This paper proposes a low-complexity greedy algorithm, termed dynamic multiple matching pursuit (DMMP), for binary sparse signal recovery using random Gaussian sensing matrices. Conventional multiple matching pursuit algorithms, such as the generalized orthogonal matching pursuit algorithm, offer robust recovery but rely heavily on computationally expensive least-squares-based estimation. To reduce this computational burden, existing binary greedy algorithms eliminate the leastsquares- based step by exploiting the binary structure of the signal. However, this simplification inherently limits them to single-index selection per iteration. To tackle this problem, the proposed algorithm introduces a dynamic selection that identifies multiple indices per iteration based on a probabilistic threshold while retaining a simple non-least-squares-based update rule. This design enables the algorithm to adaptively balance recovery accuracy and computational efficiency. Theoretically, we establish upper bounds on both the expected number of iterations and the accuracy loss relative to the single-index greedy method. Simulation results indicate that the DMMP algorithm achieves comparable recovery accuracy to the state-of-the-art greedy methods while substantially reducing the number of iterations. In particular, the DMMP algorithm can achieve a successful recovery rate of over 99.9% and reduce the average number of iterations by 80% compared to its counterparts.
The traditional diffusion algorithms usually suffer from high communication load in distributed networks. Regarding this issue, the distributed compressed estimation (DCE) scheme reduce the communication load by compressing the weight vector which needs to be estimated. However, the performance between convergence rate and steady-state error need to be balanced, and under impulsive noise interferences, the DCE performance will significantly decrease. To tackle these issues, we propose a compressive-sensing-based diffusion Bayesian (CSB-DB) algorithm with low communication burden and high estimation accuracy. To improve its robustness against impulsive noise, we design a robust CSB-DB (RCSB-DB) algorithm, leading to a selective weight function in the step-size. The selective weight function prevents the update of step-size and weight vector when outliers occur. Additionally, we design an algorithm to optimize the measurement matrix under the gradient descent to enhance the convergence rate and steady-state performance of the proposed algorithms. The mean and mean-square analyses are also conducted. Numerical experiments verify that the simulation results corroborate with the theoretical development, and reveal the excellent performance of the proposed algorithms.
We study detection of weak AM-FM modes at very low Signal-to-Noise Ratio (SNR), where ridge- and zerobased methods are often sensitive to modelling assumptions and parameter choices. We propose a Time-Frequency (TF) saliency that detects local departures from the noise covariance structure. Under circular white noise, the spectrogram covariance is, after vectorization, block-Toeplitz with Toeplitz blocks, while under wide-sense stationary (WSS) noise the complex Short-Time Fourier Transform (STFT) exhibits a Toeplitz-in-time lag structure. These templates lead to two computationally efficient local detectors operating on short TF patches: a Toeplitz-projection residual in frequency (white regime) and a short-lag coherence score on complex STFT coefficients (WSS regime). Experiments show that Detector A reveals ridge neighborhoods down to about −50 dB in white noise, while Detector B produces ridge-localized responses under strongly colored WSS noise and remains contrasted on speech and bat recordings.
Coherence analysis is commonly used to assess the frequency-dependent correlation between two time series in a wide range of disciplines, including neuroscience, astronomy, and acoustic engineering. However, its effectiveness can be substantially degraded by measurement noise, especially when both signals are contaminated. This paper proposes a weighted structured errors-in-variables (WSEIV) framework for noise-robust coherence estimation, formulated as a synchronous component recovery problem under measurement uncertainty. Within this framework, four estimators — total least squares, weighted total least squares, structured total least squares, and weighted structured total least squares — are assessed to recover noise-reduced representations of synchronous components for improved coherence estimation. The latter three formulations explicitly account for unequal noise variances and structural constraints in the data matrix, either independently or jointly. The proposed framework is validated using synthetic signals across a range of signal-to-noise ratios and further evaluated in a representative corticomuscular coupling application using electroencephalogram and electromyogram recordings. Results demonstrate that the WSEIV methods consistently enhance coherence estimation under noisy conditions, improving the recovery of coupling-related signal components from contaminated measurements. This methodology provides a generalizable framework for frequency-resolved coupling analysis in situations where connectivity must be inferred from noisy measurements.
Existing methods for universal entropy coding suffer from the dilemma between versatility to general data sources and ability in exploiting complex structured statistics. They usually rely on presumed structural and statistical assumptions to decompose joint probability distribution for tractable entropy modeling. To address this problem, in this paper, we propose the first learned universal entropy coding method that leverages tensor networks (TNs) to learn joint probability distribution of diverse data sources without presuming distribution priors or context structures. Specifically, we resort to the tensor network formulation based on matrix product states (MPS) to learn the tractable low-order tensor approximation for high-order tensor representation of joint probability distribution. Entropy encoding and decoding are achieved in a sequential fashion by constructing cumulative distribution functions with marginal probabilities of sources on top of the probabilistic modeling. We demonstrate in theory that the proposed entropy model converges to stationary distribution, guarantees upper and lower bounds of entropy rates, and exponentially decays in truncation error of entropy rate with truncation order and correlation length. Furthermore, TN-based practical coding framework is designed with unified Gray-code bit-plane decomposition to mitigate numerical overflow. Experimental results demonstrate that the proposed method consistently outperforms existing universal approaches and is comparable to task-specific approaches in the tasks of lossless graph and image compression and learned lossy image compression.
