Related papers: Towards Learning Sparsely Used Dictionaries with A…
State-of-the-art learned reconstruction methods often rely on black-box modules that, despite their strong performance, raise questions about their interpretability and robustness. Here, we build on a recently proposed image reconstruction…
Periodic signals composed of periodic mixtures admit sparse representations in nested periodic dictionaries (NPDs). Therefore, their underlying hidden periods can be estimated by recovering the exact support of said representations. In this…
A method for online tensor dictionary learning is proposed. With the assumption of separable dictionaries, tensor contraction is used to diminish a $N$-way model of $\mathcal{O}\left(L^N\right)$ into a simple matrix equation of…
We propose a new outline for adaptive dictionary learning methods for sparse encoding based on a hierarchical clustering of the training data. Through recursive application of a clustering method, the data is organized into a binary…
Sparsity and low-rank models have been popular for reconstructing images and videos from limited or corrupted measurements. Dictionary or transform learning methods are useful in applications such as denoising, inpainting, and medical image…
Dictionary learning aims at seeking a dictionary under which the training data can be sparsely represented. Methods in the literature typically formulate the dictionary learning problem as an optimization w.r.t. two variables, i.e.,…
We describe a method for automatic word sense disambiguation using a text corpus and a machine-readable dictionary (MRD). The method is based on word similarity and context similarity measures. Words are considered similar if they appear in…
We study the problem of recovering an incomplete $m\times n$ matrix of rank $r$ with columns arriving online over time. This is known as the problem of life-long matrix completion, and is widely applied to recommendation system, computer…
Big data has become a critically enabling component of emerging mathematical methods aimed at the automated discovery of dynamical systems, where first principles modeling may be intractable. However, in many engineering systems, abrupt…
In "Dictionary Learning" one tries to recover incoherent matrices $A^* \in \mathbb{R}^{n \times h}$ (typically overcomplete and whose columns are assumed to be normalized) and sparse vectors $x^* \in \mathbb{R}^h$ with a small support of…
A nonnegative matrix factorization (NMF) can be computed efficiently under the separability assumption, which asserts that all the columns of the given input data matrix belong to the cone generated by a (small) subset of them. The provably…
Sparse dictionary learning (DL) has emerged as a powerful approach to extract semantically meaningful concepts from the internals of large language models (LLMs) trained mainly in the text domain. In this work, we explore whether DL can…
This paper proposes a novel algorithm for image phase retrieval, i.e., for recovering complex-valued images from the amplitudes of noisy linear combinations (often the Fourier transform) of the sought complex images. The algorithm is…
The dictionary learning problem can be viewed as a data-driven process to learn a suitable transformation so that data is sparsely represented directly from example data. In this paper, we examine the problem of learning a dictionary that…
Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…
Auto-Encoders are unsupervised models that aim to learn patterns from observed data by minimizing a reconstruction cost. The useful representations learned are often found to be sparse and distributed. On the other hand, compressed sensing…
Dictionary learning is traditionally formulated as an $L_1$-regularized signal reconstruction problem. While recent developments have incorporated discriminative, hierarchical, or generative structures, most approaches rely on encouraging…
The thresholded feature has recently emerged as an extremely efficient, yet rough empirical approximation, of the time-consuming sparse coding inference process. Such an approximation has not yet been rigorously examined, and standard…
Finding the sparse representation of a signal in an overcomplete dictionary has attracted a lot of attention over the past years. This paper studies ProSparse, a new polynomial complexity algorithm that solves the sparse representation…
Consider the problem of recovering an unknown signal from undersampled measurements, given the knowledge that the signal has a sparse representation in a specified dictionary $D$. This problem is now understood to be well-posed and…