals that can be well approximated by just K << N elements from an N-dimensional basis. Instead of taking periodic samples, CS measures inner products with M < N random vectors and then recovers the signal via a sparsity-seeking optimization or greedy algorithm. Standard CS dictates that robust signal recovery is possible from M = O(K log(N/K)) measurements. It is possible to substantially decrease M without sacrificing robustness by leveraging more realistic signal models that go beyond simple sparsity and compressibility by including structural dependencies between the values and locations of the signal coefficients. This paper introduces a model-based CS theory that parallels the conventional theory and provides concrete guidelines on how to create model-based recovery algorithms with provable performance guarantees. A highlight is the introduction of a new class of structured compressible signals along with a new sufficient condition for robust structured compressible signal recovery that we dub the restricted amplification property, which is the natural counterpart to the restricted isometry property of conventional CS. Two examples integrate two relevant signal models - wavelet trees and block sparsity - into two state-of-the-art CS recovery algorithms and prove that they offer robust recovery from just M=O(K) measurements. Extensive numerical simulations demonstrate the validity and applicability of our new theory and algorithms.