Related papers: Dictionary Learning for the Almost-Linear Sparsity…

IR models using a pretrained language model significantly outperform lexical approaches like BM25. In particular, SPLADE, which encodes texts to sparse vectors, is an effective model for practical use because it shows robustness to…

Though the method of least squares has been used for a long time in solving signal processing problems, in the recent field of sparse recovery from compressed measurements, this method has not been given much attention. In this paper we…

Dictionary Learning (DL) is one of the leading sparsity promoting techniques in the context of image classification, where the "dictionary" matrix D of images and the sparse matrix X are determined so as to represent a redundant image…

In this paper, we study the problem of online sparse linear regression (OSLR) where the algorithms are restricted to accessing only $k$ out of $d$ attributes per instance for prediction, which was proved to be NP-hard. Previous work gave…

Greedy sparse recovery has become a popular tool in many applications, although its complexity is still prohibitive when large sparsifying dictionaries or sensing matrices have to be exploited. In this paper, we formulate first a new class…

Sparse recovery in linear systems underpins applications from signal processing to high-dimensional regression. Sparse Bayesian Learning, grounded in the principle of automatic relevance determination (ARD), offers a practical Bayesian…

Sparse approximations using highly over-complete dictionaries is a state-of-the-art tool for many imaging applications including denoising, super-resolution, compressive sensing, light-field analysis, and object recognition. Unfortunately,…

Given an overcomplete dictionary $A$ and a signal $b = Ac^*$ for some sparse vector $c^*$ whose nonzero entries correspond to linearly independent columns of $A$, classical sparse signal recovery theory considers the problem of whether…

In this work we show that iterative thresholding and K-means (ITKM) algorithms can recover a generating dictionary with K atoms from noisy $S$ sparse signals up to an error $\tilde \varepsilon$ as long as the initialisation is within a…

Sparsity-based models and techniques have been exploited in many signal processing and imaging applications. Data-driven methods based on dictionary and sparsifying transform learning enable learning rich image features from data, and can…

In this paper we consider asymptotically exact support recovery in the context of high dimensional and sparse Canonical Correlation Analysis (CCA). Our main results describe four regimes of interest based on information theoretic and…

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…

We demonstrate a simple greedy algorithm that can reliably recover a d-dimensional vector v from incomplete and inaccurate measurements x. Here our measurement matrix is an N by d matrix with N much smaller than d. Our algorithm,…

Phase retrieval aims at reconstructing unknown signals from magnitude measurements of linear mixtures. In this paper, we consider the phase retrieval with dictionary learning problem, which includes an additional prior information that the…

We present a sparse estimation and dictionary learning framework for compressed fiber sensing based on a probabilistic hierarchical sparse model. To handle severe dictionary coherence, selective shrinkage is achieved using a Weibull prior,…

Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…

Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience and signal processing. For signals such as natural images that admit such sparse…

Physics-driven deep learning (PD-DL) models have proven to be a powerful approach for improved reconstruction of rapid MRI scans. In order to train these models in scenarios where fully-sampled reference data is unavailable, self-supervised…

We study in this paper the improvement of one-class support vector machines (OC-SVM) through sparse representation techniques for unsupervised anomaly detection. As Dictionary Learning (DL) became recently a common analysis technique that…

We consider the problem of recovering a signal $\mathbf{x}^* \in \mathbf{R}^n$, from magnitude-only measurements $y_i = |\left\langle\mathbf{a}_i,\mathbf{x}^*\right\rangle|$ for $i=[m]$. Also called the phase retrieval, this is a…