Related papers: Fast and Robust High-Dimensional Sparse Representa…

In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming…

Signal reconstruction in compressive sensing involves finding a sparse solution that satisfies a set of linear constraints. Several approaches to this problem have been considered in existing reconstruction algorithms. They each provide a…

Given an overcomplete dictionary $A$ and a signal $b$ that is a linear combination of a few linearly independent columns of $A$, classical sparse recovery theory deals with the problem of recovering the unique sparse representation $x$ such…

Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…

This paper presents an innovative approach to dimensionality reduction and feature extraction in high-dimensional datasets, with a specific application focus on wood surface defect detection. The proposed framework integrates sparse…

In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider $\ell_1$ penalty to enforce sparsity in such scenarios. Sparsity enforcing methods,…

Sparse recovery is widely applied in many fields, since many signals or vectors can be sparsely represented under some frames or dictionaries. Most of fast algorithms at present are based on solving $l^0$ or $l^1$ minimization problems and…

Learned Sparse Retrieval (LSR) has traditionally focused on small-scale encoder-only transformer architectures. With the advent of large-scale pre-trained language models, their capability to generate sparse representations for retrieval…

The sparse representation classifier (SRC) has been utilized in various classification problems, which makes use of L1 minimization and works well for image recognition satisfying a subspace assumption. In this paper we propose a new…

We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix $X$. These may come from corrupted data, persistent experimental…

In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures…

We investigate the problem of estimating the 3D shape of an object defined by a set of 3D landmarks, given their 2D correspondences in a single image. A successful approach to alleviating the reconstruction ambiguity is the 3D deformable…

This paper presents a variational based approach to fusing hyperspectral and multispectral images. The fusion process is formulated as an inverse problem whose solution is the target image assumed to live in a much lower dimensional…

We develop theoretical results that establish a connection across various regression methods such as the non-negative least squares, bounded variable least squares, simplex constrained least squares, and lasso. In particular, we show in…

Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…

In this paper, we propose a novel method for fast face recognition called L1/2 Regularized Sparse Representation using Hierarchical Feature Selection (HSR). By employing hierarchical feature selection, we can compress the scale and…

In this paper an extension of the sparse decomposition problem is considered and an algorithm for solving it is presented. In this extension, it is known that one of the shifted versions of a signal s (not necessarily the original signal…

In the field of face recognition, Sparse Representation (SR) has received considerable attention during the past few years. Most of the relevant literature focuses on holistic descriptors in closed-set identification applications. The…

There are a large number of methods for solving under-determined linear inverse problem. Many of them have very high time complexity for large datasets. We propose a new method called Two-Stage Sparse Representation (TSSR) to tackle this…

One of the most promising solutions for uncertainty quantification in high-dimensional statistics is the debiased LASSO that relies on unconstrained $\ell_1$-minimization. The initial works focused on real Gaussian designs as a toy model…