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
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
By making use of multiple acquisitions of synthetic aperture radar(SAR) observations over the same area, tomographic-SAR(tomo-SAR) technology can achieve three-dimensional(3-D) imaging of the objects of interest. The ...By making use of multiple acquisitions of synthetic aperture radar(SAR) observations over the same area, tomographic-SAR(tomo-SAR) technology can achieve three-dimensional(3-D) imaging of the objects of interest. The compressive sensing(CS) approach has been applied to deal with the sparseness of the elevation signals.Due to its sparsity and convexity, the L1-norm regularization, as an approximated L0-norm with an exact solution,has been employed in CS to reconstruct the reflectivity profile of the objects. In this paper, based on our studies on polarimetric scattering and SAR imaging simulations, we produce numerical multi-pass tomo-SAR observations of the terrain object. Then, we present the CS with novel L1/2-norm regularization to realize 3-D reconstruction. As a non-convex optimization problem, the L1/2-norm regularization is solved by an iterative algorithm. This numerical simulation of tomo-SAR imaging and 3-D reconstruction of the object modeling can be of great help for parameterized analysis of tomo-SAR imagery. As an example, a tomo-SAR image and 3-D reconstruction of the Beijing National Stadium model are presented.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.
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By making use of multiple acquisitions of synthetic aperture radar(SAR) observations over the same area, tomographic-SAR(tomo-SAR) technology can achieve three-dimensional(3-D) imaging of the objects of interest. The compressive sensing(CS) approach has been applied to deal with the sparseness of the elevation signals.Due to its sparsity and convexity, the L1-norm regularization, as an approximated L0-norm with an exact solution,has been employed in CS to reconstruct the reflectivity profile of the objects. In this paper, based on our studies on polarimetric scattering and SAR imaging simulations, we produce numerical multi-pass tomo-SAR observations of the terrain object. Then, we present the CS with novel L1/2-norm regularization to realize 3-D reconstruction. As a non-convex optimization problem, the L1/2-norm regularization is solved by an iterative algorithm. This numerical simulation of tomo-SAR imaging and 3-D reconstruction of the object modeling can be of great help for parameterized analysis of tomo-SAR imagery. As an example, a tomo-SAR image and 3-D reconstruction of the Beijing National Stadium model are presented.
