This paper explores the recovery of block sparse signals in frame-based settings using the l_(2)/l_(q)-synthesis technique(0<q≤1).We propose a new null space property,referred to as block D-NSP_(q),which is based ...This paper explores the recovery of block sparse signals in frame-based settings using the l_(2)/l_(q)-synthesis technique(0<q≤1).We propose a new null space property,referred to as block D-NSP_(q),which is based on the dictionary D.We establish that matrices adhering to the block D-NSP_(q)condition are both necessary and sufficient for the exact recovery of block sparse signals via l_(2)/l_(q)-synthesis.Additionally,this condition is essential for the stable recovery of signals that are block-compressible with respect to D.This D-NSP_(q)property is identified as the first complete condition for successful signal recovery using l_(2)/l_(q)-synthesis.Furthermore,we assess the theoretical efficacy of the l2/lq-synthesis method under conditions of measurement noise.展开更多
A joint two-dimensional(2D)direction-of-arrival(DOA)and radial Doppler frequency estimation method for the L-shaped array is proposed in this paper based on the compressive sensing(CS)framework.Revised from the conven...A joint two-dimensional(2D)direction-of-arrival(DOA)and radial Doppler frequency estimation method for the L-shaped array is proposed in this paper based on the compressive sensing(CS)framework.Revised from the conventional CS-based methods where the joint spatial-temporal parameters are characterized in one large scale matrix,three smaller scale matrices with independent azimuth,elevation and Doppler frequency are introduced adopting a separable observation model.Afterwards,the estimation is achieved by L1-norm minimization and the Bayesian CS algorithm.In addition,under the L-shaped array topology,the azimuth and elevation are separated yet coupled to the same radial Doppler frequency.Hence,the pair matching problem is solved with the aid of the radial Doppler frequency.Finally,numerical simulations corroborate the feasibility and validity of the proposed algorithm.展开更多
A sparsifying transform for use in Compressed Sensing (CS) is a vital piece of image reconstruction for Magnetic Resonance Imaging (MRI). Previously, Translation Invariant Wavelet Transforms (TIWT) have been shown to ...A sparsifying transform for use in Compressed Sensing (CS) is a vital piece of image reconstruction for Magnetic Resonance Imaging (MRI). Previously, Translation Invariant Wavelet Transforms (TIWT) have been shown to perform exceedingly well in CS by reducing repetitive line pattern image artifacts that may be observed when using orthogonal wavelets. To further establish its validity as a good sparsifying transform, the TIWT is comprehensively investigated and compared with Total Variation (TV), using six under-sampling patterns through simulation. Both trajectory and random mask based under-sampling of MRI data are reconstructed to demonstrate a comprehensive coverage of tests. Notably, the TIWT in CS reconstruction performs well for all varieties of under-sampling patterns tested, even for cases where TV does not improve the mean squared error. This improved Image Quality (IQ) gives confidence in applying this transform to more CS applications which will contribute to an even greater speed-up of a CS MRI scan. High vs low resolution time of flight MRI CS re-constructions are also analyzed showing how partial Fourier acquisitions must be carefully addressed in CS to prevent loss of IQ. In the spirit of reproducible research, novel software is introduced here as FastTestCS. It is a helpful tool to quickly develop and perform tests with many CS customizations. Easy integration and testing for the TIWT and TV minimization are exemplified. Simulations of 3D MRI datasets are shown to be efficiently distributed as a scalable solution for large studies. Comparisons in reconstruction computation time are made between the Wavelab toolbox and Gnu Scientific Library in FastTestCS that show a significant time savings factor of 60×. The addition of FastTestCS is proven to be a fast, flexible, portable and reproducible simulation aid for CS research.展开更多
The traditional compressed sensing method for improving resolution is realized in the frequency domain.This method is aff ected by noise,which limits the signal-to-noise ratio and resolution,resulting in poor inversio...The traditional compressed sensing method for improving resolution is realized in the frequency domain.This method is aff ected by noise,which limits the signal-to-noise ratio and resolution,resulting in poor inversion.To solve this problem,we improved the objective function that extends the frequency domain to the Gaussian frequency domain having denoising and smoothing characteristics.Moreover,the reconstruction of the sparse refl ection coeffi cient is implemented by the mixed L1_L2 norm algorithm,which converts the L0 norm problem into an L1 norm problem.Additionally,a fast threshold iterative algorithm is introduced to speed up convergence and the conjugate gradient algorithm is used to achieve debiasing for eliminating the threshold constraint and amplitude error.The model test indicates that the proposed method is superior to the conventional OMP and BPDN methods.It not only has better denoising and smoothing eff ects but also improves the recognition accuracy of thin interbeds.The actual data application also shows that the new method can eff ectively expand the seismic frequency band and improve seismic data resolution,so the method is conducive to the identifi cation of thin interbeds for beach-bar sand reservoirs.展开更多
Tomographic synthetic aperture radar(TomoSAR)imaging exploits the antenna array measurements taken at different elevation aperture to recover the reflectivity function along the elevation direction.In these years,for ...Tomographic synthetic aperture radar(TomoSAR)imaging exploits the antenna array measurements taken at different elevation aperture to recover the reflectivity function along the elevation direction.In these years,for the sparse elevation distribution,compressive sensing(CS)is a developed favorable technique for the high-resolution elevation reconstruction in TomoSAR by solving an L_(1) regularization problem.However,because the elevation distribution in the forested area is nonsparse,if we want to use CS in the recovery,some basis,such as wavelet,should be exploited in the sparse L_(1/2) representation of the elevation reflectivity function.This paper presents a novel wavelet-based L_(2) regularization CS-TomoSAR imaging method of the forested area.In the proposed method,we first construct a wavelet basis,which can sparsely represent the elevation reflectivity function of the forested area,and then reconstruct the elevation distribution by using the L_(1/2) regularization technique.Compared to the wavelet-based L_(1) regularization TomoSAR imaging,the proposed method can improve the elevation recovered quality efficiently.展开更多
A hybrid Compressed Sensing and Primal-Dual Wavelet(CSP-PDW)technique is proposed for the compression and reconstruction of ECG signals.The compression and reconstruction algorithms are implemented using four key conc...A hybrid Compressed Sensing and Primal-Dual Wavelet(CSP-PDW)technique is proposed for the compression and reconstruction of ECG signals.The compression and reconstruction algorithms are implemented using four key concepts:Sparsifying Basis,Restricted Isometry Principle,Gaussian Random Matrix,and Convex Minimization.In addition to the conventional compression sensing reconstruction approach,wavelet-based processing is employed to enhance reconstruction efficiency.A mathematical model of the proposed algorithm is derived analytically to obtain the essential parameters of compression sensing,including the sparsifying basis,measurement matrix size,and number of iterations required for reconstructing the original signal and determining the type and level of wavelet processing.The low time complexity of the proposed algorithm makes it an ideal candidate for ECG monitoring systems in IoT-based e-healthcare applications.A feature extraction algorithm is also developed to show that the important ECG peaks remain unaltered after reconstruction.The clinical relevance of the reconstructed signal and the efficiency of the developed algorithm are evaluated using four validation parameters at three different compression ratios.展开更多
Compressive sensing(CS)is an emerging methodology in computational signal processing that has recently attracted intensive research activities.At present,the basic CS theory includes recoverability and stability:the f...Compressive sensing(CS)is an emerging methodology in computational signal processing that has recently attracted intensive research activities.At present,the basic CS theory includes recoverability and stability:the former quantifies the central fact that a sparse signal of length n can be exactly recovered from far fewer than n measurements via l1-minimization or other recovery techniques,while the latter specifies the stability of a recovery technique in the presence of measurement errors and inexact sparsity.So far,most analyses in CS rely heavily on the Restricted Isometry Property(RIP)for matrices.In this paper,we present an alternative,non-RIP analysis for CS via l1-minimization.Our purpose is three-fold:(a)to introduce an elementary and RIP-free treatment of the basic CS theory;(b)to extend the current recoverability and stability results so that prior knowledge can be utilized to enhance recovery via l1-minimization;and(c)to substantiate a property called uniform recoverability of l1-minimization;that is,for almost all random measurement matrices recoverability is asymptotically identical.With the aid of two classic results,the non-RIP approach enables us to quickly derive from scratch all basic results for the extended theory.展开更多
Recently, the 1-bit compressive sensing （1-bit CS） has been studied in the field of sparse signal recovery. Since the amplitude information of sparse signals in 1-bit CS is not available, it is often the support or ...Recently, the 1-bit compressive sensing （1-bit CS） has been studied in the field of sparse signal recovery. Since the amplitude information of sparse signals in 1-bit CS is not available, it is often the support or the sign of a signal that can be exactly recovered with a decoding method. We first show that a necessary assumption （that has been overlooked in the literature） should be made for some existing theories and discussions for 1-bit CS. Without such an assumption, the found solution by some existing decoding algorithms might be inconsistent with 1-bit measurements. This motivates us to pursue a new direction to develop uniform and nonuniform recovery theories for 1-bit CS with a new decoding method which always generates a solution consistent with 1-bit measurements. We focus on an extreme case of 1-bit CS, in which the measurements capture only the sign of the product of a sensing matrix and a signal. We show that the 1-bit CS model can be reformulated equivalently as an t0-minimization problem with linear constraints. This reformulation naturally leads to a new linear-program-based decoding method, referred to as the 1-bit basis pursuit, which is remarkably different from existing formulations. It turns out that the uniqueness condition for the solution of the 1-bit basis pursuit yields the so-called restricted range space property （RRSP） of the transposed sensing matrix. This concept provides a basis to develop sign recovery conditions for sparse signals through 1-bit measurements. We prove that if the sign of a sparse signal can be exactly recovered from 1-bit measurements with 1-bit basis pursuit, then the sensing matrix must admit a certain RRSP, and that if the sensing matrix admits a slightly enhanced RRSP, then the sign of a k-sparse signal can be exactly recovered with 1-bit basis pursuit.展开更多
The generalized l1 greedy algorithm was recently introduced and used to reconstruct medical images in computerized tomography in the compressed sensing framework via total variation minimization. Experimental results ...The generalized l1 greedy algorithm was recently introduced and used to reconstruct medical images in computerized tomography in the compressed sensing framework via total variation minimization. Experimental results showed that this algorithm is superior to the reweighted l1-minimization and l1 greedy algorithms in reconstructing these medical images. In this paper the effectiveness of the generalized l1 greedy algorithm in finding random sparse signals from underdetermined linear systems is investigated. A series of numerical experiments demonstrate that the generalized l1 greedy algorithm is superior to the reweighted l1-minimization and l1 greedy algorithms in the successful recovery of randomly generated Gaussian sparse signals from data generated by Gaussian random matrices. In particular, the generalized l1 greedy algorithm performs extraordinarily well in recovering random sparse signals with nonzero small entries. The stability of the generalized l1 greedy algorithm with respect to its parameters and the impact of noise on the recovery of Gaussian sparse signals are also studied.展开更多
An algorithmic framework, based on the difference of convex functions algorithm （D- CA）, is proposed for minimizing a class of concave sparse metrics for compressed sensing problems. The resulting algorithm iterates...An algorithmic framework, based on the difference of convex functions algorithm （D- CA）, is proposed for minimizing a class of concave sparse metrics for compressed sensing problems. The resulting algorithm iterates a sequence ofl1 minimization problems. An exact sparse recovery theory is established to show that the proposed framework always improves on the basis pursuit （l1 minimization） and inherits robustness from it. Numerical examples on success rates of sparse solution recovery illustrate further that, unlike most existing non-convex compressed sensing solvers in the literature, our method always out- performs basis pursuit, no matter how ill-conditioned the measurement matrix is. Moreover, the iterative l1 （ILl） algorithm lead by a wide margin the state-of-the-art algorithms on l1/2 and logarithimic minimizations in the strongly coherent （highly ill-conditioned） regime, despite the same objective functions. Last but not least, in the application of magnetic resonance imaging （MRI）, IL1 algorithm easily recovers the phantom image with just 7 line projections.展开更多
针对测距仪(distance measure equipment,DME)信号干扰L频段数字航空通信系统1(L-band digital aeronautical communication system 1,L-DACS1)正交频分复用(orthogonal frequency-division multiplexing,OFDM)接收机的问题,提出基于块...针对测距仪(distance measure equipment,DME)信号干扰L频段数字航空通信系统1(L-band digital aeronautical communication system 1,L-DACS1)正交频分复用(orthogonal frequency-division multiplexing,OFDM)接收机的问题,提出基于块稀疏贝叶斯学习边界优化(block sparsEbayesian learning-thEbound optimization,BSBL-BO)算法的DME脉冲干扰抑制方法。首先,利用OFDM接收机空子载波不传输有用信号的特点构造针对DME脉冲干扰信号的压缩感知模型;然后基于BSBL-BO算法重构DME脉冲干扰信号;最后在时域进行干扰消除。仿真结果表明,该方法比已有的脉冲干扰抑制方法具有更高的重构精度和更快的运算速度,进一步降低了OFDM接收机的误比特率,提高了L-DACS1系统前向链路传输性能。展开更多
Fixed-point continuation(FPC)is an approach,based on operator-splitting and continuation,for solving minimization problems with l1-regularization:min||x||1+uf(x).We investigate the application of this algorithm to com...Fixed-point continuation(FPC)is an approach,based on operator-splitting and continuation,for solving minimization problems with l1-regularization:min||x||1+uf(x).We investigate the application of this algorithm to compressed sensing signal recovery,in which f(x)=1/2||Ax-b||2M,A∈m×n and m≤n.In particular,we extend the original algorithm to obtain better practical results,derive appropriate choices for M and u under a given measurement model,and present numerical results for a variety of compressed sensing problems.The numerical results show that the performance of our algorithm compares favorably with that of several recently proposed algorithms.展开更多
This paper aims to meet the requirements of reducing the scanning time of magnetic resonance imaging （MRI）, accelerating MRI and reconstructing a high quality image from less acquisition data as much as possible. MR...This paper aims to meet the requirements of reducing the scanning time of magnetic resonance imaging （MRI）, accelerating MRI and reconstructing a high quality image from less acquisition data as much as possible. MRI method based on compressed sensing （CS） with multiple regularizations （two regularizations including total variation （TV） norm and L1 norm or three regularizations consisting of total variation, L1 norm and wavelet tree structure） is proposed in this paper, which is implemented by applying split augmented lagrangian shrinkage algorithm （SALSA）. To solve magnetic resonance image reconstruction problems with linear combinations of total variation and L1 norm, we utilized composite spht denoising （CSD） to split the original complex problem into TV norm and L1 norm regularization subproblems which were simple and easy to be solved respectively in this paper. The reconstructed image was obtained from the weighted average of solutions from two subprohlems in an iterative framework. Because each of the splitted subproblems can be regarded as MRI model based on CS with single regularization, and for solving the kind of model, split augmented lagrange algorithm has advantage over existing fast algorithm such as fast iterative shrinkage thresholding（FIST） and two step iterative shrinkage thresholding （TWIST） in convergence speed. Therefore, we proposed to adopt SALSA to solve the subproblems. Moreover, in order to solve magnetic resonance image reconstruction problems with linear combinations of total variation, L1 norm and wavelet tree structure, we can split the original problem into three subproblems in the same manner, which can be processed by existing iteration scheme. A great deal of experimental results show that the proposed methods can effectively reconstruct the original image. Compared with existing algorithms such as TVCMRI, RecPF, CSA, FCSA and WaTMRI, the proposed methods have greatly improved the quality of the reconstructed images and have better visual effect.展开更多
The use of frames is analyzed in Compressed Sensing (CS) through proofs and experiments. First, a new generalized Dictionary-Restricted Isometry Property (D-RIP) sparsity bound constant for CS is established. Second, ...The use of frames is analyzed in Compressed Sensing (CS) through proofs and experiments. First, a new generalized Dictionary-Restricted Isometry Property (D-RIP) sparsity bound constant for CS is established. Second, experiments with a tight frame to analyze sparsity and reconstruction quality using several signal and image types are shown. The constant is used in fulfilling the definition of D-RIP. It is proved that k-sparse signals can be reconstructed if by using a concise and transparent argument1. The approach could be extended to obtain other D-RIP bounds (i.e. ). Experiments contrast results of a Gabor tight frame with Total Variation minimization. In cases of practical interest, the use of a Gabor dictionary performs well when achieving a highly sparse representation and poorly when this sparsity is not achieved.展开更多
基金Supported by The Featured Innovation Projects of the General University of Guangdong Province(2023KTSCX096)The Special Projects in Key Areas of Guangdong Province(ZDZX1088)Research Team Project of Guangdong University of Education(2024KYCXTD018)。
文摘This paper explores the recovery of block sparse signals in frame-based settings using the l_(2)/l_(q)-synthesis technique(0<q≤1).We propose a new null space property,referred to as block D-NSP_(q),which is based on the dictionary D.We establish that matrices adhering to the block D-NSP_(q)condition are both necessary and sufficient for the exact recovery of block sparse signals via l_(2)/l_(q)-synthesis.Additionally,this condition is essential for the stable recovery of signals that are block-compressible with respect to D.This D-NSP_(q)property is identified as the first complete condition for successful signal recovery using l_(2)/l_(q)-synthesis.Furthermore,we assess the theoretical efficacy of the l2/lq-synthesis method under conditions of measurement noise.
文摘A joint two-dimensional(2D)direction-of-arrival(DOA)and radial Doppler frequency estimation method for the L-shaped array is proposed in this paper based on the compressive sensing(CS)framework.Revised from the conventional CS-based methods where the joint spatial-temporal parameters are characterized in one large scale matrix,three smaller scale matrices with independent azimuth,elevation and Doppler frequency are introduced adopting a separable observation model.Afterwards,the estimation is achieved by L1-norm minimization and the Bayesian CS algorithm.In addition,under the L-shaped array topology,the azimuth and elevation are separated yet coupled to the same radial Doppler frequency.Hence,the pair matching problem is solved with the aid of the radial Doppler frequency.Finally,numerical simulations corroborate the feasibility and validity of the proposed algorithm.
文摘A sparsifying transform for use in Compressed Sensing (CS) is a vital piece of image reconstruction for Magnetic Resonance Imaging (MRI). Previously, Translation Invariant Wavelet Transforms (TIWT) have been shown to perform exceedingly well in CS by reducing repetitive line pattern image artifacts that may be observed when using orthogonal wavelets. To further establish its validity as a good sparsifying transform, the TIWT is comprehensively investigated and compared with Total Variation (TV), using six under-sampling patterns through simulation. Both trajectory and random mask based under-sampling of MRI data are reconstructed to demonstrate a comprehensive coverage of tests. Notably, the TIWT in CS reconstruction performs well for all varieties of under-sampling patterns tested, even for cases where TV does not improve the mean squared error. This improved Image Quality (IQ) gives confidence in applying this transform to more CS applications which will contribute to an even greater speed-up of a CS MRI scan. High vs low resolution time of flight MRI CS re-constructions are also analyzed showing how partial Fourier acquisitions must be carefully addressed in CS to prevent loss of IQ. In the spirit of reproducible research, novel software is introduced here as FastTestCS. It is a helpful tool to quickly develop and perform tests with many CS customizations. Easy integration and testing for the TIWT and TV minimization are exemplified. Simulations of 3D MRI datasets are shown to be efficiently distributed as a scalable solution for large studies. Comparisons in reconstruction computation time are made between the Wavelab toolbox and Gnu Scientific Library in FastTestCS that show a significant time savings factor of 60×. The addition of FastTestCS is proven to be a fast, flexible, portable and reproducible simulation aid for CS research.
基金National Science and Technology Major Project(No.2016ZX05006-002 and 2017ZX05072-001).
文摘The traditional compressed sensing method for improving resolution is realized in the frequency domain.This method is aff ected by noise,which limits the signal-to-noise ratio and resolution,resulting in poor inversion.To solve this problem,we improved the objective function that extends the frequency domain to the Gaussian frequency domain having denoising and smoothing characteristics.Moreover,the reconstruction of the sparse refl ection coeffi cient is implemented by the mixed L1_L2 norm algorithm,which converts the L0 norm problem into an L1 norm problem.Additionally,a fast threshold iterative algorithm is introduced to speed up convergence and the conjugate gradient algorithm is used to achieve debiasing for eliminating the threshold constraint and amplitude error.The model test indicates that the proposed method is superior to the conventional OMP and BPDN methods.It not only has better denoising and smoothing eff ects but also improves the recognition accuracy of thin interbeds.The actual data application also shows that the new method can eff ectively expand the seismic frequency band and improve seismic data resolution,so the method is conducive to the identifi cation of thin interbeds for beach-bar sand reservoirs.
基金This work was supported by the Fundamental Research Funds for the Central Universities(NE2020004)the National Natural Science Foundation of China(61901213)+3 种基金the Natural Science Foundation of Jiangsu Province(BK20190397)the Aeronautical Science Foundation of China(201920052001)the Young Science and Technology Talent Support Project of Jiangsu Science and Technology Associationthe Foundation of Graduate Innovation Center in Nanjing University of Aeronautics and Astronautics(kfjj20200419).
文摘Tomographic synthetic aperture radar(TomoSAR)imaging exploits the antenna array measurements taken at different elevation aperture to recover the reflectivity function along the elevation direction.In these years,for the sparse elevation distribution,compressive sensing(CS)is a developed favorable technique for the high-resolution elevation reconstruction in TomoSAR by solving an L_(1) regularization problem.However,because the elevation distribution in the forested area is nonsparse,if we want to use CS in the recovery,some basis,such as wavelet,should be exploited in the sparse L_(1/2) representation of the elevation reflectivity function.This paper presents a novel wavelet-based L_(2) regularization CS-TomoSAR imaging method of the forested area.In the proposed method,we first construct a wavelet basis,which can sparsely represent the elevation reflectivity function of the forested area,and then reconstruct the elevation distribution by using the L_(1/2) regularization technique.Compared to the wavelet-based L_(1) regularization TomoSAR imaging,the proposed method can improve the elevation recovered quality efficiently.
文摘A hybrid Compressed Sensing and Primal-Dual Wavelet(CSP-PDW)technique is proposed for the compression and reconstruction of ECG signals.The compression and reconstruction algorithms are implemented using four key concepts:Sparsifying Basis,Restricted Isometry Principle,Gaussian Random Matrix,and Convex Minimization.In addition to the conventional compression sensing reconstruction approach,wavelet-based processing is employed to enhance reconstruction efficiency.A mathematical model of the proposed algorithm is derived analytically to obtain the essential parameters of compression sensing,including the sparsifying basis,measurement matrix size,and number of iterations required for reconstructing the original signal and determining the type and level of wavelet processing.The low time complexity of the proposed algorithm makes it an ideal candidate for ECG monitoring systems in IoT-based e-healthcare applications.A feature extraction algorithm is also developed to show that the important ECG peaks remain unaltered after reconstruction.The clinical relevance of the reconstructed signal and the efficiency of the developed algorithm are evaluated using four validation parameters at three different compression ratios.
文摘Compressive sensing(CS)is an emerging methodology in computational signal processing that has recently attracted intensive research activities.At present,the basic CS theory includes recoverability and stability:the former quantifies the central fact that a sparse signal of length n can be exactly recovered from far fewer than n measurements via l1-minimization or other recovery techniques,while the latter specifies the stability of a recovery technique in the presence of measurement errors and inexact sparsity.So far,most analyses in CS rely heavily on the Restricted Isometry Property(RIP)for matrices.In this paper,we present an alternative,non-RIP analysis for CS via l1-minimization.Our purpose is three-fold:(a)to introduce an elementary and RIP-free treatment of the basic CS theory;(b)to extend the current recoverability and stability results so that prior knowledge can be utilized to enhance recovery via l1-minimization;and(c)to substantiate a property called uniform recoverability of l1-minimization;that is,for almost all random measurement matrices recoverability is asymptotically identical.With the aid of two classic results,the non-RIP approach enables us to quickly derive from scratch all basic results for the extended theory.
基金supported by the Engineering and Physical Sciences Research Council of UK (Grant No. #EP/K00946X/1)
文摘Recently, the 1-bit compressive sensing （1-bit CS） has been studied in the field of sparse signal recovery. Since the amplitude information of sparse signals in 1-bit CS is not available, it is often the support or the sign of a signal that can be exactly recovered with a decoding method. We first show that a necessary assumption （that has been overlooked in the literature） should be made for some existing theories and discussions for 1-bit CS. Without such an assumption, the found solution by some existing decoding algorithms might be inconsistent with 1-bit measurements. This motivates us to pursue a new direction to develop uniform and nonuniform recovery theories for 1-bit CS with a new decoding method which always generates a solution consistent with 1-bit measurements. We focus on an extreme case of 1-bit CS, in which the measurements capture only the sign of the product of a sensing matrix and a signal. We show that the 1-bit CS model can be reformulated equivalently as an t0-minimization problem with linear constraints. This reformulation naturally leads to a new linear-program-based decoding method, referred to as the 1-bit basis pursuit, which is remarkably different from existing formulations. It turns out that the uniqueness condition for the solution of the 1-bit basis pursuit yields the so-called restricted range space property （RRSP） of the transposed sensing matrix. This concept provides a basis to develop sign recovery conditions for sparse signals through 1-bit measurements. We prove that if the sign of a sparse signal can be exactly recovered from 1-bit measurements with 1-bit basis pursuit, then the sensing matrix must admit a certain RRSP, and that if the sensing matrix admits a slightly enhanced RRSP, then the sign of a k-sparse signal can be exactly recovered with 1-bit basis pursuit.
文摘The generalized l1 greedy algorithm was recently introduced and used to reconstruct medical images in computerized tomography in the compressed sensing framework via total variation minimization. Experimental results showed that this algorithm is superior to the reweighted l1-minimization and l1 greedy algorithms in reconstructing these medical images. In this paper the effectiveness of the generalized l1 greedy algorithm in finding random sparse signals from underdetermined linear systems is investigated. A series of numerical experiments demonstrate that the generalized l1 greedy algorithm is superior to the reweighted l1-minimization and l1 greedy algorithms in the successful recovery of randomly generated Gaussian sparse signals from data generated by Gaussian random matrices. In particular, the generalized l1 greedy algorithm performs extraordinarily well in recovering random sparse signals with nonzero small entries. The stability of the generalized l1 greedy algorithm with respect to its parameters and the impact of noise on the recovery of Gaussian sparse signals are also studied.
文摘An algorithmic framework, based on the difference of convex functions algorithm （D- CA）, is proposed for minimizing a class of concave sparse metrics for compressed sensing problems. The resulting algorithm iterates a sequence ofl1 minimization problems. An exact sparse recovery theory is established to show that the proposed framework always improves on the basis pursuit （l1 minimization） and inherits robustness from it. Numerical examples on success rates of sparse solution recovery illustrate further that, unlike most existing non-convex compressed sensing solvers in the literature, our method always out- performs basis pursuit, no matter how ill-conditioned the measurement matrix is. Moreover, the iterative l1 （ILl） algorithm lead by a wide margin the state-of-the-art algorithms on l1/2 and logarithimic minimizations in the strongly coherent （highly ill-conditioned） regime, despite the same objective functions. Last but not least, in the application of magnetic resonance imaging （MRI）, IL1 algorithm easily recovers the phantom image with just 7 line projections.
文摘针对测距仪(distance measure equipment,DME)信号干扰L频段数字航空通信系统1(L-band digital aeronautical communication system 1,L-DACS1)正交频分复用(orthogonal frequency-division multiplexing,OFDM)接收机的问题,提出基于块稀疏贝叶斯学习边界优化(block sparsEbayesian learning-thEbound optimization,BSBL-BO)算法的DME脉冲干扰抑制方法。首先,利用OFDM接收机空子载波不传输有用信号的特点构造针对DME脉冲干扰信号的压缩感知模型;然后基于BSBL-BO算法重构DME脉冲干扰信号;最后在时域进行干扰消除。仿真结果表明,该方法比已有的脉冲干扰抑制方法具有更高的重构精度和更快的运算速度,进一步降低了OFDM接收机的误比特率,提高了L-DACS1系统前向链路传输性能。
基金supported by an NSF VIGRE grant(DMS-0240058)supported in part by NSF CAREER Award DMS-0748839 and ONR Grant N00014-08-1-1101supported in part by NSF Grant DMS-0811188 and ONR Grant N00014-08-1-1101
文摘Fixed-point continuation(FPC)is an approach,based on operator-splitting and continuation,for solving minimization problems with l1-regularization:min||x||1+uf(x).We investigate the application of this algorithm to compressed sensing signal recovery,in which f(x)=1/2||Ax-b||2M,A∈m×n and m≤n.In particular,we extend the original algorithm to obtain better practical results,derive appropriate choices for M and u under a given measurement model,and present numerical results for a variety of compressed sensing problems.The numerical results show that the performance of our algorithm compares favorably with that of several recently proposed algorithms.
基金Natural Science Foundation of Chinagrant number:81371635+3 种基金Research Fund for the Doctoral Program of Higher Education of Chinagrant number:20120131110062Shandong Province Science and Technology Development Plangrant number:2013GGX10104
文摘This paper aims to meet the requirements of reducing the scanning time of magnetic resonance imaging （MRI）, accelerating MRI and reconstructing a high quality image from less acquisition data as much as possible. MRI method based on compressed sensing （CS） with multiple regularizations （two regularizations including total variation （TV） norm and L1 norm or three regularizations consisting of total variation, L1 norm and wavelet tree structure） is proposed in this paper, which is implemented by applying split augmented lagrangian shrinkage algorithm （SALSA）. To solve magnetic resonance image reconstruction problems with linear combinations of total variation and L1 norm, we utilized composite spht denoising （CSD） to split the original complex problem into TV norm and L1 norm regularization subproblems which were simple and easy to be solved respectively in this paper. The reconstructed image was obtained from the weighted average of solutions from two subprohlems in an iterative framework. Because each of the splitted subproblems can be regarded as MRI model based on CS with single regularization, and for solving the kind of model, split augmented lagrange algorithm has advantage over existing fast algorithm such as fast iterative shrinkage thresholding（FIST） and two step iterative shrinkage thresholding （TWIST） in convergence speed. Therefore, we proposed to adopt SALSA to solve the subproblems. Moreover, in order to solve magnetic resonance image reconstruction problems with linear combinations of total variation, L1 norm and wavelet tree structure, we can split the original problem into three subproblems in the same manner, which can be processed by existing iteration scheme. A great deal of experimental results show that the proposed methods can effectively reconstruct the original image. Compared with existing algorithms such as TVCMRI, RecPF, CSA, FCSA and WaTMRI, the proposed methods have greatly improved the quality of the reconstructed images and have better visual effect.
文摘The use of frames is analyzed in Compressed Sensing (CS) through proofs and experiments. First, a new generalized Dictionary-Restricted Isometry Property (D-RIP) sparsity bound constant for CS is established. Second, experiments with a tight frame to analyze sparsity and reconstruction quality using several signal and image types are shown. The constant is used in fulfilling the definition of D-RIP. It is proved that k-sparse signals can be reconstructed if by using a concise and transparent argument1. The approach could be extended to obtain other D-RIP bounds (i.e. ). Experiments contrast results of a Gabor tight frame with Total Variation minimization. In cases of practical interest, the use of a Gabor dictionary performs well when achieving a highly sparse representation and poorly when this sparsity is not achieved.
