Sparse coding is typically solved by iterative optimization techniques, such as the Iterative Shrinkage-Thresholding Algorithm (ISTA). Unfolding and learning weights of ISTA using neural networks is a practical way to accelerate estimation. In this paper, we study the selection of adapted step sizes for ISTA. We show t…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
Trend · papers per month
23 results for “ISTA”
Paper analyzes adaptive ISTA with MAD for LASSO problem.
problem Finding solutions to LASSO problems without tuning .
method Adaptive ISTA with median absolute deviation (MAD) for estimating noise level.
result Local linear convergence and global convergence of the algorithm.
Iterative shrinkage/thresholding algorithm (ISTA) is a well-studied method for finding sparse solutions to ill-posed inverse problems. In this letter, we present a data-driven scheme for learning optimal thresholding functions for ISTA. The proposed scheme is obtained by relating iterations of ISTA to layers of a simpl…
The L1-regularized maximum likelihood estimation problem has recently become a topic of great interest within the machine learning, statistics, and optimization communities as a method for producing sparse inverse covariance estimators. In this paper, a proximal gradient method (G-ISTA) for performing L1-regularized co…
In recent years, unfolding iterative algorithms as neural networks has become an empirical success in solving sparse recovery problems. However, its theoretical understanding is still immature, which prevents us from fully utilizing the power of neural networks. In this work, we study unfolded ISTA (Iterative Shrinkage…
Paper shows linear convergence of ISTA and FISTA for ill-conditioned images.
problem Solving linear inverse problems with sparse representation in signal and image processing.
method Revisits iterative shrinkage-thresholding algorithms (ISTA) and improves their convergence properties.
result Linear convergence of ISTA and FISTA for strongly convex smooth parts, even in ill-conditioned cases.
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.
The paper accelerates ISTA and FISTA algorithms for composite optimization problems.
problem Improving convergence rates of ISTA and FISTA for composite optimization.
method Improved proximal subgradient norm minimization using Lyapunov function.
result Convergence rates of ISTA and FISTA are accelerated.
This review summarizes five Lasso optimization algorithms.
problem Optimizing the Lasso objective function.
method Five representative algorithms: ISTA, FISTA, CGDA, SLA, PFA.
result Comparison of convergence rates and strengths/weaknesses.
Parsimonious representations are ubiquitous in modeling and processing information. Motivated by the recent Multi-Layer Convolutional Sparse Coding (ML-CSC) model, we herein generalize the traditional Basis Pursuit problem to a multi-layer setting, introducing similar sparse enforcing penalties at different representat…
Improved neural network reconstruction from sparse measurements with theoretical guarantees.
problem Improving neural network performance in sparse signal reconstruction from few measurements.
method Combining iterative reconstruction algorithms with neural networks, analyzing generalization properties, and deriving a generalization bound.
result Theoretical guarantees for neural network reconstruction from compressive linear measurements, with generalization error scaling logarithmically in the number of layers and linearly in the number of measurements.
Deep learning has gained great popularity due to its widespread success on many inference problems. We consider the application of deep learning to the sparse linear inverse problem encountered in compressive sensing, where one seeks to recover a sparse signal from a small number of noisy linear measurements. In this p…
This work improves uncertainty estimates for LISTA estimators.
problem Lack of certainty estimates for LISTA estimators.
method Proposes a rigorous method to obtain confidence intervals for LISTA.
result Provides a way to quantify uncertainty for LISTA estimators.
Rank minimization (RM) is a wildly investigated task of finding solutions by exploiting low-rank structure of parameter matrices. Recently, solving RM problem by leveraging non-convex relaxations has received significant attention. It has been demonstrated by some theoretical and experimental work that non-convex relax…
Neurally Augmented ALISTA improves sparse reconstruction performance.
problem Improving sparse reconstruction performance with theoretical guarantees and empirical improvements.
method Integrates an LSTM network to compute adaptive step sizes and thresholds for each target vector during reconstruction.
result Empirical performance is further improved, especially as compression ratios become more challenging.
Model-based neural networks generalize better than ReLU networks for sparse recovery.
problem Understanding and quantifying the superior generalization of model-based neural networks.
method Using complexity measures like global and local Rademacher complexities, the paper provides theoretical bounds on generalization and estimation errors.
result Model-based neural networks exhibit higher generalization capabilities for sparse recovery problems compared to ReLU networks.
In this paper, we propose a novel recurrent neural network architecture for speech separation. This architecture is constructed by unfolding the iterations of a sequential iterative soft-thresholding algorithm (ISTA) that solves the optimization problem for sparse nonnegative matrix factorization (NMF) of spectrograms.…
Novel algorithm accelerates PnP methods for image deblurring and super-resolution.
problem Efficiently solving inverse problems and imaging with provable convergence guarantees.
method Incorporates quasi-Newton steps into provable PnP framework based on proximal denoisers.
result 2--8x faster convergence compared to other provable PnP methods with similar quality.
Sparse coding is a core building block in many data analysis and machine learning pipelines. Typically it is solved by relying on generic optimization techniques, that are optimal in the class of first-order methods for non-smooth, convex functions, such as the Iterative Soft Thresholding Algorithm and its accelerated …
Towards Understanding Residual and Dilated Dense Neural Networks via Convolutional Sparse Codingcs.LG
Convolutional neural network (CNN) and its variants have led to many state-of-art results in various fields. However, a clear theoretical understanding about them is still lacking. Recently, multi-layer convolutional sparse coding (ML-CSC) has been proposed and proved to equal such simply stacked networks (plain networ…
Sparse coding is a core building block in many data analysis and machine learning pipelines. Typically it is solved by relying on generic optimization techniques, such as the Iterative Soft Thresholding Algorithm and its accelerated version (ISTA, FISTA). These methods are optimal in the class of first-order methods fo…
Sparse high dimensional graphical model selection is a popular topic in contemporary machine learning. To this end, various useful approaches have been proposed in the context of -penalized estimation in the Gaussian framework. Though many of these inverse covariance estimation approaches are demonstrably scala…
Proposes a novel neural architecture for sparse coding using learned greedy pursuit.
problem Lack of interpretability in neural network architectures for sparse coding.
method Unfolded and learned version of Orthogonal Matching Pursuit (OMP) algorithm.
result Demonstrates flexibility and efficiency of the Learned Greedy Method (LGM) in various experiments.