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Sparsity is a ubiquitous feature of many real world signals such as natural images and neural spiking activities. Conventional compressed sensing utilizes sparsity to recover low dimensional signal structures in high ambient dimensions…
Compressed sensing is a technique for recovering a high-dimensional signal from lower-dimensional data, whose components represent partial information about the signal, utilizing prior knowledge on the sparsity of the signal. For further…
B. Schumacher and M. Westmoreland have established a quantum analog of a well-known classical information theory result on a role of relative entropy as a measure of non-optimality in (classical) data compression. In this paper, we provide…
Much research in stringology focuses on structures that can, in a way, ``grasp'' repeats (substrings that occur multiple times) as, for example, the so-called runs, a.k.a. maximal repetitions, compactly describe all tandem repeats. In this…
The past decade has witnessed substantial developments in string solving. Motivated by the complexity of string solving strategies adopted in existing string solvers, we investigate a simple and generic method for solving string…
In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to…
Here we study the complexity of string problems as a function of the size of a program that generates input. We consider straight-line programs (SLP), since all algorithms on SLP-generated strings could be applied to processing…
While dense retrieval models, which embed queries and documents into a shared low-dimensional space, have gained widespread popularity, they were shown to exhibit important theoretical limitations and considerably lag behind traditional…
Dense Retrieval (DR) has achieved state-of-the-art first-stage ranking effectiveness. However, the efficiency of most existing DR models is limited by the large memory cost of storing dense vectors and the time-consuming nearest neighbor…
It is known that modeling an information source via a symbolic dynamical system evolving over the unit interval, leads to a natural lossless compression scheme attaining the entropy rate of the source, under general conditions. We extend…
Sparse representation has attracted great attention because it can greatly save storage resources and find representative features of data in a low-dimensional space. As a result, it may be widely applied in engineering domains including…
Motivated by mass-spectrometry protein sequencing, we consider a simply-stated problem of reconstructing a string from the multiset of its substring compositions. We show that all strings of length 7, one less than a prime, or one less than…
Sparse recovery and subset selection are fundamental problems in varied communities, including signal processing, statistics and machine learning. Herein, we focus on an important greedy algorithm for these problems: Backward Stepwise…
The rise of internet has resulted in an explosion of data consisting of millions of articles, images, songs, and videos. Most of this data is high dimensional and sparse. The need to perform an efficient search for similar objects in such…
Sampling and quantization are standard practices in signal and image processing, but a theoretical understanding of their impact is incomplete. We consider discrete image registration when the underlying function is a one-dimensional…
Deep Neural Networks have achieved remarkable success relying on the developing availability of GPUs and large-scale datasets with increasing network depth and width. However, due to the expensive computation and intensive memory,…
Dynamic tracking of sparse targets has been one of the important topics in array signal processing. Recently, compressed sensing (CS) approaches have been extensively investigated as a new tool for this problem using partial support…
Conventional compressed sensing theory assumes signals have sparse representations in a known, finite dictionary. Nevertheless, in many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the…
This paper is concerned with the lossy compression of general random variables, specifically with rate-distortion theory and quantization of random variables taking values in general measurable spaces such as, e.g., manifolds and fractal…
The primary goal of this work is to review the importance of data compression and present a fast Fourier-based method for generating the deterministic compression matrix in the area of deterministic compressed sensing. The principle…