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With the objective of employing graphs toward a more generalized theory of signal processing, we present a novel sampling framework for (wavelet-)sparse signals defined on circulant graphs which extends basic properties of Finite Rate 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…
This work concerns sampling of smooth signals on arbitrary graphs. We first study a structured sampling strategy for such smooth graph signals that consists of a random selection of few pre-defined groups of nodes. The number of groups to…
A central limitation of multiple-acquisition magnetic resonance imaging (MRI) is the degradation in scan efficiency as the number of distinct datasets grows. Sparse recovery techniques can alleviate this limitation via randomly undersampled…
We study signal recovery on graphs based on two sampling strategies: random sampling and experimentally designed sampling. We propose a new class of smooth graph signals, called approximately bandlimited, which generalizes the bandlimited…
In this paper, we propose a general framework for designing sensing matrix $\boldsymbol{A} \in \mathbb{R}^{d\times p}$, for estimation of sparse covariance matrix from compressed measurements of the form $\boldsymbol{y} =…
de Bruijn graph-based algorithms are one of the two most widely used approaches for de novo genome assembly. A major limitation of this approach is the large computational memory space requirement to construct the de Bruijn graph, which…
The sampling of graph signals has recently drawn much attention due to the wide applications of graph signal processing. While a lot of efficient methods and interesting results have been reported to the sampling of band-limited or smooth…
We revisit the probabilistic construction of sparse random matrices where each column has a fixed number of nonzeros whose row indices are drawn uniformly at random with replacement. These matrices have a one-to-one correspondence with the…
We show that the symmetries of image formation by scattering enable graph-theoretic manifold-embedding techniques to extract structural and timing information from simulated and experimental snapshots at extremely low signal. The approach…
In recent years, a variety of randomized constructions of sketching matrices have been devised, that have been used in fast algorithms for numerical linear algebra problems, such as least squares regression, low-rank approximation, and the…
We propose and analyze a novel framework for learning sparse representations, based on two statistical techniques: kernel smoothing and marginal regression. The proposed approach provides a flexible framework for incorporating feature…
Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…
Linear sketching and recovery of sparse vectors with randomly constructed sparse matrices has numerous applications in several areas, including compressive sensing, data stream computing, graph sketching, and combinatorial group testing.…
Sparse autoencoders (SAEs) have become central to mechanistic interpretability, decomposing transformer activations into monosemantic features. Yet existing analyses characterise features almost exclusively through top-activating token…
Atomistic simulations are employed to study structural evolution of pore ensembles in binary glasses under periodic shear deformation with varied amplitude. The consideration is given to porous systems in the limit of low porosity. The…
In this paper we study the compressive sensing effects on 2D signals exhibiting sparsity in 2D DFT domain. A simple algorithm for reconstruction of randomly under-sampled data is proposed. It is based on the analytically determined…
Compressive sensing is an impressive approach for fast MRI. It aims at reconstructing MR image using only a few under-sampled data in k-space, enhancing the efficiency of the data acquisition. In this study, we propose to learn priors based…
In this work, we investigate the sampling and reconstruction of spectrally $s$-sparse bandlimited graph signals governed by heat diffusion processes. We propose a random space-time sampling regime, referred to as {randomized} dynamical…
In this paper, we present several density-type theorems which show how to find a copy of a sparse bipartite graph in a graph of positive density. Our results imply several new bounds for classical problems in graph Ramsey theory and improve…