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We introduce a novel uncertainty principle for generalized graph signals that extends classical time-frequency and graph uncertainty principles into a unified framework. By defining joint vertex-time and spectral-frequency spreads, we…
The detection of periodic signals in irregularly-sampled time series is a problem commonly encountered in astronomy. Traditional tools used for periodic searches, such as the periodogram, have poorly defined statistical properties under…
Many modern data analysis algorithms either assume that or are considerably more efficient if the distances between the data points satisfy a metric. These algorithms include metric learning, clustering, and dimensionality reduction.…
Adaptive sampling results in dramatic improvements in the recovery of sparse signals in white Gaussian noise. A sequential adaptive sampling-and-refinement procedure called Distilled Sensing (DS) is proposed and analyzed. DS is a form of…
In this paper, we present an approach to the reconstruction of signals exhibiting sparsity in a transformation domain, having some heavily disturbed samples. This sparsity-driven signal recovery exploits a carefully suited random sampling…
This paper addresses the reconstruction of an unknown signal vector with sublinear sparsity from generalized linear measurements. Generalized approximate message-passing (GAMP) is proposed via state evolution in the sublinear sparsity…
Linear inverse problems are ubiquitous in various science and engineering disciplines. Of particular importance in the past few decades, is the incorporation of sparsity based priors, in particular $\ell_1$ priors, into linear inverse…
One of the key challenges in sensor networks is the extraction of information by fusing data from a multitude of distinct, but possibly unreliable sensors. Recovering information from the maximum number of dependable sensors while…
In this paper, we present a convergence analysis of the Group Projected Subspace Pursuit (GPSP) algorithm proposed by He et al. [HKL+23] (Group Projected subspace pursuit for IDENTification of variable coefficient differential equations…
We consider the problem of robustly testing the norm of a high-dimensional sparse signal vector under two different observation models. In the first model, we are given $n$ i.i.d. samples from the distribution…
Partial differential equations are central to describing many physical phenomena. In many applications these phenomena are observed through a sensor network, with the aim of inferring their underlying properties. Leveraging from certain…
The Gini Multidimensional Scaling (Gini MDS) framework extends the Euclidean multidimensional scaling. We introduce a Gini pseudo-distance based on values and their ranks that depends on a fine-tunable hyperparameter. This pseudo-distance…
We investigate the recovery of signals exhibiting a sparse representation in a general (i.e., possibly redundant or incomplete) dictionary that are corrupted by additive noise admitting a sparse representation in another general dictionary.…
Inverse problems describe the process of estimating the causal factors from a set of measurements or data. Mapping of often incomplete or degraded data to parameters is ill-posed, thus data-driven iterative solutions are required, for…
The recovery of sparsest overcomplete representation has recently attracted intensive research activities owe to its important potential in the many applied fields such as signal processing, medical imaging, communication, and so on. This…
In the social sciences, small- to medium-scale datasets are common, and linear regression is canonical. In privacy-aware settings, much work has focused on differentially private (DP) linear regression, but mostly on point estimation with…
Most compressed sensing algorithms do not account for the effect of saturation in noisy compressed measurements, though saturation is an important consequence of the limited dynamic range of existing sensors. The few algorithms that handle…
Divergence measures play a central role and become increasingly essential in deep learning, yet efficient measures for multiple (more than two) distributions are rarely explored. This becomes particularly crucial in areas where the…
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,…
Deep Neural Networks(DNN) have excessively advanced the field of computer vision by achieving state of the art performance in various vision tasks. These results are not limited to the field of vision but can also be seen in speech…