Compressive Sensing Algorithm Research Articles

Efficient gridless 2D DOA estimation based on generalized matrix‐form atomic norm minimization

AbstractTwo‐dimensional (2D) direction‐of‐arrival (DOA) estimation is crucial in array signal processing. Compressed sensing (CS) provides a superior alternative to spatial spectrum estimation algorithms by enabling 2D DOA estimation of correlated sources from single snapshot data. However, the grid mismatch effect inherent in grid‐based CS algorithms impacts estimation accuracy. Despite recent advancements, the state‐of‐the‐art gridless CS algorithm, decoupled atomic norm minimization, is limited to specific 2D array geometries, such as uniform rectangular arrays. This letter presents an efficient gridless 2D DOA estimation algorithm for generalized rectangular arrays, including both uniform and sparse arrays. The proposed algorithm achieves high accuracy through a novel approach called generalized matrix‐form atomic norm minimization and provides a fast solution using the alternating direction method of multipliers. Validation through computer simulations and practical experiments underscores its efficacy.

Iterative Adaptive Based Multi-Polarimetric SAR Tomography of the Forested Areas

Synthetic aperture radar tomography (TomoSAR) is an extension of synthetic aperture radar (SAR) imaging. It introduces the synthetic aperture principle into the elevation direction to achieve three-dimensional (3-D) reconstruction of the observed target. Compressive sensing (CS) is a favorable technology for sparse elevation recovery. However, for the non-sparse elevation distribution of the forested areas, if CS is selected to reconstruct it, it is necessary to utilize some orthogonal bases to first represent the elevation reflectivity sparsely. The iterative adaptive approach (IAA) is a non-parametric algorithm that enables super-resolution reconstruction with minimal snapshots, eliminates the need for hyperparameter optimization, and requires fewer iterations. This paper introduces IAA to tomographicinversion of the forested areas and proposes a novel multi-polarimetric-channel joint 3-D imaging method. The proposed method relies on the characteristics of the consistent support of the elevation distribution of different polarimetric channels and uses the L2-norm to constrain the IAA-based 3-D reconstruction of each polarimetric channel. Compared with typical spectral estimation (SE)-based algorithms, the proposed method suppresses the elevation sidelobes and ambiguity and, hence, improves the quality of the recovered 3-D image. Compared with the wavelet-based CS algorithm, it reduces computational cost and avoids the influence of orthogonal basis selection. In addition, in comparison to the IAA, it demonstrates greater accuracy in identifying the support of the elevation distribution in forested areas. Experimental results based on BioSAR 2008 data are used to validate the proposed method.

Weighted Compressive Sensing Applied to Seismic Interferometry: Wavefield Reconstruction Using Prior Information

Abstract Seismic interferometry is widely used for passive subsurface investigation using seismic noise. The technique requires much storage for long noise records to suppress interferometric noise, which consists of spurious arrivals that do not correspond to the inter-receiver surface waves. Such long recordings may not be available in practice. Compressive sensing (CS), which is a wavefield reconstruction technique operating on incomplete data, may increase the availability, and reduce storage limitations of long noise time series. Using a numerical example of a linear array surrounded by sources and the Fourier basis for a sparse transform, we show that inter-receiver wavefields can be recovered at the locations where seismometers are unavailable, reducing the storage required for interferometry. We propose and develop a weighted CS algorithm that helps suppress the spurious arrivals by incorporating a priori information about the arrivals of surface waves that can be expected.

Fresnel incoherent compressive holography toward 3D videography via dual-channel simultaneous phase-shifting interferometry.

Fresnel incoherent correlation holography (FINCH) enables high-resolution 3D imaging of objects from several 2D holograms under incoherent light and has many attractive applications in motionless 3D fluorescence imaging. However, FINCH has difficulty implementing 3D imaging of dynamic scenes since multiple phase-shifting holograms need to be recorded for removing the bias term and twin image in the reconstructed scene, which requires the object to remain static during this progress. Here, we propose a dual-channel Fresnel noncoherent compressive holography method. First, a pair of holograms with π phase shifts obtained in a single shot are used for removing the bias term noise. Then, a physic-driven compressive sensing (CS) algorithm is used to achieve twin-image-free reconstruction. In addition, we analyze the reconstruction effect and suitability of the CS algorithm and two-step phase-shift filtering algorithm for objects with different complexities. The experimental results show that the proposed method can record hologram videos of 3D dynamic objects and scenes without sacrificing the imaging field of view or resolution. Moreover, the system refocuses images at arbitrary depth positions via computation, hence providing a new method for fast high-throughput incoherent 3D imaging.

An Off-Grid Compressive Sensing Algorithm Based on Sparse Bayesian Learning for RFPA Radar

In the application of Compressive Sensing (CS) theory for sidelobe suppression in Random Frequency and Pulse Repetition Interval Agile (RFPA) radar, the off−grid issues affect the performance of target parameter estimation in RFPA radar. Therefore, to address this issue, this paper presents an off−grid CS algorithm named Refinement and Generalized Double Pareto (GDP) distribution based on Sparse Bayesian Learning (RGDP−SBL) for RFPA radar that utilizes a coarse−to−fine grid refinement approach, allowing precise and cost−effective signal recovery while mitigating the impact of off−grid issues on target parameter estimation. To obtain a high-precision signal recovery, especially in scenarios involving closely spaced targets, the RGDP−SBL algorithm makes use of a three−level hierarchical prior model. Furthermore, the RGDP−SBL algorithm efficiently utilizes diagonal elements during the coarse search and exploits the convexity of the grid energy curve during the fine search, therefore significantly reducing computational complexity. Simulation results demonstrate that the RGDP−SBL algorithm significantly improves signal recovery performance while maintaining low computational complexity in multiple scenarios for RFPA radar.

A Lightweight Recurrent Learning Network for Sustainable Compressed Sensing

Recently, deep learning-based compressed sensing (CS) has achieved great success in reducing the sampling and computational cost of sensing systems and improving the reconstruction quality. These approaches, however, largely overlook the issue of the computational cost; they rely on complex structures and task-specific operator designs, resulting in extensive storage and high energy consumption in CS imaging systems. In this article, we propose a lightweight but effective deep neural network based on recurrent learning to achieve a sustainable CS system; it requires a smaller number of parameters but obtains high-quality reconstructions. Specifically, our proposed network consists of an initial reconstruction sub-network and a residual reconstruction sub-network. While the initial reconstruction sub-network has a hierarchical structure to progressively recover the image, reducing the number of parameters, the residual reconstruction sub-network facilitates recurrent residual feature extraction via recurrent learning to perform both feature fusion and deep reconstructions across different scales. In addition, we also demonstrate that, after the initial reconstruction, feature maps with reduced sizes are sufficient to recover the residual information, and thus we achieved a significant reduction in the amount of memory required. Extensive experiments illustrate that our proposed model can achieve a better reconstruction quality than existing state-of-the-art CS algorithms, and it also has a smaller number of network parameters than these algorithms. Our source codes are available at: <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/C66YU/CSRN</uri> .

AdaCS: Adaptive Compressive Sensing with Restricted Isometry Property-Based Error-clamping.

Scene-dependent adaptive compressive sensing (CS) has been a long pursuing goal that has huge potential to significantly improve the performance of CS. However, with no access to the ground truth, how to design the scene-dependent adaptive strategy is still an open problem. In this paper, a restricted isometry property (RIP) condition-based error-clamping is proposed, which could directly predict the reconstruction error, i.e., the difference between the current-stage reconstructed image and the ground truth image, and adaptively allocate more samples to regions with larger reconstruction error at the next sampling stage. Furthermore, we propose a CS reconstruction network composed of Progressively inverse transform and Alternating Bi-directional Multi-grid Network, named PiABM-Net, that could efficiently utilize the multi-scale information for reconstructing the target image. The effectiveness of the proposed adaptive and cascaded CS method is demonstrated with extensive quantitative and qualitative experiments, compared with the state-of-the-art CS algorithms.

A fast threshold OMP based on self-learning dictionary for propeller signal reconstruction

The acquisition of propeller signals can be applied to localization and fault diagnosis, etc. However, recording a large amount of propeller signals results in higher costs. Compressive sensing (CS) is an effective approach to processing large data. CS algorithms work well for sparse signals, but propeller signals are non-sparse in both the time and frequency domains. Therefore, the traditional fixed dictionary, such as discrete cosine transform (DCT), has a limited sparse representation of propeller signals. We propose a self-learning dictionary in this study, the self-learning dictionary uses the propeller signal as input to train the dictionary, and the trained dictionary can be stored and used for sparse representation of propeller signals. Based on the self-learning dictionary, we propose a threshold orthogonal matching pursuit based on QR decomposition (TOMP-QR) algorithm. We use the ratio of two energy thresholds as the stopping condition of the TOMP-QR algorithm, which is more robust under arbitrary noise. Then, we use QR decomposition to reduce the complexity of the algorithm. The simulation results verify the effectiveness of the proposed method in signal reconstruction accuracy and running time. Based on DCT, discrete wavelet transform (DWT) and self-learning dictionary, we compare the TOMP-QR algorithm with TOMP, OMP, sparsity adaptive matching pursuit (SAMP) and stage wise OMP (StOMP) algorithm to reconstruct propeller signals in the experiment, the results show that the effectiveness and superiority of the self-learning dictionary and TOMP-QR algorithm.

Orthogonalization of the Sensing Matrix Through Dominant Columns in Compressive Sensing for Speech Enhancement

This paper introduces a novel speech enhancement approach called dominant columns group orthogonalization of the sensing matrix (DCGOSM) in compressive sensing (CS). DCGOSM optimizes the sensing matrix using particle swarm optimization (PSO), ensuring separate basis vectors for speech and noise signals. By utilizing an orthogonal matching pursuit (OMP) based CS signal reconstruction with this optimized matrix, noise components are effectively avoided, resulting in lower noise in the reconstructed signal. The reconstruction process is accelerated by iterating only through the known speech-contributing columns. DCGOSM is evaluated against various noise types using speech quality measures such as SNR, SSNR, STOI, and PESQ. Compared to other OMP-based CS algorithms and deep neural network (DNN)-based speech enhancement techniques, DCGOSM demonstrates significant improvements, with maximum enhancements of 42.54%, 62.97%, 27.48%, and 8.72% for SNR, SSNR, PESQ, and STOI, respectively. Additionally, DCGOSM outperforms DNN-based techniques by 20.32% for PESQ and 8.29% for STOI. Furthermore, it reduces recovery time by at least 13.2% compared to other OMP-based CS algorithms.

Sparse Signal Recovery through Long Short-Term Memory Networks for Compressive Sensing-Based Speech Enhancement

This paper presents a novel speech enhancement approach based on compressive sensing (CS) which uses long short-term memory (LSTM) networks for the simultaneous recovery and enhancement of the compressed speech signals. The advantage of this algorithm is that it does not require an iterative process to recover the compressed signals, which makes the recovery process fast and straight forward. Furthermore, the proposed approach does not require prior knowledge of signal and noise statistical properties for sensing matrix optimization because the used LSTM can directly extract and learn the required information from the training data. The proposed technique is evaluated against white, babble, and f-16 noises. To validate the effectiveness of the proposed approach, perceptual evaluation of speech quality (PESQ), short-time objective intelligibility (STOI), and signal-to-distortion ratio (SDR) were compared to other variants of OMP-based CS algorithms The experimental outcomes show that the proposed approach achieves the maximum improvements of 50.06%, 43.65%, and 374.16% for PESQ, STOI, and SDR respectively, over the different variants of OMP-based CS algorithms.

FECG compressed sensing mode based on joint block sparsity

The development of medical Internet of Things technology has enabled the rise of telemedicine. For medical signals, real-time transmission, accuracy of signals and portability of equipment are required to be strict. The telemedicine system based on Compressed Sensing (CS) technology can avoid sampling a large number of redundant information, and reduce the complexity of data processing and computing time. However, the performance of existing Compressed Sensing algorithms in processing and reconstructing medical signals is poor. It is difficult to meet the strict requirements. In this paper, the sparse representation method which is most suitable for Fetal Electrocardiogram (FECG) signals is obtained by comparison experiment. And a Logistics-Tent Sine Bernoulli Measurement Matrix (LTSBM) construction algorithm is proposed for more convenient hardware applications. Based on the characteristics of FECG signals, a Joint Block Multiple Orthogonal Least Squares (JBMOLS) algorithm is proposed to improve the reconstruction performance in this paper. Combined with the above algorithms, the FECG compressed sensing mode is constituted, which is used to improve the compression, sampling and reconstruction performance of FECG signals. The experimental results show that, compared with traditional compressed sensing technology, the FECG compressed sensing mode improves the overall signal reconstruction performance, the running time is greatly reduced, and the practicability is stronger.

Multi-beam X-ray optical system for high-speed tomography using a σ-polarization diffraction geometry

A multi-beam X-ray optical system using a σ-polarization diffraction geometry is proposed and its potential for high-speed tomography using synchrotron radiation is experimentally evaluated. Projection images of a sample are obtained simultaneously from different directions with X-ray beams generated by diffraction of a white synchrotron radiation beam at silicon single crystals. This makes it possible to record a tomographic dataset without rotation of the sample or X-ray source. Data sets of two samples obtained in a proof-of-principle experiment with an exposure time of 1 ms were successfully reconstructed using an advanced compressed-sensing algorithm.

Compressive sensing of ultrasonic array data with full matrix capture in nozzle welds inspection

The phased array ultrasonic technique (PAUT) with full matrix capture (FMC) exhibits the advantages of high imaging accuracy and great defect characterization ability, which play important roles in the nondestructive testing of welded structures. To address the problem of a large amount of signal acquisition, storage, and transmission data in nozzle weld defect monitoring, a PAUT with an FMC data compression method based on compressive sensing (CS) was proposed. To accomplish this, the detection of nozzle welds using PAUT with FMC was performed by simulation and experiment, and the obtained FMC data were compressed and reconstructed. A suitable sparse representation was found dedicated to the FMC data of nozzle welds, and the reconstruction performance was compared between the greedy theory-based orthogonal matching pursuit (OMP) algorithm and the convex optimization theory-based basis pursuit (BP). Also, an empirical mode decomposition (EMD)-based intrinsic mode function (IMF) circular matrix was constructed to provide another idea for the construction of the sensing matrix. Although the experimental results were not able to reach the ideal effect in the simulation, the image was restored accurately with a small number of measured values, and flaw identification could be guaranteed, indicating that the CS algorithm can effectively improve the defect detection efficiency of the phased array.

Preface

The 2nd International Conference on Electronics and Integrated Circuit Technology (EICT 2023) was held in Chengdu, China from February 24th to 26th, 2023 (virtual conference). The first workshop of the series was held in Shenzhen in virtual form last year. The purpose of EICT 2023 was to discuss the present status and future perspectives of the electronics and integrated circuit technology. The following five topics were selected in order to cover most of the scientific program and highlight an area where new ideas have emerged over recent years:(1) Electronic Science and Technology;(2) Integrated Circuit Design and Integrated System;(3) Electronic Materials and Devices;(4) Digital Information Processing;(5) Magneto-electronic Materials and Applications, etc.There were about 60 participants. In addition to the keynote speeches, we had many talks selected from contributed papers. There were invited, oral, and poster sessions. This proceedings contains the papers presented in invited and selected talks together with those presented in poster sessions.At the Conference, the participants discussed a wide range of issues affecting the theoretical and computational aspects of research problems in the electronics and integrated circuit technology. Besides, we had a comprehensive overview of this fascinating field and of future scenarios thanks to the participation of leaders of the most important projects. Associate Professor Cheng Zhang from Anhui University, China performed a keynote speech and shared with us his own research experience and professional view with the report Compressed Sensing and Deep Learning for Optical Imaging. Compressive Sensing (CS) provides an innovative sampling framework based on the rate of information of a signal rather than the bandwidth, which enables efficient data sampling at a rate much below the Shannon Nyquist rate, thereby minimizing redundancy during sampling. The emerging of Deep Learning (DL) naturally complements the practical limitations with the CS sampling and reconstruction algorithms and provides a powerful framework to address the most practical limitations to achieve higher-accuracy reconstructions from extremely fewer measurements by adapting the sampling matrix, reconstructing the signal, learning from the compressed samples, etc.We wish to acknowledge our host institutions, sponsors, and the many people whose work made this Conference possible. We would like to express our gratitude to the members of the Technical Program Committee and those of the Organizing Committee for their efforts which made this Workshop successful. In particular we would like to present our great thanks to the editors and other colleagues of Journal of Physics: Conference Series for their patience and kind assistance in publishing this paper volume.The Committee of EICT 2023.List of Committee Member is available in the pdf.

Deep Learning-Based Soft Iterative-Detection of Channel-Coded Compressed Sensing-Aided Multi-Dimensional Index Modulation

The concept of Index Modulation (IM) has been actively researched as a benefit of its flexible trade-off between performance, achievable rate, energy efficiency, hardware cost and complexity. In order to fully exploit its the degrees of freedom, the concept of Multi-dimensional IM (MIM) has been developed in literature, where Compressed Sensing (CS) is often utilized to exploit the sparsity of the multi-dimensional transmitted signals. However, this flexibility and performance gains are attained at the cost of a substantially increased detection complexity. In this paper, we propose Deep Learning (DL) based detection for CS-aided MIM (CS-MIM), where both Hard-Decision (HD) as well as Soft-Decision (SD) detection combined with iterative decoding are conceived. More explicitly, firstly, we propose learning aided hard and soft detection for CS-MIM. Secondly, two novel neural network aided methods are proposed for Iterative Soft Detection (ISD), where iterations are carried out between the CS-MIM detector and a channel decoder. In contrast to the conventional detection of CS-MIM system, which critically relies on the knowledge of Channel State Information (CSI) at the receiver, the proposed learning-aided methods are capable of eliminating the overhead and complexity of Channel Estimation (CE), which results in an improved transmission rate. Explicitly, we develop an advanced DL architecture for blind-detection-aided MIM for the first time in the open literature, where the HD and SD CS algorithms are implemented by learning without the need for CE. Our simulation results demonstrate that the proposed learning techniques conceived for SD CS-MIM combined with iterative detection are capable of achieving near-capacity performance at a reduced complexity compared to the conventional model-based SD relying on CSI acquisition.

Deep Learning-Based Channel Estimation for Wideband Hybrid MmWave Massive MIMO

Hybrid analog-digital (HAD) architecture is widely adopted in practical millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems to reduce hardware cost and energy consumption. However, channel estimation in the context of HAD is challenging due to only limited radio frequency (RF) chains at transceivers. Although various compressive sensing (CS) algorithms have been developed to solve this problem by exploiting inherent channel sparsity and sparsity structures, practical effects, such as power leakage and beam squint, can still make the real channel features deviate from the assumed models and result in performance degradation. Besides, the high complexity of CS algorithms caused by a large number of iterations hinders their applications in practice. To tackle these issues, we develop a deep learning (DL)-based channel estimation approach where the sparse Bayesian learning (SBL) algorithm is unfolded into a deep neural network (DNN). In each SBL layer, Gaussian variance parameters of the sparse angular domain channel are updated by a tailored DNN, which is able to capture complicated channel sparsity structures in various domains effectively and efficiently. The measurement matrix is jointly optimized for performance improvement. Then, the proposed approach is extended to the multi-block case where channel correlation in time is further exploited to adaptively predict the measurement matrix and facilitate the update of variance parameters. Simulation results show that the proposed approaches outperform existing approaches in terms of both performance and complexity.

Feasibility of accelerated non-contrast-enhanced whole-heart bSSFP coronary MR angiography by deep learning-constrained compressed sensing.

To examine a compressed sensing artificial intelligence (CSAI) framework to accelerate image acquisition in non-contrast-enhanced whole-heart bSSFP coronary magnetic resonance (MR) angiography. Thirty healthy volunteers and 20 patients with suspected coronary artery disease (CAD) scheduled for coronary computed tomography angiography (CCTA) were enrolled. Non-contrast-enhanced coronary MR angiography was performed with CSAI, compressed sensing (CS), and sensitivity encoding (SENSE) methods in healthy participants and with CSAI in patients. Acquisition time, subjective image quality score, and objective image quality measurement (blood pool homogeneity, signal-to-noise ratio [SNR], and contrast-to-noise ratio [CNR]) were compared among the three protocols. The diagnostic performance of CASI coronary MR angiography for predicting significant stenosis (≥ 50% diameter stenosis) on CCTA was evaluated. The Friedman test was performed to compare the three protocols. Acquisition time was significantly shorter in the CSAI and CS groups than in the SENSE group (10.2 ± 3.2min vs. 10.9 ± 2.9min vs. 13.0 ± 4.1min, p < 0.001). However, the CSAI approach had the highest image quality scores, blood pool homogeneity, mean SNR value, and mean CNR value (all p < 0.001) compared with the CS and SENSE approaches. The sensitivity, specificity, and accuracy of CSAI coronary MR angiography per patient were 87.5% (7/8), 91.7% (11/12), and 90.0% (18/20); those per vessel were 81.8% (9/11), 93.9% (46/49), and 91.7% (55/60); and those per segment were 84.6% (11/13), 98.0% (244/249), and 97.3% (255/262), respectively. CSAI yielded superior image quality within a clinically feasible acquisition time in healthy participants and patients with suspected CAD. The non-invasive and radiation-free CSAI framework could be a promising tool for rapid screening and comprehensive examination of the coronary vasculature in patients with suspected CAD. • This prospective study showed that CSAI enables a reduction in acquisition time by 22% with superior diagnostic image quality compared with the SENSE protocol. • CSAI replaces the wavelet transform with a CNN as a sparsifying transform in the CS algorithm, achieving high coronary MR image quality with reduced noise. • CSAI achieved per-patient sensitivity of 87.5% (7/8) and specificity of 91.7% (11/12) respectively for detecting significant coronary stenosis.

Survey on compressed sensing over the past two decades

Compressed Sensing (CS) is a novel data acquisition theorem exploiting the signals sparsity differing from traditional Nyquist theorem in the ability of obtaining all information of such signal in fewer samples. CS can enable full use of sparsity, where the sparse signal can be reconstructed using fewer measurements. Over the past decade, several papers have investigated the feasibility of deploying CS in current applications. A lot of developments are performed in this area in order to enhance the performance and re-usability. The CS algorithm involves many phases at the transmitter side, including: transformation, compression, encoding, encryption, and modulation. Meanwhile the receiver involves: demodulation, decryption, decoding, and reconstruction. This work assembles most of the published papers in the CS area, listing the important details and showing their contributions. Each building block of the CS system is studied solely and compared with its reference in the literature. A comparative study is performed reviewing the work in the literature with respect to compression metrics, deployed reconstruction algorithm, system complexity. Tabulated results are studied with respect to hardware and memory computation complexity. Recommendations and conclusions are illustrated at the end of our work.

Quantitative, Spectro-kinetic Analysis of Oxygen in Electron-Beam Sensitive, Multimetallic Oxide Nanostructures.

The oxygen stoichiometry of hollandite, KxMnO2-δ, nanorods has been accurately determined from a quantitative analysis of scanning-transmission electron microscopy (STEM) X-Ray Energy Dispersive Spectroscopy (XEDS) experiments carried out in chrono-spectroscopy mode. A methodology combining 3D reconstructions of high-angle annular dark field electron tomography experiments, using compressed-sensing algorithms, and quantification through the so-called ζ-factors method of XEDS spectra recorded on a high-sensitivity detector has been devised to determine the time evolution of the oxygen content of nanostructures of electron-beam sensitive oxides. Kinetic modeling of O-stoichiometry data provided K0.13MnO1.98 as overall composition for nanorods of the hollandite. The quantitative agreement, within a 1% mol error, observed with results obtained by macroscopic techniques (temperature-programmed reduction and neutron diffraction) validate the proposed methodology for the quantitative analysis, at the nanoscale, of light elements, as it is the case of oxygen, in the presence of heavy ones (K, Mn) in the highly compromised case of nanostructured materials which are prone to electron-beam reduction. Moreover, quantitative comparison of oxygen evolution data measured at macroscopic and nanoscopic levels allowed us to rationalize beam damage effects in structural terms and clarify the exact nature of the different steps involved in the reduction of these oxides with hydrogen.

A novel block compressive sensing algorithm for SAR image formation

Compressive Sensing (CS) theory has been used for Synthetic Aperture Radar (SAR) imaging due to the sparsity feature of SAR images. Therefore, some well-known CS algorithms like Orthogonal Matching Pursuit (OMP) and Regularized OMP (ROMP) methods have been employed for SAR image formation with a very small number of samples. On the other hand, it has been shown that the SAR signal is consistent with the definition of block sparsity. Hence, compressive sensing methods employing block structure, known as Block Compressive Sensing (BCS), are presented and used for SAR image formation to achieve more accuracy with a smaller number of samples. In this paper, first, a new BCS-based algorithm, namely, Block Norm Regularized Orthogonal Matching Pursuit (BNROMP), is introduced which can be used in all BCS applications. Then, this novel method is used for SAR image formation to achieve more accuracy and excellent resolution with a small number of samples. The simulation results for the synthesized data, as well as real data, show that by using the novel BNROMP method, we could form SAR images with higher quality, as compared to those for the standard image formation algorithms and other CS-SAR or BCS-SAR methods.