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Compressed sensing is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
Given sufficiently many components, it is often cited that finite mixture models can approximate any other probability density function (pdf) to an arbitrary degree of accuracy. Unfortunately, the nature of this approximation result is…
Quantization is an essential step in digitizing signals, and, therefore, an indispensable component of any modern acquisition system. This book chapter explores the interaction of quantization and compressive sensing and examines practical…
This paper proposes a new methodology to perform Bayesian inference for a class of multidimensional Cox processes in which the intensity function is piecewise constant. Poisson processes with piecewise constant intensity functions are…
We consider the fundamental learning problem of estimating properties of distributions over large domains. Using a novel piecewise-polynomial approximation technique, we derive the first unified methodology for constructing sample- and…
Devising optimal operating strategies for a compressor station relies on the knowledge of compressor characteristics. As the compressor characteristics change with time and use, it is necessary to provide accurate models of the…
In most compressive sensing problems l1 norm is used during the signal reconstruction process. In this article the use of entropy functional is proposed to approximate the l1 norm. A modified version of the entropy functional is continuous,…
In the first part of the work, the equivalence of quantum deterministic and probabilistic processors was investigated. A programmable quantum processor is a device able to transform input data states in a desired way. Deterministic…
A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is…
Compressive sensing is the newly emerging method in information technology that could impact array beamforming and the associated engineering applications. However, practical measurements are inevitably polluted by noise from external…
A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…
A number of engineering and scientific problems require representing and manipulating probability distributions over large alphabets, which we may think of as long vectors of reals summing to $1$. In some cases it is required to represent…
In this article we introduce a quasiprobability distribution of work that is based on the Wigner function. This construction rests on the idea that the work done on an isolated system can be coherently measured by coupling the system to a…
Diffusion models have become fundamental tools for modeling data distributions in machine learning. Despite their success, these models face challenges when generating data with extreme brightness values, as evidenced by limitations…
The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…
This paper considers the problem of estimating probabilities of the form $\mathbb{P}(Y \leq w)$, for a given value of $w$, in the situation that a sample of i.i.d.\ observations $X_1, \ldots, X_n$ of $X$ is available, and where we…
Based on the maximum likelihood estimation principle, we derive a collaborative estimation framework that fuses several different estimators and yields a better estimate. Applying it to compressive sensing (CS), we propose a collaborative…
Compressive sensing (CS) is a new methodology to capture signals at lower rate than the Nyquist sampling rate when the signals are sparse or sparse in some domain. The performance of CS estimators is analyzed in this paper using tools from…
A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally…
This paper presents new uniform Gaussian strong approximations for empirical processes indexed by classes of functions based on $d$-variate random vectors ($d\geq1$). First, a uniform Gaussian strong approximation is established for general…