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• A joint learning model for superpixel-based fuzzy sparse subspace clustering is established. • A four-level alteration iterative algorithm for superpixel-based image segmentation is proposed. • A centroid shift strategy suitable for image contents is used to generate superpixels. • Experimental results indicate that the proposed algorithm has very good performance. Sparse subspace clustering (SSC) is an important image segmentation method that constructs a self-representation coefficient matrix to represent the relationships between pixels, and then uses spectral clustering to achieve clustering. Compared with other unsupervised segmentation algorithms, SSC has good segmentation performance. However, SSC has a high computational complexity when processing large-sized image. To improve computational efficiency, many researchers have proposed superpixel-based SSC algorithms, which process superpixels instead of pixels and improve efficiency through preprocessing. Due to the sensitivity of superpixel generation to noise, superpixel-based SSC algorithms still have poor robustness. Additionally, preprocessing increases the complexity of the algorithm. To address these issues, this paper proposes a robust superpixel-based fuzzy sparse subspace clustering algorithm. This algorithm combines fuzzy sparse subspace clustering with superpixel generation, and it constructs a unified optimization learning framework through fuzzy C-multiple-means clustering to improve segmentation performance and reduce complexity. Additionally, this paper introduces additional features of superpixel in sparse subspace clustering to further enhance the segmentation performance of the algorithm. Experiment results indicate that the proposed algorithm not only outperforms existing state-of-the-art robust segmentation algorithms independent of superpixels, but also is superior to the latest superpixel-based segmentation algorithms. [ABSTRACT FROM AUTHOR]

High-quality underwater optical images are essential for various applications of underwater vision. However, these images often suffer from severe degradation, complex noise, low contrast, and color cast, leading to poor image quality. To address these issues and accomplish related underwater vision tasks more smoothly, researchers have made many efforts to improve the quality of underwater optical images. This paper presents a comprehensive review of recent research, focusing on specific algorithms published between 2013 and 2023, while also predicting future research trends in this field. In light of the observed ambiguities and inconsistencies in previous review studies' classification frameworks, this paper introduces a novel classification framework, grounded in the specific challenges in this domain, including issues unique to the imaging medium and imaging environment. Additionally, the proposed framework offers a more detailed categorization based on the algorithmic ideology of the authors. Furthermore, this paper addresses a significant gap in the literature by providing an in-depth assessment of the methods for removing marine snow noise from underwater optical images. By complementing existing research, this paper aims to enhance understanding of this subject and provide a clearer, more comprehensive, and in-depth exploration of underwater image quality improvement. [ABSTRACT FROM AUTHOR]

• This paper proposes a WL Hammerstein model and develops a robust recursive adaptive algorithm. • This paper also gives the simplified version of the proposed algorithm. • The performance analysis is derived and verified by simulations. • The superior behavior is demonstrated by example of system identification and SAEC. The Hammerstein model is a crucial model frequently employed in the field of signal processing. This paper focuses on the widely-linear (WL) complex-valued adaptive filtering and proposes a WL Hammerstein system model. Firstly, a cost function which minimizes the complex correntropic loss criterion is constructed. Subsequently, by extending the alternate direction method of multipliers (ADMM) optimization and non-convex projection method to the WL model, and leveraging the special structure of the autocorrelation matrix in the WL Hammerstein system, a robust recursive adaptive filtering algorithm for the WL Hammerstein system is proposed, along with its simplified version. More importantly, the performance analysis is studied, in which the convergence performance and the mean-square performance are provided. Simulations about system identification and stereophonic acoustic echo cancelation (SAEC) are carried out to validate the theoretical analysis and demonstrate the superior performance of the algorithms in this paper. [ABSTRACT FROM AUTHOR]

Tensor decomposition is an essential tool for multiway signal processing. At present, large-scale high-order tensor data require fast and efficient decomposing algorithms. In this paper, we propose accelerated regularized tensor decomposition algorithms using the alternating direction method of multipliers with multiple Nesterov's extrapolations in the block coordinate descent framework. We implement the acceleration in three cases: only in the inner loop, only in the outer loop, and in both the inner and outer loops. Adaptive safeguard strategies are developed following the acceleration to guarantee monotonic convergence. Afterwards, we utilize the proposed algorithms to accelerate two types of conventional decomposition: nonnegative CANDECOMP/PARAFAC (NCP) and sparse CANDECOMP/PARAFAC (SCP). The experimental results on synthetic and real-world tensors demonstrate that the proposed algorithms achieve significant acceleration effects and outperform state-of-the-art algorithms. The accelerated algorithm with extrapolations in both the inner and outer loops has the fastest convergence speed and takes almost one-third of the running time of typical algorithms. • Accelerate regularized tensor decomposition using ADMM with multiple extrapolations. • Extrapolations are utilized in three cases: inner loop, outer loop, and both loops. • Adaptive safeguard strategies are developed to guarantee monotonic convergence. • The accelerated algorithms converge in almost one-third of conventional running time. [ABSTRACT FROM AUTHOR]

This paper presents a comparison of contemporary algorithms aimed at mitigating the saturation-induced challenges in active noise control (ANC) systems. The saturation effect introduces nonlinear elements into the adaptive algorithm, consequently impacting the ANC system's performance and degrading the system's stability. The detailed theoretical analysis indicates that the cause of the output saturation issue lies in the exceeding output power of the control signal. Recently, two categories of adaptive algorithms have been developed to address this issue. The first category focuses on effectively constraining the output signal to manage the saturation effect, exhibiting notable practical efficacy. The second category employs nonlinear ANC algorithms (NANC) to model the inherent signal nonlinearity, controlling harmonic distortion caused by saturation effects. This work summarizes the key results in the literature and demonstrates that output constraint algorithms outperform the NANC algorithms in computational efficiency and robustness. Hence, they should be a more practical choice than others in coping with the output-saturation issue in ANC systems. • Output saturation deforms the control signal and degrades the stability of adaptive algorithms. • Output-constraint algorithms constrain output saturation with low computational complexity. • Nonlinear algorithms use nonlinear models to counteract output saturation. [ABSTRACT FROM AUTHOR]

Radar signal recognition based on micro-Doppler spectrogram has been widely used in human action recognition tasks. However, in practical application scenarios, radar signals inevitably have noise, which leads to different degrees of deformation of the spectrogram graph structure and affects the accuracy of subsequent recognition algorithms. In this paper, we present "ACFL", a novel algorithm for micro-Doppler spectrogram denoising, which aims to reduce the impact of noise on human action recognition. ACFL employs amplitude–frequency two-dimensional clustering and fuzzy logic clustering selection mechanism to remove noise elements from the spectrogram. Moreover, to address the issue of noise leakage or target missing under time-varying noise and action conditions, ACFL adopts spectrogram segmentation based on short-term Rényi entropy. By dividing the spectrogram into intervals with different time–frequency distributions, the dynamic spectrogram denoise over time is achieved. Simulation and measured data experiments demonstrate that the proposed algorithm not only achieves a higher-quality denoised spectrogram but also significantly improves the accuracy of human action recognition under noisy conditions. • Proposed a novel algorithm for denoising human action micro-Doppler spectrograms. • Algorithm consists of clustering with fuzzy logic and spectrogram segmentation. • Algorithm verification using both simulated and measured human action data. [ABSTRACT FROM AUTHOR]

• A fourth-order polynomial phase signal model is used to model the echo, and a novel parameter estimation method is proposed. • A frequency domain implementation method of SoWVD is proposed, which reduce the computational cost of SoWVD significantly. • For the fourth order polynomial phase signal model, the proposed algorithm achieves a balance between the accumulation performance and the operational complexity. The high maneuvering target with jerk motion detection suffers from range migration (RM) and Doppler frequency migration (DFM). In this paper, the fourth order polynomial signal model is used to model the radar echo signal, and a novel high maneuvering target detection method is proposed. The RM is eliminated with Keystone transform (KT) and acceleration searching, and then the aligned echoes are extracted. With two defined symmetric autocorrelation functions (SAF) and the scaled Fourier transform, the third and fourth order motion parameters are estimated. Based on the estimated high order motion parameters, the fourth order polynomial phase signal is turned into linear frequency modulated (LFM) signal. To estimate the chirp rate of the LFM signal, a fast implementation method of second order Wigner Ville Distribution (SoWVD), named frequency domain SoWVD (FDSoWVD) is proposed. Based on the triple estimated motion parameters, the DFM is compensated and then the coherent integration can be achieved by fast Fourier transform, followed which the detection process is performed. Compared with other representative algorithms, the proposed method achieves a good balance between the computation complexity and detection ability. The effectiveness of the proposed method is verified by experiment with synthetic and raw data. [ABSTRACT FROM AUTHOR]

• Behavior of the diffusion LMS algorithm is analyzed in the presence of delays in probing the unknown system. • Cyclostationary white Gaussian and non-Gaussian nodal inputs are considered. • The types of input distribution and the probing delays can be different for different nodes. • The derived models facilitate the understanding of the algorithm dependence upon the network parameters. • Significant differences are found between the algorithm behavior for equal and unequal probing delays. The paper studies the behavior of the diffusion least mean square (DLMS) algorithm in the presence of delays in probing the unknown system by the nodes. The types of input distribution and the probing delays can be different for different nodes. The analysis is done for a network having a central combiner. This structure reduces the dimensionality of the resulting stochastic models while preserving important diffusion properties. Communication delays between the nodes and the central combiner are also considered in the analysis. The analysis is done for system identification for cyclostationary white nodal inputs. Mean and mean-square behaviors of the algorithm are analyzed. The derived models consist of simple scalar recursions. These recursions facilitate the understanding of the algorithm mean and mean-square dependence upon the 1) nodal input kurtosis, 2) nodal probing delays, 3) communication delays between the nodes and the central combiner, 4) nodal noise powers, and 5) nodal weighting coefficients. Significant differences are found between the algorithm behavior for equal probing delays and that for unequal probing delays. Results for unequal probing delays are surprising. Simulations are in excellent agreement with the theory. [ABSTRACT FROM AUTHOR]

This paper presents two new trajectory probability hypothesis density (TPHD) and trajectory cardinality probability hypothesis density (TCPHD) filters for joint tracking and classification (JTC), namely JTC-TPHD and JTC-TCPHD filters. We first introduce the classified trajectory RFS model to accommodate the motion model-based class information. The adaptation of the TPHD and TCPHD filters to the classified trajectory RFS is then formulated, i.e., JTC-TPHD and JTC-TCPHD, which are capable of jointly estimating the number, class, motion model, and trajectory status of multiple targets. We also develop the linear Gaussian implementation (LGM) as an analytic closed-form solution of the proposed filters. Simulation experiments discuss the validity and superiority of the proposed filters for multi-target JTC. • The classified trajectory variable to accommodate class information. • The proposal of JTC-T(C)PHD filters for joint tracking and classification. • The development of linear Gaussian mixture implementations. • The simulation demonstration of algorithms' validity and superiority. [ABSTRACT FROM AUTHOR]

In this paper, two new algorithms are proposed using modified sigmoid activation function as the cost function and combining with affine projection (AP) method, which are sigmoid affine projection sign algorithm (SAPSA) and sigmoid affine projection algorithm (SAPA). Conventional AP-type algorithms converge fast but are susceptible to impulsive interference. The sigmoid function has an upper bound, thus reducing the effect of impulse interference. The proposed algorithms combine the advantages of fast convergence speed of the affine projection method and strong noise resistance of the sigmoid cost function. Meanwhile the L 2 -norm constraint is used to adjust the updating formula of the weight vector, which further improves noise resistance. Several simulation experiments show that SAPSA and SAPA are superior to other AP-type algorithms under impulse interference. • A new cost function based on sigmoidal activation function is proposed. • The sigmoid affine projection sign algorithm (SAPSA) and sigmoid affine projection algorithm (SAPA) are proposed. • A new L 2 -norm constraint method is proposed. [ABSTRACT FROM AUTHOR]

This paper proposes a novel augmented space robust adaptive filter by reusing the errors for online applications. First, a batched augmented space constrained model (ASCM) is constructed to combat non-Gaussian noise. In ASCM, the errors are reused by k nearest neighbors (k -NN) estimation. Then, an augmented space recursive least-constrained-squares algorithm integrating with distance-based k -NN method (ARLCS- d k) is developed within the framework of ASCM for adaptive filtering. Finally, to curb the size of ever-growing error network, a sliding window ARLCS- d k (SW-ARLCS- d k) is proposed to reduce the computational burden. Theoretical analyses of excess mean square error (EMSE) and testing mean square error (TMSE) are carried out for performance evaluation. Examples on time-series prediction of simulated and real-world data are used to illustrate the advantages of proposed algorithms on robustness and prediction accuracy. • A batched augmented space constrained model (ASCM) with k nearest neighbors (k -NN) method is constructed to combat impulsive noise. • An online augmented recursive least-constrained-squares algorithm using distance-based k -NN method (ARLCS- dk) is developed for adaptive filtering. • A sliding window is designed for ARLCS- dk to reduce its computational complexity. • Theoretical results of mean square error are illustrated the effectiveness of ARLCS- dk in prediction of time-series. [ABSTRACT FROM AUTHOR]

The random sample consensus algorithm has been successfully employed for the estimation of parameters in polynomial phase signals. It significantly reduces the signal-to-noise ratio threshold by 3 dB compared to current state-of-the-art algorithms. In this paper, we have developed a random sample consensus algorithm-based estimator for hyperbolic frequency modulated signals parameters. Our proposed parameter and instantaneous frequency estimator demonstrate exceptional accuracy, surpassing existing estimators by achieving the signal-to-noise ratio threshold improvement of up to 7 dB. Furthermore, we have examined the limits of applicability of our proposed approach, particularly in terms of computational complexity. • The RANSAC algorithm is applied to the HFM signals parameter estimation. • The algorithm setup in both fine and rough stage is considered in details. • Calculation complexity analysis is provided. • Simulations are performed on aliased signal. [ABSTRACT FROM AUTHOR]

This paper analyzes the correlation matrix between the a priori error and measurement noise vectors for standard and augmented affine projection algorithms using a unified approach. This correlation stems from the dependence between the filter tap estimates and the noise samples, and has a strong influence on the mean square behavior of the algorithm. We show that the correlation matrix is upper triangular, and compute the diagonal elements in closed form, showing that they are independent of the input process statistics. Also, for white inputs we show that the matrix is fully diagonal. These results are valid in the transient and steady states, considering a possibly variable step-size. Our only assumption is that the filter order is large compared to its projection order and that the input signal is stationary. Using these results, we perform a steady-state analysis for small step size and provide a new simple closed-form expression for the mean-square error, which has comparable or better accuracy to many preexisting expressions, and is much simpler to compute. Finally, we also obtain expressions for the steady-state energy of the other components of the error vector. • Unifies treatment for linear and widely linear affine projection algorithms. • Analyzes of the correlation between the noise and the a priori error vectors. • Provides a simple and accurate mean-square error formulas. [ABSTRACT FROM AUTHOR]

The generalized eigenvalue problem (GEP) plays a significant role in signal processing and machine learning. This paper proposes a consensus-based distributed algorithm for GEP in multi-agent systems, where the data are distributively stored across agents. The distributed GEP is reformulated as a consensus optimization, but the presence of its quadratic inseparable constraint makes the considered problem more challenging. To deal with it, a sequential method combined with the alternating direction method of multipliers is proposed, which requires communication between multiple pairs of nodes. Theoretical analysis shows the proposed algorithm will converge to the set of stationary solutions. And the numerical experiments on synthetic and real-world datasets validate that the approximated solution is competitive to the centered results. • Reformulation of consensus-based distributed Generalized Eigenvalue Problem. • A sequential method to decouple the inseparable constraint. • Convergence to the set of stationary solutions under mild assumptions. • Performance of the proposed algorithm is competitive to the ground truth. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel family of online censoring (OC) based complex-valued least mean kurtosis (CLMK) algorithms by inspiring the advantages of the online censoring strategy and kurtosis-based cost function. We first develop important members of this family of algorithms such as OC based CLMK (OC-CLMK) and augmented CLMK (OC-ACLMK). These algorithms censor less informative complex-valued data streams in an online manner and keep only the most informative ones for performing their weight vector updates. Thus, they reduce the costs of data processing without markedly affecting performance accuracy. However, they do not take into account possible outliers that disturb their performances considerably. Therefore, we also develop robust members such as robust OC-CLMK (ROC-CLMK) and OC-ACLMK (ROC-CLMK) algorithms, which censor less informative complex-valued data streams as well as possible outliers. The convergence analyses of the proposed algorithms in the sense of Lyapunov are also presented to derive the bounds of their step sizes in a compact form. The simulation results on large-scale system identification and regression scenarios affirm the mentioned attractive features of the proposed algorithms. This study also shows that the noteworthy properties of the proposed algorithms will provide important contributions to the processing of complex-valued big data streams. • A novel family of online censoring (OC) based CLMK algorithms is proposed. • The proposed OC-CLMK and OC-ACLMK censor less informative complex-valued data streams in an online manner. • They reduce data processing costs without markedly affecting performance accuracy. • We also develop robust members such as robust OC-CLMK and OC-ACLMK algorithms. • They censor both less informative complex-valued data streams and possible outliers. [ABSTRACT FROM AUTHOR]

For the correlated input, the Volterra kernel-based least mean-square (LMS) algorithm in the time-domain exhibits a slow learning rate caused by the large eigenvalue spread of the input covariance matrix. To tackle such an issue, this paper develops a novel frequency-domain Volterra kernel-based filter, resulting in the periodic update constrained frequency-domain second-order Volterra normalized LMS (named as P-CFDSOV-NLMS1) algorithm. Subsequently, by using one- and two-dimensional discrete Fourier transforms (DFTs) simultaneously, another frequency-domain implementation and corresponding P-CFDSOV-NLMS2 algorithm are constructed. In contrast, the P-CFDSOV-NLMS1 scheme only requires one-dimensional DFT operations and takes advantage of the joint information between the block input vectors. Then, the mean and mean-square convergence behaviors of the P-CFDSOV-NLMS1 algorithm are investigated. Furthermore, the designed frequency-domain method is extended to three different widely complex-valued Volterra kernel-based models. Finally, computer simulations reveal that the suggested algorithms outperform the previously reported frequency-domain techniques in terms of convergence speed and tracking ability. • Frequency-domain implementation of the Volterra kernel-based adaptive filtering method is studied. • Using 1-D and 2-D DFTs, two normalized implementations (P-CFDSOV-NLMS1 and P-CFDSOV-NLMS2) are given. • A joint-normalized matrix is devised to accelerate the convergence speed for colored input signals. • Mean and mean-square analyses of P-CFDSOV-NLMS1 are made with the steady-state expression for MSD. • The designed method is extended to three widely complex-valued second-order Volterra kernel-based models. [ABSTRACT FROM AUTHOR]

In numerous applications, such as DNA microarrays, face recognition, and spectral unmixing, we need to acquire a non-negative K -sparse signal x from an underdetermined linear model y = A x + v , where A is a sensing matrix and v is a noise vector. In this paper, we first propose a ReLU-based hard-thresholding algorithm (RHT) to recover x by taking advantage of its non-negative sparsity. Two sufficient conditions for stable recovery with RHT are then developed, which are respectively based on the restricted isometry property (RIP) and mutual coherence of the sensing matrix A. As far as we know, these two sufficient conditions are the best for hard-thresholding-type algorithms. Numerical experiments show that RHT has better overall recovery performance in the recovery non-negative sparse signals than the non-negative least squares (NNLS) algorithm, some hard-thresholding-type algorithms including the iterative hard-thresholding (IHT) algorithm, hard-thresholding pursuit (HTP), Newton-step-based iterative hard-thresholding algorithm (NSIHT), and Newton-step-based hard-thresholding pursuit (NSHTP), several non-negative sparse recovery approaches including non-negative orthogonal matching pursuit (NNOMP), fast NNOMP (FNNOMP), non-negative orthogonal least squares (NNOLS), and non-negative regularization (NNREG) method. In terms of efficiency, RHT has a similar performance to IHT, and is much more efficient than other tested algorithms. • Efficient hard-thresholding-type algorithm for non-negative sparse recovery. • Sufficient conditions for stable recovery with RHT based on RIP and mutual coherence. • RHT achieves good recovery performance in both stimulated and real-world experiments. • RHT shows similar efficiency with IHT, and outperforms the remaining algorithms. [ABSTRACT FROM AUTHOR]

Range ambiguity is a significant challenge in conventional pulse-Doppler radar systems with medium or high pulse repetition frequencies, greatly impacting radar detection and imaging capabilities. The classic approaches such as waveform diversity and compressed sensing are based on the isolation between pulses. However, these methods encounter issues like residual ambiguity and grid mismatch, resulting in poor range ambiguity suppression performance. In this paper, the multiple signal classification-alternating projection (MUSIC-AP) method is proposed to address these challenges and achieve high-resolution estimation. The proposed method converts the range-velocity estimate into a spectrum estimate, enabling the utilization of the MUSIC algorithm to solve the grid mismatch problem and improve echo reconstruction. Then, to mitigate the effect of ambiguous energy on reconstruction, the MUSIC reconstruction subprocess is embedded into the AP framework. Through iterative approximation, the method gradually suppresses ambiguous and noise energy, thereby further enhancing the echo reconstruction accuracy and range ambiguity suppression performance. Simulations demonstrate the effectiveness of the proposed method. Moreover, algorithm analysis is conducted, considering aspects such as resolution, robustness, and sparsity, which provides a basis for parameter selection and applicability conditions. [Display omitted] • The range-velocity estimation is transformed into spectrum estimation problem. • Unambiguous range-velocity high-resolution estimation via the MUSIC algorithm. • The MUSIC is embedded into AP outer frame to gradually suppress ambiguity and noise. [ABSTRACT FROM AUTHOR]

Video snapshot compressive imaging (SCI) is a new compressive imaging system that aims to recover multiple video frames from a single measurement. Recent plug-and-play (PnP) imaging methods have been used for solving SCI inverse problems by leveraging pre-trained deep Gaussian denoisers. Under the condition of diminishing noise levels, a necessary assumption for the fixed-point convergence of PnP imaging algorithms is that the plugged denoisers are bounded denoisers. However, it is difficult to prove that existing deep Gaussian denoisers meet this assumption due to the complex network architectures, limiting the convergence analysis of these algorithms. This paper aims to elaborate a bounded deep video denoiser to remedy such a gap. Concretely, we propose a denoiser using double tight frames dubbed as VDTF and plug it into the PnP framework to construct the PnP-VDTF algorithm. In VDTF, a constant network (CNet) is designed, wherein a Swin Transformer-based module and a 3D convolution module extract the spatial information of the global features and the temporal information of the input video, respectively. Theoretically, we provide a strict boundary proof of VDTF, and show that PnP-VDTF can generate fixed-point convergent trajectories. Experiments show that PnP-VDTF can achieve higher-quality reconstructions compared with benchmark SCI algorithms. • We propose a provable and trainable bounded denoiser dubbed as VDTF. • Spatial–temporal information is utilized to generate adaptive thresholds. • The proposed PnP-VDTF algorithm can achieve high-quality reconstructions. • We explicitly prove that VDTF is a bounded denoiser. • We prove that PnP-VDTF can generate fixed-point convergent trajectories. [ABSTRACT FROM AUTHOR]

The index of the peak magnitude of the fractional Fourier transform (FrFT) of linear frequency modulated (LFM) signals has been widely used as a powerful chirp-rate estimator. In this paper, we propose analytical approximations for the peak FrFT magnitude (PFM) of mono and multicomponent LFM signals, both for noiseless and noisy cases. In addition, we present a novel coarse-to-fine FrFT-based algorithm designed specifically for chirp-rate estimation of multi-component LFM signals. Our approach entails an initial coarse estimation of the chirp-rates for each component by utilizing our proposed mathematical models. By leveraging these models, we achieve improved performance and a reduced signal-to-noise breakdown threshold. Furthermore, we incorporate a unique and efficient estimate-and-subtract strategy to refine the estimated parameters using our proposed models. Rather than removing the components from the LFM signal, we utilize the derived model to identify and remove peaks in the PFM. This strategy enhances the algorithm's capability to handle challenging scenarios. Extensive simulation results demonstrate that our proposed algorithm performs very close to the Cramér–Rao lower bound. It effectively eliminates the leakage effect between signal components, avoids error propagation, and maintains an acceptable computational cost compared to other state-of-the-art methods. • Analytical approximations for the peak FrFT magnitude of LFM signals are presented. • We propose a fine-to-coarse estimation approach, which uses our models in parameter estimation of multi-component LFM signals. • Simulations show that the algorithm performs very close to the Cramer–Rao bound. • The algorithm has a very low computational cost, compared to the other methods. [ABSTRACT FROM AUTHOR]