相关论文: Analysis vs. synthesis sparsity for $\alpha$-shear…

In this paper two novel possibilistic clustering algorithms are presented, which utilize the concept of sparsity. The first one, called sparse possibilistic c-means, exploits sparsity and can deal well with closely located clusters that may…

We study statistical and computational limits of clustering when the means of the centres are sparse and their dimension is possibly much larger than the sample size. Our theoretical analysis focuses on the model $X_i = z_i \theta +…

A common task in inverse problems and imaging is finding a solution that is sparse, in the sense that most of its components vanish. In the framework of compressed sensing, general results guaranteeing exact recovery have been proven. In…

We assume the direct sum <A> o <B> for the signal subspace. As a result of post- measurement, a number of operational contexts presuppose the a priori knowledge of the LB -dimensional "interfering" subspace <B> and the goal is to estimate…

We propose a probe for the analysis of deep learning architectures that is based on machine learning and approximation theoretical principles. Given a deep learning architecture and a training set, during or after training, the Sparsity…

Recently introduced inpainting algorithms using a combination of applied harmonic analysis and compressed sensing have turned out to be very successful. One key ingredient is a carefully chosen representation system which provides…

In this paper, we propose an interesting semi-sparsity smoothing algorithm based on a novel sparsity-inducing optimization framework. This method is derived from the multiple observations that semi-sparsity prior knowledge is more…

A traditional assumption underlying most data converters is that the signal should be sampled at a rate exceeding twice the highest frequency. This statement is based on a worst-case scenario in which the signal occupies the entire…

A coreset for a set of points is a small subset of weighted points that approximately preserves important properties of the original set. Specifically, if $P$ is a set of points, $Q$ is a set of queries, and $f:P\times Q\to\mathbb{R}$ is a…

Applying compressive sensing (CS) allows for sub-Nyquist sampling in several application areas in 5G and beyond. This reduces the associated training, feedback, and computation overheads in many applications. However, the applicability of…

The sparse modeling is an evident manifestation capturing the parsimony principle just described, and sparse models are widespread in statistics, physics, information sciences, neuroscience, computational mathematics, and so on. In…

Many image processing applications benefited remarkably from the theory of sparsity. One model of sparsity is the cosparse analysis one. It was shown that using l_1-minimization one might stably recover a cosparse signal from a small set of…

In many signal processing applications, one wishes to acquire images that are sparse in transform domains such as spatial finite differences or wavelets using frequency domain samples. For such applications, overwhelming empirical evidence…

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is,…

Sparse connectivity is a hallmark of the brain and a desired property of artificial neural networks. It promotes energy efficiency, simplifies training, and enhances the robustness of network function. Thus, a detailed understanding of how…

Sparsity is a desirable attribute. It can lead to more efficient and more effective representations compared to the dense model. Meanwhile, learning sparse latent representations has been a challenging problem in the field of computer…

We propose a novel regularization method for compressive imaging in the context of the compressed sensing (CS) theory with coherent and redundant dictionaries. Natural images are often complicated and several types of structures can be…

Shapley values, a gold standard for feature attribution in Explainable AI, face two key challenges. First, the canonical Shapley framework assumes that the worth function is additive, yet real-world payoff constructions--driven by…

This thesis presents two similarity-based approaches to sparse data problems. The first approach is to build soft, hierarchical clusters: soft, because each event belongs to each cluster with some probability; hierarchical, because cluster…

We study Fourier-sparse Boolean functions over general finite Abelian groups. A Boolean function $f : G \to \{-1,+1\}$ is $s$-sparse if it has at most $s$ non-zero Fourier coefficients. We introduce a general notion of granularity of…