Pub Date : 2024-10-11DOI: 10.1016/j.sigpro.2024.109738
Qiankun Diao , Dongpo Xu , Shuning Sun , Danilo P. Mandic
Recent advances in quaternion signal processing have drawn attention to the Quaternion Beamforming Problem (QBP). By leveraging appropriate relaxation techniques, QBP can be transformed into a constrained quaternion matrix optimization problem, aiming to develop a simple and effective solution. To this end, this paper first establishes a comprehensive theory of convex optimization for quaternion matrices based on the GHR calculus, covering quadratic upper bounds and projection theorems. In particular, we propose a quaternion projected gradient descent (QPGD) for constrained quaternion matrix optimization problems and prove the convergence of the QPGD algorithms, showing the monotonic decrease of the objective function. The numerical experiments verify the applicability and effectiveness of the QPGD algorithm in solving constrained quaternion matrices least squares problems in Frobenius norm and the quaternion beamforming problem.
{"title":"Optimizing beamforming in quaternion signal processing using projected gradient descent algorithm","authors":"Qiankun Diao , Dongpo Xu , Shuning Sun , Danilo P. Mandic","doi":"10.1016/j.sigpro.2024.109738","DOIUrl":"10.1016/j.sigpro.2024.109738","url":null,"abstract":"<div><div>Recent advances in quaternion signal processing have drawn attention to the Quaternion Beamforming Problem (QBP). By leveraging appropriate relaxation techniques, QBP can be transformed into a constrained quaternion matrix optimization problem, aiming to develop a simple and effective solution. To this end, this paper first establishes a comprehensive theory of convex optimization for quaternion matrices based on the GHR calculus, covering quadratic upper bounds and projection theorems. In particular, we propose a quaternion projected gradient descent (QPGD) for constrained quaternion matrix optimization problems and prove the convergence of the QPGD algorithms, showing the monotonic decrease of the objective function. The numerical experiments verify the applicability and effectiveness of the QPGD algorithm in solving constrained quaternion matrices least squares problems in Frobenius norm and the quaternion beamforming problem.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"227 ","pages":"Article 109738"},"PeriodicalIF":3.4,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-11DOI: 10.1016/j.sigpro.2024.109733
Hongxia Miao
Synchrosqueezing transforms have aroused great attention for its ability in time–frequency energy rearranging and signal reconstruction, which are post-processing techniques of the time–frequency distribution. However, the time–frequency distributions, such as short-time Fourier transform and short-time fractional Fourier transform, cannot change the shape of the time–frequency distribution. The linear canonical transform (LCT) can simultaneously rotate and scale the time–frequency distribution, which enlarges the distance between different signal components with proper parameters. In this study, a convolution-type short-time LCT is proposed to present the time–frequency distribution of a signal, from which the signal reconstruction formula is given. Its resolutions in time and LCT domains are demonstrated, which helps to select suitable window functions. A fast implementation algorithm for the short-time LCT is provided. Further, the synchrosqueezing LCT (SLCT) transform is designed by performing synchrosqueezing technique on the short-time LCT. The SLCT inherits many properties of the LCT, and the signal reconstruction formula is obtained from the SLCT. Adaptive selections of the parameter matrix of LCT and the length of the window function are introduced, thereby enabling proper compress direction and resolution of the signal. Finally, numerical experiments are presented to verify the efficiency of the SLCT.
{"title":"A novel synchrosqueezing transform associated with linear canonical transform","authors":"Hongxia Miao","doi":"10.1016/j.sigpro.2024.109733","DOIUrl":"10.1016/j.sigpro.2024.109733","url":null,"abstract":"<div><div>Synchrosqueezing transforms have aroused great attention for its ability in time–frequency energy rearranging and signal reconstruction, which are post-processing techniques of the time–frequency distribution. However, the time–frequency distributions, such as short-time Fourier transform and short-time fractional Fourier transform, cannot change the shape of the time–frequency distribution. The linear canonical transform (LCT) can simultaneously rotate and scale the time–frequency distribution, which enlarges the distance between different signal components with proper parameters. In this study, a convolution-type short-time LCT is proposed to present the time–frequency distribution of a signal, from which the signal reconstruction formula is given. Its resolutions in time and LCT domains are demonstrated, which helps to select suitable window functions. A fast implementation algorithm for the short-time LCT is provided. Further, the synchrosqueezing LCT (SLCT) transform is designed by performing synchrosqueezing technique on the short-time LCT. The SLCT inherits many properties of the LCT, and the signal reconstruction formula is obtained from the SLCT. Adaptive selections of the parameter matrix of LCT and the length of the window function are introduced, thereby enabling proper compress direction and resolution of the signal. Finally, numerical experiments are presented to verify the efficiency of the SLCT.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"227 ","pages":"Article 109733"},"PeriodicalIF":3.4,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142442297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-11DOI: 10.1016/j.sigpro.2024.109730
Jiaqi Wang, Bo Ou
Recently, the rapid development of reversible data hiding (RDH) for video copyright protection has attracted more attentions of academic community. In this paper, a local distortion-tolerance video RDH method is proposed to achieve a compensatory embedding on multiple blocks for a higher embedding efficiency. Specifically, the effect of distortion drift is calibrated in a local region rather than in the single block, and the performance enhancement is obtained by the reduction of distortion drift over the region. The distortion-tolerance vector is used to rank the blocks in the local region and the blocks being independent of the adjacent regions will have higher chance to be embedded with secret bits. Then, the coefficients are modified in a pairwise manner. Since only one coefficient in a pair is used for embedding, the other one can be modified symmetrically for compensation. The experimental results validate the effectiveness of the proposed method to decrease the intra-frame distortion drift, increase the capacity and minimize the bit rate increase.
{"title":"Video reversible data hiding: An evolution to local distortion-tolerance framework","authors":"Jiaqi Wang, Bo Ou","doi":"10.1016/j.sigpro.2024.109730","DOIUrl":"10.1016/j.sigpro.2024.109730","url":null,"abstract":"<div><div>Recently, the rapid development of reversible data hiding (RDH) for video copyright protection has attracted more attentions of academic community. In this paper, a local distortion-tolerance video RDH method is proposed to achieve a compensatory embedding on multiple blocks for a higher embedding efficiency. Specifically, the effect of distortion drift is calibrated in a local region rather than in the single block, and the performance enhancement is obtained by the reduction of distortion drift over the region. The distortion-tolerance vector is used to rank the blocks in the local region and the blocks being independent of the adjacent regions will have higher chance to be embedded with secret bits. Then, the coefficients are modified in a pairwise manner. Since only one coefficient in a pair is used for embedding, the other one can be modified symmetrically for compensation. The experimental results validate the effectiveness of the proposed method to decrease the intra-frame distortion drift, increase the capacity and minimize the bit rate increase.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"227 ","pages":"Article 109730"},"PeriodicalIF":3.4,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142442296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-11DOI: 10.1016/j.sigpro.2024.109731
Huagui Du, Jiahua Zhu, Yongping Song, Chongyi Fan, Xiaotao Huang
Moving target detection (MTD) is a research hotspot in radar signal processing. Generally, the time information of non-cooperative moving targets entering and leaving a radar coverage area is unknown, which would lead to severe performance loss for target parameter estimation, detection, and imaging. Unlike our previous research work, this paper addresses the motion parameters estimation and refocusing problem for a radar maneuvering target with unknown entry and departure time. A computationally efficient method that utilizes extended Kalman filtering (EKF) for phase tracking is proposed to estimate the entry and departure times. The proposed method first performs range cell migration correction (RCMC) on the pulse compression echo signal. Then, the maneuvering target signal is modeled as a polynomial phase signal (PPS) and utilizes the EKF to construct a binary state-space equation for polynomial phase tracking. Finally, by comparing the phase tracking results of the noise cell and the signal cell, one can derive estimates for the entry/departure time and motion parameters. Compared with existing methods, the proposed method avoids multi-dimension searching on the parameter space, so it has a prominent advantage in computational complexity. Moreover, the core of the proposed method lies in tracking the polynomial phase, which is not constrained by the order of target motion, and has wider applicability in practice. Both simulated and public radar data are used to validate the effectiveness of the proposed method.
{"title":"EKF-based parameter estimation method for radar maneuvering target with unknown time information","authors":"Huagui Du, Jiahua Zhu, Yongping Song, Chongyi Fan, Xiaotao Huang","doi":"10.1016/j.sigpro.2024.109731","DOIUrl":"10.1016/j.sigpro.2024.109731","url":null,"abstract":"<div><div>Moving target detection (MTD) is a research hotspot in radar signal processing. Generally, the time information of non-cooperative moving targets entering and leaving a radar coverage area is unknown, which would lead to severe performance loss for target parameter estimation, detection, and imaging. Unlike our previous research work, this paper addresses the motion parameters estimation and refocusing problem for a radar maneuvering target with unknown entry and departure time. A computationally efficient method that utilizes extended Kalman filtering (EKF) for phase tracking is proposed to estimate the entry and departure times. The proposed method first performs range cell migration correction (RCMC) on the pulse compression echo signal. Then, the maneuvering target signal is modeled as a polynomial phase signal (PPS) and utilizes the EKF to construct a binary state-space equation for polynomial phase tracking. Finally, by comparing the phase tracking results of the noise cell and the signal cell, one can derive estimates for the entry/departure time and motion parameters. Compared with existing methods, the proposed method avoids multi-dimension searching on the parameter space, so it has a prominent advantage in computational complexity. Moreover, the core of the proposed method lies in tracking the polynomial phase, which is not constrained by the order of target motion, and has wider applicability in practice. Both simulated and public radar data are used to validate the effectiveness of the proposed method.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"227 ","pages":"Article 109731"},"PeriodicalIF":3.4,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-11DOI: 10.1016/j.sigpro.2024.109736
Yu-Qi Niu, Bing Zheng
The randomized sparse Kaczmarz (RSK) method is an iterative algorithm for computing sparse solutions of linear systems. Recently, Tondji and Lorenz analyzed the parallel version of the RSK method and established its linear expected convergence by implementing a randomized control scheme for subset selection at each iteration. Expanding upon this groundwork, we explore a natural extension of the randomized control scheme: greedy strategies such as the Motzkin criteria. Specifically, we propose a fast block sparse Kaczmarz algorithm based on the Motzkin criterion. It is proved that the proposed method converges linearly to the sparse solutions of the linear systems. Additionally, we offer error estimates for linear systems with noisy right-hand sides, and show that the proposed method converges within an error threshold of the noise level. Numerical results substantiate the feasibility of our proposed method and highlight its superior convergence rate compared to the parallel version of the RSK method.
{"title":"A fast block sparse Kaczmarz algorithm for sparse signal recovery","authors":"Yu-Qi Niu, Bing Zheng","doi":"10.1016/j.sigpro.2024.109736","DOIUrl":"10.1016/j.sigpro.2024.109736","url":null,"abstract":"<div><div>The randomized sparse Kaczmarz (RSK) method is an iterative algorithm for computing sparse solutions of linear systems. Recently, Tondji and Lorenz analyzed the parallel version of the RSK method and established its linear expected convergence by implementing a randomized control scheme for subset selection at each iteration. Expanding upon this groundwork, we explore a natural extension of the randomized control scheme: greedy strategies such as the Motzkin criteria. Specifically, we propose a fast block sparse Kaczmarz algorithm based on the Motzkin criterion. It is proved that the proposed method converges linearly to the sparse solutions of the linear systems. Additionally, we offer error estimates for linear systems with noisy right-hand sides, and show that the proposed method converges within an error threshold of the noise level. Numerical results substantiate the feasibility of our proposed method and highlight its superior convergence rate compared to the parallel version of the RSK method.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"227 ","pages":"Article 109736"},"PeriodicalIF":3.4,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-10DOI: 10.1016/j.sigpro.2024.109729
Dezheng Kong , Shuisheng Zhou , Sheng Jin , Feng Ye , Ximin Zhang
Multi-view clustering has attracted increasing attention for handling complex data with multiple views or sources. Among them, spectral clustering-based methods become more and more popular due to it can make full use of information from different views. However, most existing multi-view spectral clustering methods typically adopt a two-step scheme, which firstly obtains the spectral embedding matrix through graph fusion or multi-feature fusion, and then uses the k-means algorithm to cluster the spectral embedding matrix to obtain the final clustering result. This two-step scheme inevitably leads to information loss, resulting in a suboptimal solution. Furthermore, the methods of graph fusion and multi-feature fusion have not taken into account the inconsistency of features between different views and the unordered nature of clustering labels, which also decreases the clustering performance. To solve these problems, we propose a novel one-step multi-view spectral clustering based on multi-feature similarity fusion. This model simultaneously conducts graph learning, multi-feature similarity fusion and discretization in a unified framework, which can mutually negotiate and optimize each other to achieve better results. Furthermore, compared to directly fusing affinity matrices or spectral embedding matrixs from different views, we take advantage of the property of the spectral embedding matrix, fuse the similarity of samples in feature space, better handle the differences between different views. Finally, the superiority of our method is verified by the experimental evaluation of several data sets. The demo code of this work is publicly available at https://github.com/kong-de-zheng/MOMSC.
{"title":"One-step multi-view spectral clustering based on multi-feature similarity fusion","authors":"Dezheng Kong , Shuisheng Zhou , Sheng Jin , Feng Ye , Ximin Zhang","doi":"10.1016/j.sigpro.2024.109729","DOIUrl":"10.1016/j.sigpro.2024.109729","url":null,"abstract":"<div><div>Multi-view clustering has attracted increasing attention for handling complex data with multiple views or sources. Among them, spectral clustering-based methods become more and more popular due to it can make full use of information from different views. However, most existing multi-view spectral clustering methods typically adopt a two-step scheme, which firstly obtains the spectral embedding matrix through graph fusion or multi-feature fusion, and then uses the k-means algorithm to cluster the spectral embedding matrix to obtain the final clustering result. This two-step scheme inevitably leads to information loss, resulting in a suboptimal solution. Furthermore, the methods of graph fusion and multi-feature fusion have not taken into account the inconsistency of features between different views and the unordered nature of clustering labels, which also decreases the clustering performance. To solve these problems, we propose a novel one-step multi-view spectral clustering based on multi-feature similarity fusion. This model simultaneously conducts graph learning, multi-feature similarity fusion and discretization in a unified framework, which can mutually negotiate and optimize each other to achieve better results. Furthermore, compared to directly fusing affinity matrices or spectral embedding matrixs from different views, we take advantage of the property of the spectral embedding matrix, fuse the similarity of samples in feature space, better handle the differences between different views. Finally, the superiority of our method is verified by the experimental evaluation of several data sets. The demo code of this work is publicly available at <span><span>https://github.com/kong-de-zheng/MOMSC</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"227 ","pages":"Article 109729"},"PeriodicalIF":3.4,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142530833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-09DOI: 10.1016/j.sigpro.2024.109737
Cong Wang , Ming Wu , Jianfeng Guo , Jun Yang
Online secondary path modeling (SPM) is a practical method for real-time noise reduction in narrowband active noise control (NANC) systems, particularly when addressing variations in the secondary path. However, the common practice of using auxiliary noise for online SPM increases the residual noise power and deteriorates the noise reduction performance. The present study proposes a strategy that does not rely on auxiliary noise for online SPM in NANC systems. The proposed algorithm comprises two stages: Stage A models the primary path, whereas Stage B concurrently engages in online SPM and active noise control. The control signal is used to model the discrete Fourier transform (DFT) coefficients of the secondary path, avoiding the need for an auxiliary noise and significantly reducing the computational complexity. Moreover, the predicted primary path from Stage A is employed to obtain the pure desired signal of the online SPM. This strategy decorrelates the primary noise and the modeling signal, and accelerates the convergence of the algorithm. Simulations of recorded data demonstrate that the proposed algorithm can quickly track variations in both the primary and secondary paths, and maintain the noise reduction performance and stability of the system.
{"title":"Online secondary path modeling algorithm without auxiliary noise for narrowband active noise control","authors":"Cong Wang , Ming Wu , Jianfeng Guo , Jun Yang","doi":"10.1016/j.sigpro.2024.109737","DOIUrl":"10.1016/j.sigpro.2024.109737","url":null,"abstract":"<div><div>Online secondary path modeling (SPM) is a practical method for real-time noise reduction in narrowband active noise control (NANC) systems, particularly when addressing variations in the secondary path. However, the common practice of using auxiliary noise for online SPM increases the residual noise power and deteriorates the noise reduction performance. The present study proposes a strategy that does not rely on auxiliary noise for online SPM in NANC systems. The proposed algorithm comprises two stages: Stage A models the primary path, whereas Stage B concurrently engages in online SPM and active noise control. The control signal is used to model the discrete Fourier transform (DFT) coefficients of the secondary path, avoiding the need for an auxiliary noise and significantly reducing the computational complexity. Moreover, the predicted primary path from Stage A is employed to obtain the pure desired signal of the online SPM. This strategy decorrelates the primary noise and the modeling signal, and accelerates the convergence of the algorithm. Simulations of recorded data demonstrate that the proposed algorithm can quickly track variations in both the primary and secondary paths, and maintain the noise reduction performance and stability of the system.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"227 ","pages":"Article 109737"},"PeriodicalIF":3.4,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142438425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-04DOI: 10.1016/j.sigpro.2024.109727
Long Du , Shunsheng Zhang , Libing Huang , Wen-Qin Wang
Dual-functional Radar-Communication (DFRC) systems have been recognized as one of the most promising technologies in the field of wireless communications. Nevertheless, the low probability of intercept (LPI) performance in the DFRC systems cannot be overlooked. Based on the frequency diverse array multiple-input–multiple output (FDA-MIMO) radar, a DFRC system is proposed to enhance target detection in clutter environment and achieve desirable LPI against an underlying hostile interceptor. The issue can be cast into an optimization problem that maximizes the radar signal-to-interference-plus-noise ratio (SINR) while satisfying the communication quality-of-service (QoS) requirement of each user under one of three metrics, the required LPI performance and the constant-modulus waveform constraint. To solve this challenging problem, we reformulate it into an equivalent but more tractable form by resorting to an auxiliary variable. Subsequently, we employ the alternative direction method of multipliers (ADMM) and majorization-minimization (MM) algorithms to solve the resultant problem. Simulation results validate that the proposed LPI FDA-MIMO-DFRC scheme exhibits superior sensing performance over the conventional scheme with MIMO.
{"title":"Joint LPI waveform and passive beamforming design for FDA-MIMO-DFRC systems","authors":"Long Du , Shunsheng Zhang , Libing Huang , Wen-Qin Wang","doi":"10.1016/j.sigpro.2024.109727","DOIUrl":"10.1016/j.sigpro.2024.109727","url":null,"abstract":"<div><div>Dual-functional Radar-Communication (DFRC) systems have been recognized as one of the most promising technologies in the field of wireless communications. Nevertheless, the low probability of intercept (LPI) performance in the DFRC systems cannot be overlooked. Based on the frequency diverse array multiple-input–multiple output (FDA-MIMO) radar, a DFRC system is proposed to enhance target detection in clutter environment and achieve desirable LPI against an underlying hostile interceptor. The issue can be cast into an optimization problem that maximizes the radar signal-to-interference-plus-noise ratio (SINR) while satisfying the communication quality-of-service (QoS) requirement of each user under one of three metrics, the required LPI performance and the constant-modulus waveform constraint. To solve this challenging problem, we reformulate it into an equivalent but more tractable form by resorting to an auxiliary variable. Subsequently, we employ the alternative direction method of multipliers (ADMM) and majorization-minimization (MM) algorithms to solve the resultant problem. Simulation results validate that the proposed LPI FDA-MIMO-DFRC scheme exhibits superior sensing performance over the conventional scheme with MIMO.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"227 ","pages":"Article 109727"},"PeriodicalIF":3.4,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142418348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-04DOI: 10.1016/j.sigpro.2024.109728
Menglin Ye , Shidong Li , Cheng Cheng , Jun Xian
We investigate the effectiveness and efficiency of the iterative tail- minimization (tail--min) technique for its sparse selection capabilities. We conduct profile analyses on the tail--min, establishing the equivalence of the tail--min problem to a two-stage profile formulation, both featuring analytical solutions. The tail null space property (NSP) of sensing matrix is shown to be equivalent to the NSP of the newly defined profile matrix . Besides the error bound analysis for the tail--min under the typical tail-NSP condition, a novel error bound of the tail--min formulation is also established without relying on NSP or restricted isometry property (RIP) assumptions. It merely contains tractable coefficients of , and offers insights into successful recovery, with the observation of the convergent iterative procedure. Numerical studies and the applications to image reconstruction demonstrate the superiority and fast convergence of the tail- sparse solution over state-of-the-art sparse selection methodologies. The sparsity level of a signal that the tail- profile algorithm guarantees the recovery is around 41% higher than that of the basis pursuit algorithm. The analytical solutions of the tail- method at each iteration also ensure that the tail- sparse recovery process is notably fast, especially for high dimensions and high sparsity levels.
{"title":"Analyses of the tail-ℓ2 minimization for fast and enhanced sparse selections","authors":"Menglin Ye , Shidong Li , Cheng Cheng , Jun Xian","doi":"10.1016/j.sigpro.2024.109728","DOIUrl":"10.1016/j.sigpro.2024.109728","url":null,"abstract":"<div><div>We investigate the effectiveness and efficiency of the iterative tail-<span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> minimization (tail-<span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-min) technique for its sparse selection capabilities. We conduct profile analyses on the tail-<span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-min, establishing the equivalence of the tail-<span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-min problem to a two-stage profile <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> formulation, both featuring analytical solutions. The tail null space property (NSP) of sensing matrix <span><math><mi>A</mi></math></span> is shown to be equivalent to the NSP of the newly defined profile matrix <span><math><mover><mrow><mi>A</mi></mrow><mrow><mo>̃</mo></mrow></mover></math></span>. Besides the error bound analysis for the tail-<span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-min under the typical tail-NSP condition, a novel error bound of the tail-<span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-min formulation is also established without relying on NSP or restricted isometry property (RIP) assumptions. It merely contains tractable coefficients of <span><math><mi>A</mi></math></span>, and offers insights into successful recovery, with the observation of the convergent iterative procedure. Numerical studies and the applications to image reconstruction demonstrate the superiority and fast convergence of the tail-<span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> sparse solution over state-of-the-art sparse selection methodologies. The sparsity level of a signal that the tail-<span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> profile algorithm guarantees the recovery is around 41% higher than that of the basis pursuit algorithm. The analytical solutions of the tail-<span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> method at each iteration also ensure that the tail-<span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> sparse recovery process is notably fast, especially for high dimensions and high sparsity levels.</div></div>","PeriodicalId":49523,"journal":{"name":"Signal Processing","volume":"227 ","pages":"Article 109728"},"PeriodicalIF":3.4,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142418357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-03DOI: 10.1016/j.sigpro.2024.109726
Ji Zhao , Lvyu Li , Qiang Li , Bo Li , Hongbin Zhang
Linearly-constrained adaptive filtering algorithms have emerged as promising candidates for system estimation. The existing methods such as the constrained least mean square algorithm rely on mean square error based learning, which delivers suboptimal performance under non-Gaussian noise environments. Therefore, the recursive constrained maximum Versoria criterion (RCMVC) algorithm has been derived and is robust against impulsive distortions. Nonetheless, RCMVC suffers from a notable computational overhead stemming from matrix inversion operations. To circumvent this issue, utilizing the weighting method and the dichotomous coordinate descent (DCD) iteration method, this paper derives a low-complexity version of the RCMVC algorithm called DCD-RCMVC, which alleviates the requirement of matrix inversion and enhances the estimation accuracy and robustness against non-Gaussian interference. Furthermore, we also present a comprehensive theoretical analysis of the DCD-RCMVC algorithm, encompassing discussions on its equivalence, convergence properties, and computational complexity. Simulations performed for system identification problems indicate that the DCD-RCMVC algorithm outperforms the existing state-of-art approaches.
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