CRsAE auto-encoder recovers convolutional dictionary from noisy signals.
problem Recovering a convolutional dictionary from noisy signals.
method Constrained recurrent sparse auto-encoder (CRsAE) architecture.
result CRsAE successfully recovers the underlying dictionary in the presence of noise.
NOODL solves dictionary and coefficient recovery for online learning.
problem Non-convex optimization challenges in dictionary learning.
method NOODL: Neurally plausible alternating Optimization-based Online Dictionary Learning.
result Exact recovery of dictionary and coefficients at geometric rate.
We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is a popular heuristic for sparse coding, where the dictionary and the coefficient…
A new method learns a sparse dictionary and optimizes its size for better image processing.
problem Choosing the right size of the dictionary for optimal performance.
method Employed a novel regularization method (GSCAD) combined with ADMM for simultaneous sparse dictionary learning and size selection.
result The method improves image denoising performance compared to existing approaches.
We ensure the stability and uniqueness of sparse coding dictionaries in noisy signals.
problem Stability and uniqueness of sparse coding dictionaries in noisy signals.
method Very general conditions guaranteeing stability and uniqueness of sparse coding dictionaries in the presence of noise.
result Recoverability of original dictionary elements from noisy data.
A parallel algorithm learns efficient Kronecker product dictionaries.
problem Sparse representation of 2D signals like images and hyperspectral data.
method Highly parallelizable algorithm for learning separable dictionaries.
result Competitive sparse representations at lower computational cost.
A new method for fiber sensing using sparse estimation and dictionary learning.
problem Compressed fiber sensing with severe dictionary coherence issues.
method Probabilistic hierarchical sparse model, selective shrinkage with Weibull prior, collective shrinkage based on local similarity, kernel function in joint prior density, hybrid inference technique (Hamilton Monte Carlo and Gibbs sampling), and two strategies for dictionary parameter estimation.
result Improved performance compared to existing methods in simulations and experiments.
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.
This work combines deep learning and sparse coding for CT image reconstruction.
problem Improving image quality in low-dose CT scans.
method Sparse signal representation using learned dictionaries, inspired by variational autoencoders and deep learning techniques.
result Regularization with learned dictionaries achieves competitive performance in CT reconstruction.
This work learns sparse tensor representations using mixtures of separable dictionaries.
problem Learning sparse representations of tensor data with structured models.
method Proposes and explores learning a mixture of separable dictionaries with sufficient conditions for local identifiability.
result Developed computational algorithms for batch and online learning.
Sparse representations using data dictionaries provide an efficient model particularly for signals that do not enjoy alternate analytic sparsifying transformations. However, solving inverse problems with sparsifying dictionaries can be computationally expensive, especially when the dictionary under consideration has a …
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 …
We consider the problem of learning overcomplete dictionaries in the context of sparse coding, where each sample selects a sparse subset of dictionary elements. Our main result is a strategy to approximately recover the unknown dictionary using an efficient algorithm. Our algorithm is a clustering-style procedure, wher…
New algorithms compare and improve convolutional dictionary learning methods.
problem Challenges in learning convolutional dictionaries.
method Comprehensive comparison and development of new algorithms.
result Identifies most effective methods for convolutional dictionary learning.
Sparse representations using learned dictionaries are being increasingly used with success in several data processing and machine learning applications. The availability of abundant training data necessitates the development of efficient, robust and provably good dictionary learning algorithms. Algorithmic stability an…
Unified analysis for robust PCA decomposition with sparse components in known dictionaries.
problem Robust PCA decomposition with sparse components in known dictionaries.
method Convex demixing method for undercomplete and overcomplete dictionary cases.
result Successful recovery of constituent components up to a certain global sparsity level.
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.
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 …
PUDLE method analyzes and improves unrolled sparse coding networks for dictionary learning.
problem Dictionary learning problem, representing data as a combination of few atoms.
method PUDLE method addresses challenges in unrolled sparse coding networks through theoretical analysis and practical strategies.
result PUDLE method provides conditions for recovering and preserving the support of the latent code, and resolves bias and instability issues.
OnAIR reconstructs dynamic images from sparse measurements online.
problem Reconstructing dynamic images from limited or corrupted measurements.
method Online adaptive reconstruction using sparsity and low-rank models with dictionary learning.
result Memory-efficient online algorithms for sequential estimation of dictionary and images.
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 proposes semi-supervised method for dictionary learning.
problem Learning from both labeled and unlabeled data.
method Uses semi-supervised dictionary learning with LLE for manifold preservation.
result Significant improvements over other methods demonstrated.
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 …
Efficient algorithm selects atoms from dictionaries with complex sparsity constraints.
problem Dictionary selection with complex sparsity constraints.
method Novel efficient greedy algorithm for dictionary selection.
result Outperforms known methods in faster running time and competitive performance.
LASSI models improve dynamic imaging from sparse data.
problem Efficiently reconstruct dynamic images from limited data.
method Data-adaptive decomposition of dynamic signals into low-rank and sparse components.
result LASSI models outperform existing methods in dynamic MRI reconstruction.
This paper studies CSDL's reconstruction risk and finds it consistent in the ultra-sparse setting.
problem The statistical properties of convolutional sparse dictionary learning (CSDL).
method Identifies the minimax convergence rate of CSDL in terms of reconstruction risk, upper bounds the risk of an established CSDL estimator, and proves a matching lower bound.
result Consistency in reconstruction risk is possible precisely in the ultra-sparse setting.
New algorithm recovers sparse signals from linearly sparse dictionaries efficiently.
problem Recovering sparse signals from linearly sparse dictionaries.
method Spectral method on reweighted covariance matrices.
result First polynomial-time algorithm for near-linear sparsity in overcomplete dictionaries.
Bayesian method improves dictionary learning for complex problems.
problem Efficiently identifying relevant dictionary entries for complex inverse problems.
method Bayesian group sparsity coding and deflation steps to compress and identify relevant subdictionaries.
result Significant computational complexity reduction and improved glitch detection in LIGO experiment.
We study the Dictionary Learning (aka Sparse Coding) problem of obtaining a sparse representation of data points, by learning \emph{dictionary vectors} upon which the data points can be written as sparse linear combinations. We view this problem from a geometry perspective as the spanning set of a subspace arrangement,…
A new tensor decomposition method using a dictionary for better interpretability.
problem Ensuring interpretability in tensor decomposition models.
method Dictionary-based tensor canonical polyadic decomposition with sparse coding.
result Improves parameter identifiability and estimation accuracy in tensor decomposition.
Paper sets limits on tensor data dictionary learning sample complexity.
problem Estimating atomic elements for tensor data with sparse representation.
method Proves minimax lower bound on sample complexity for Kronecker-structured dictionaries.
result Sample complexity for tensor data can be significantly lower than for unstructured data.
A-DLISTA and VLISTA learn dictionaries and sparse representations under varying sensing matrices.
problem Learning dictionaries and sparse representations under varying sensing matrices.
method Augmented Dictionary Learning ISTA (A-DLISTA) and Variational Learning ISTA (VLISTA).
result VLISTA provides a probabilistic way to jointly learn the dictionary distribution and the reconstruction algorithm.
This work improves SINDy-type algorithms for system identification using score-guided dictionary selection.
problem Improving accuracy and interpretability in dynamical system identification.
method Score-guided library selection to refine dictionary terms in sparse regression.
result Score-guided methods enhance SINDy's robustness in discovering governing equations.
A new method for subspace decomposition using an over-complete dictionary.
problem Signal subspace decomposition over dependent basis sets.
method Sparse Signal Subspace Decomposition (3SD) method based on an over-complete dictionary and novel criterion.
result Demonstrates high performance in image denoising.
The paper provides guarantees for an alternating minimization algorithm in dictionary learning.
problem Dictionary learning problem of factorizing samples into a basis and sparse vectors.
method Alternating minimization procedure switching between ℓ1 minimization and gradient descent. result Local convergence guarantees for the alternating minimization algorithm under a new matrix infinity norm condition.
New algorithm recovers dictionaries with arbitrary supports in polynomial time.
problem Learning dictionaries with arbitrary supports in polynomial time.
method Semirandom model with a mix of arbitrary and random supports; polynomial time algorithm.
result Polynomial time recovery of incoherent over-complete dictionaries with arbitrary supports.
DOLPHIn learns a dictionary for phase retrieval of images.
problem Phase retrieval of images from magnitude measurements.
method Jointly reconstructs and learns a dictionary for sparse representation.
result Significantly better reconstructions for noisy phase retrieval problems.
Performing signal processing tasks on compressive measurements of data has received great attention in recent years. In this paper, we extend previous work on compressive dictionary learning by showing that more general random projections may be used, including sparse ones. More precisely, we examine compressive K-mean…
The paper proposes a method to learn discriminative multilevel dictionaries for supervised image classification.
problem Improving sparse representation for supervised image classification.
method Learning structured multilevel dictionaries with discriminative constraints for each class, using reconstruction errors of image patches.
result Competitive results compared to state-of-the-art methods on texture image classification.
New algorithms learn sparse dictionaries from incomplete data.
problem Learning dictionaries from incomplete data.
method Iterative descent algorithm with initialization using extra samples.
result Provable polynomial-time algorithms for dictionary learning from incomplete data.
The paper proposes efficient dictionary learning algorithms that avoid multiplications for sparse representations.
problem Sparse representation with reduced computational complexity.
method Factorizations of the dictionary into binary orthonormal, scaling, and shear transformations with closed-form solutions.
result The proposed methods are effective and can be compared to well-known transforms like FFT and DCT.
MSBDL learns multimodal dictionaries with flexibility and superior performance.
problem Learning dictionaries for datasets from multiple data sources.
method Multimodal sparse Bayesian dictionary learning (MSBDL) with joint sparsity constraint.
result MSBDL outperforms existing methods on synthetic and real datasets.
Optimal dictionaries minimize the average squared error in representing random vectors.
problem Finding optimal dictionaries for minimizing ℓ2-norm of coefficients in random vector representations. method Using rank-1 decompositions of symmetric positive semidefinite matrices, explicit descriptions and polynomial-time algorithms for ℓ2-optimal dictionaries are provided. result Explicit descriptions and polynomial-time algorithms for ℓ2-optimal dictionaries are provided. Paper studies Frank-Wolfe algorithm for solving sparse reconstruction problems.
problem Sparse reconstruction problem
method Frank-Wolfe algorithm applied to quasi-incoherent dictionaries
result Algorithm converges exponentially fast for quasi-incoherent dictionaries
This work tackles sparse coding in DLRA for interpretable multiway data.
problem Sparse coding in DLRA for interpretable multiway data.
method Proposes a new sparse-coding subproblem (MSC) and several algorithms to solve it.
result DLRA extends low-rank approximations, reducing variance and enhancing interpretability.
Many signal processing and machine learning methods share essentially the same linear-in-the-parameter model, with as many parameters as available samples as in kernel-based machines. Sparse approximation is essential in many disciplines, with new challenges emerging in online learning with kernels. To this end, severa…
In sparse recovery we are given a matrix A (the dictionary) and a vector of the form AX where X is sparse, and the goal is to recover X. This is a central notion in signal processing, statistics and machine learning. But in applications such as sparse coding, edge detection, compression and super resolution, t…
Study analyzes feedback complexity for sparse feature retrieval in deep networks.
problem Learning sparse superposed features with feedback.
method Analysis of feedback complexity in sparse settings, including triplet comparisons.
result Establishes tight bounds and strong upper bounds for feature recovery.