Related papers: Walsh Sampling with Incomplete Noisy Signals
Separating signals from an additive mixture may be an unnecessarily hard problem when one is only interested in specific properties of a given signal. In this work, we tackle simpler "statistical component separation" problems that focus on…
Shannon's secrecy system is studied in a setting, where both the legitimate decoder and the wiretapper have access to side information sequences correlated to the source, but the wiretapper receives both the coded information and the side…
We consider a statistical problem of detection of a signal with unknown energy in a multi-channel system, observed in a Gaussian noise. We assume that the signal can appear in the $k$-th channel with a known small prior probability…
This paper presents a tutorial for CS applications in communications networks. The Shannon's sampling theorem states that to recover a signal, the sampling rate must be as least the Nyquist rate. Compressed sensing (CS) is based on the…
The Shannon Noiseless coding theorem (the data-compression principle) asserts that for an information source with an alphabet $\mathcal X=\{0,\ldots ,\ell -1\}$ and an asymptotic equipartition property, one can reduce the number of stored…
We revisit the well-studied problem of estimating the Shannon entropy of a probability distribution, now given access to a probability-revealing conditional sampling oracle. In this model, the oracle takes as input the representation of a…
Manifold amount of video data gets generated every minute as we read this document, ranging from surveillance to broadcasting purposes. There are two roadblocks that restrain us from using this data as such, first being the storage which…
This paper presents a new method for signal reconstruction by leveraging sampled-data control theory. We formulate the signal reconstruction problem in terms of an analog performance optimization problem using a stable discrete-time filter.…
In this paper, we consider the problem of sparse signal detection based on partial support set estimation with compressive measurements in a distributed network. Multiple nodes in the network are assumed to observe sparse signals which…
In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation…
In the first part of this thesis, we discuss the algebraic approach to classical and quantum physics and develop information theoretic concepts within this setup. In the second part, we discuss the uncertainty principle in quantum…
Sampling of signals defined over the nodes of a graph is one of the crucial problems in graph signal processing. While in classical signal processing sampling is a well defined operation, when we consider a graph signal many new challenges…
We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are…
As an example of the recently-introduced concept of rate of innovation, signals that are linear combinations of a finite number of Diracs per unit time can be acquired by linear filtering followed by uniform sampling. However, in reality,…
Multiple stochastic signals possess inherent statistical correlations, yet conventional sampling methods that process each channel independently result in data redundancy. To leverage this correlation for efficient sampling, we model…
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…
Stochastic encoders for channel coding and lossy source coding are introduced with a rate close to the fundamental limits, where the only restriction is that the channel input alphabet and the reproduction alphabet of the lossy source code…
The sampling rate of input and output signals is known to play a critical role in the identification and control of dynamical systems. For slow-sampled continuous-time systems that do not satisfy the Nyquist-Shannon sampling condition for…
The detection and estimation of signals in noisy, limited data is a problem of interest to many scientific and engineering communities. We present a computationally simple, sample eigenvalue based procedure for estimating the number of…
Shannon's channel coding theorem describes the maximum possible rate of reliable information transfer through a classical noisy communication channel. It, together with the source coding theorem, characterizes lossless channel communication…