New method recovers block-sparse signals with common sparsity patterns.
problem Recovering block-sparse signals with common sparsity patterns in MMV.
method Pattern-coupled hierarchical Gaussian prior model with EM framework.
result Proposed method automatically captures block sparse structure.
TSN improves sparse signal recovery with less complexity.
problem Sparse regression problem of recovering sparse signals from measurements.
method Tree search algorithm driven by deep neural network with pruning.
result TSN outperforms conventional methods in various sensing matrices.
This paper presents a novel Block Iterative Bayesian Algorithm (Block-IBA) for reconstructing block-sparse signals with unknown block structures. Unlike the existing algorithms for block sparse signal recovery which assume the cluster structure of the nonzero elements of the unknown signal to be independent and identic…
Using a Bayesian approach, we consider the problem of recovering sparse signals under additive sparse and dense noise. Typically, sparse noise models outliers, impulse bursts or data loss. To handle sparse noise, existing methods simultaneously estimate the sparse signal of interest and the sparse noise of no interest.…
The paper infers graph structure from sparse signal observations.
problem Inferring graph structure from sparse signal observations.
method Formulates a non-convex graph learning problem and solves it via alternating signal sparse coding and graph update steps.
result The method generally outperforms other network inference algorithms in graph recovery.
Sparse manifold transform linearizes non-linear signal transformations.
problem Non-linear signal transformations in sensory data.
method Combines sparse coding, manifold learning, and slow feature analysis.
result Models sparse discreteness and low-dimensional manifold structure in natural scenes.
New method for robustly recovering sparse signals from noisy data.
problem Recovering sparse signals from corrupted measurements with outliers.
method Sparse Bayesian learning with binary indicator hyperparameters and hierarchical priors.
result The method achieves better performance than existing techniques.
We consider the problem of recovering block-sparse signals whose structures are unknown \emph{a priori}. Block-sparse signals with nonzero coefficients occurring in clusters arise naturally in many practical scenarios. However, the knowledge of the block structure is usually unavailable in practice. In this paper, we d…
Algorithm estimates sparse signals from linear measurements, improving recovery guarantees.
problem Estimating gradient-sparse signals from noisy linear measurements.
method Iterative alpha expansion with proximal descent and geometric penalty decay.
result Global recovery guarantees under cut-restricted isometry property for Gaussian designs.
Graph-Dictionary model for sparse multivariate signal representation.
problem Capturing complex relational information in multivariate signals.
method Graph dictionaries and bilinear primal-dual splitting algorithm.
result Graph-dictionary model outperforms baselines in signal reconstruction and classification.
A new method for joint noise removal and trend estimation from sparse signals.
problem Jointly removing noise and estimating trends from sparse signals.
method PENDANTSS combines SOOT/SPOQ penalties with BEADS algorithm in a Trust-Region block alternating variable metric forward-backward approach.
result Outperforms comparable methods in deconvolving analytical chemistry signals.
This paper tackles sparse blind deconvolution with short signals and demonstrates recovery of near ground truth kernels.
problem Recovering two unknown signals from their convolution, especially when one is short and sparsely supported.
method Formulated as a nonconvex optimization problem over the sphere, using a descent algorithm that escapes strict saddle points.
result Near shift truncation of the ground truth kernel can be recovered under specific conditions.
Hadamard Wirtinger Flow recovers sparse signals from fewer measurements.
problem Reconstructing sparse signals from magnitude-only measurements.
method Gradient descent with Hadamard parametrization (HWF).
result A single step of HWF recovers support from k(xmax∗)−2 samples. Signal recovery is one of the key techniques of Compressive sensing (CS). It reconstructs the original signal from the linear sub-Nyquist measurements. Classical methods exploit the sparsity in one domain to formulate the L0 norm optimization. Recent investigation shows that some signals are sparse in multiple domains.…
A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical successes in various fields ranging from image to audio processing, there have only …
Paper improves learning mixtures of sparse signals from noisy measurements.
problem Learning mixtures of sparse linear regressions from noisy measurements.
method Improves upon state-of-the-art results using sparse polynomials and error-correcting codes.
result First robust reconstruction algorithm for mixtures of more than two sparse signals.
GRRT recovers sparse signals without prior sparsity or noise variance knowledge.
problem Recovering sparse signals without prior sparsity or noise variance knowledge.
method Generalized residual ratio thresholding (GRRT) for SOMP and BOMP.
result Finite sample and finite SNR guarantees for exact support recovery.
A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical successes in various fields ranging from image to audio processing, there have only …
New RNN reconstructs video frames from sparse measurements.
problem Sequential signal reconstruction from compressive measurements.
method Unfolding proximal gradient method for l1-l1 minimization.
result Outperforms state-of-the-art RNN models in video frame reconstruction.
This work optimizes signal estimation for sparse MRA with collision-free signals.
problem Recovering an unknown signal from repeated observations under cyclic isometries with high noise.
method Investigates minimax optimality for collision-free signals in the MRA model.
result The minimax optimal rate of estimation is \( \sigma^2/\sqrt{n} \) for sparse MRA.
New algorithm reduces phase retrieval sample complexity for sparse and block-sparse signals.
problem Recovering signals from magnitude-only measurements, especially sparse and block-sparse signals.
method Compressive Phase Retrieval with Alternating Minimization (CoPRAM) combining classical alternating minimization and CoSaMP.
result Achieves sample complexity of O(s^2 log n) for s-sparse signals and O(s log n) for power-law decay signals, matching or improving existing results.
The paper shows exchanging estimates over networks is effective for learning sparse signals.
problem Learning sparse signals over networks with limited communication.
method Iterative algorithm exchanging intermediate estimates over a network, with theoretical and simulation analysis.
result The iterative algorithm provides competitive performance in learning sparse signals.
Novel algorithm learns sparse signal representations over topological spaces.
problem Sparse representation of signals over combinatorial topological spaces.
method Leveraging Hodge theory, the paper embeds topology into a dictionary structure via concatenated sub-dictionaries, each as a polynomial of Hodge Laplacians, and optimizes the dictionary coefficients and sparse signal representation via iterative alternating algorithms.
result Efficiently learned sparse representations and underlying relational structure of topological signals.
We consider an important class of signal processing problems where the signal of interest is known to be sparse, and can be recovered from data given auxiliary information about how the data was generated. For example, a sparse Green's function may be recovered from seismic experimental data using sparsity optimization…
Majority voting neural networks improve binary compressed sensing for sparse signal recovery.
problem Sparse signal recovery in binary compressed sensing.
method Majority voting neural networks with a cross entropy-like term and L1 regularization.
result The majority voting neural network achieves excellent recovery performance, approaching optimal performance as the number of component nets grows.
The paper focuses on the sparse approximation of signals using overcomplete representations, such that it preserves the (prior) structure of multi-dimensional signals. The underlying optimization problem is tackled using a multi-dimensional split Bregman optimization approach. An extensive empirical evaluation shows ho…
Study on signal detection in sparse additive models with nonasymptotic minimax rates.
problem Signal detection in sparse additive models.
method Nonasymptotic minimax analysis of signal detection in sparse additive models.
result Established minimax separation rate for signal detection.
Sparse-Gen uses generative models to improve compressed sensing with full signal recovery.
problem Recovering signals with fewer measurements than traditional methods allow.
method Sparse-Gen framework that allows for sparse deviations from the support set.
result Achieves full signal recovery over the full space of signals, not just the support.
Paper discusses new stochastic algorithms for sparse signal recovery.
problem Sparse signal recovery in medical imaging and remote sensing.
method Proposes and analyzes stochastic natural thresholding algorithms.
result Demonstrates improved performance of StoNT algorithms.
Paper reveals hidden convexities in deep learning models using sparse signal processing.
problem Non-convex loss functions in deep learning models complicate optimization and theoretical understanding.
method Developed convex equivalences of ReLU NNs and their connections to sparse signal processing models.
result Recent research has uncovered hidden convexities in certain NN architectures, notably two-layer ReLU networks and other architectures.
Goal: This paper deals with the problems that some EEG signals have no good sparse representation and single channel processing is not computationally efficient in compressed sensing of multi-channel EEG signals. Methods: An optimization model with L0 norm and Schatten-0 norm is proposed to enforce cosparsity and low r…
Survey on nonconvex penalties for sparse and low-rank recovery in various fields.
problem Achieving sparsity and low-rankness in signal processing, statistics, and machine learning.
method Analysis of nonconvex penalties and their applications.
result Nonconvex penalties can significantly improve performance in various applications.
This paper establishes conditions for sparse signal recovery with sparse measurements.
problem Recovering the support of a sparse signal using noisy projections with sparse measurement matrices.
method Establishes sufficient conditions for successful sparse recovery using sparse measurement matrices.
result A phase transition threshold for sparse recovery in the sparse setting is discovered, revealing a trade-off between sampling complexity and measurement sparsity.
Semi-supervised learning identifies radio signals from sparse data.
problem Lack of labeled data for radio emitter recognition.
method Combines unsupervised and supervised learning for feature learning and clustering.
result Semi-supervised learning can identify new radio signals efficiently.
Develops algorithms for sparse signal reconstruction without needing signal sparsity or noise variance.
problem Sparse signal reconstruction challenges due to unknown signal sparsity and noise variance.
method TF-IGP and RRT-IGP frameworks for OMP and OLS without prior knowledge of k0 and σ2. result TF-IGP and RRT-IGP achieve successful sparse recovery under restricted isometry conditions.
A field known as Compressive Sensing (CS) has recently emerged to help address the growing challenges of capturing and processing high-dimensional signals and data sets. CS exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive (or random) linear…
This letter presents a novel Block Bayesian Hypothesis Testing Algorithm (Block-BHTA) for reconstructing block sparse signals with unknown block structures. The Block-BHTA comprises the detection and recovery of the supports, and the estimation of the amplitudes of the block sparse signal. The support detection and rec…
DeepFPC uses neural networks to recover sparse signals from quantized measurements.
problem Recovering sparse signals from quantized measurements.
method Unfolding the fixed-point continuation algorithm into a deep neural network.
result DeepFPC outperforms state-of-the-art algorithms in DOA estimation.
This paper considers compressed sensing and affine rank minimization in both noiseless and noisy cases and establishes sharp restricted isometry conditions for sparse signal and low-rank matrix recovery. The analysis relies on a key technical tool which represents points in a polytope by convex combinations of sparse v…
In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent signals residing on weighted graphs, an additional design challenge is to incorporate …
Matching Pursuit LASSIn Part I \cite{TanPMLPart1}, a Matching Pursuit LASSO ({MPL}) algorithm has been presented for solving large-scale sparse recovery (SR) problems. In this paper, we present a subspace search to further improve the performance of MPL, and then continue to address another major challenge of SR -- bat…
Algorithm improves search efficiency for sparse signals using region sensing.
problem Efficiently search for sparse signals in large spaces.
method Greedy maximization of information gain using noisy average region measurements.
result Requires fewer measurements to recover signal locations compared to passive methods.
In compressed sensing, we wish to reconstruct a sparse signal x from observed data y. In sparse coding, on the other hand, we wish to find a representation of an observed signal y as a sparse linear combination, with coefficients x, of elements from an overcomplete dictionary. While many algorithms are competit…
Study on signal recovery from low-rank matrix with sparse noise.
problem Inference of a rank-one signal in the presence of sparse noise.
method Replica method from statistical physics, recursive distributional equations, population dynamics algorithm.
result Critical signal strength for recovery via top eigenvector identified.
New lower bounds show sparse recovery is hard even with multiple preconditioners.
problem Sparse recovery with ill-conditioned designs is hard for certain algorithms.
method Constructing a single signal distribution that multiple preconditioned Lasso programs fail on.
result Standard sparse random designs are robust to erasures, aiding sparse recovery.
New method solves large-scale linear programming problems for sparse signal reconstruction.
problem Efficiently solving large-scale linear programming problems for sparse signal reconstruction.
method Combining constraint and column generation techniques with simplex method initialization.
result Highly efficient solutions for many settings.
Sparse coding in learned dictionaries has been established as a successful approach for signal denoising, source separation and solving inverse problems in general. A dictionary learning method adapts an initial dictionary to a particular signal class by iteratively computing an approximate factorization of a training …
Proposes a Monte-Carlo method for sparse signal reconstruction.
problem Reconstructing sparse signals in high-dimensional settings.
method Greedy Monte-Carlo (GMC) search algorithm.
result GMC can achieve perfect reconstruction in undersampling situations.