Related papers: Can compressed sensing beat the Nyquist sampling r…
Data compression capability of "Compressed sensing (sampling)" in signal discretization is numerically evaluated and found to be far from the theoretical upper bound defined by signal sparsity. It is shown that, for the cases when ordinary…
Compressed sensing is a signal processing technique that allows for the reconstruction of a signal from a small set of measurements. The key idea behind compressed sensing is that many real-world signals are inherently sparse, meaning that…
Compressed sensing is a signal processing technique whereby the limits imposed by the Shannon--Nyquist theorem can be exceeded provided certain conditions are imposed on the signal. Such conditions occur in many real-world scenarios, and…
The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an…
As an alternative to the traditional sampling theory, compressed sensing allows acquiring much smaller amount of data, still estimating the spectra of frequency-sparse signals accurately. However, compressed sensing usually requires random…
We survey a new paradigm in signal processing known as "compressive sensing". Contrary to old practices of data acquisition and reconstruction based on the Shannon-Nyquist sampling principle, the new theory shows that it is possible to…
Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…
The fundamental principle underlying compressed sensing is that a signal, which is sparse under some basis representation, can be recovered from a small number of linear measurements. However, prior knowledge of the sparsity basis is…
Spectrum sensing research has mostly been focusing on narrowband access, and not until recently have researchers started looking at wideband spectrum. Broadly speaking, wideband spectrum sensing approaches can be categorized into two…
This article extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a…
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…
Compressed sensing is a scheme that allows for sparse signals to be acquired, transmitted and stored using far fewer measurements than done by conventional means employing Nyquist sampling theorem. Since many naturally occurring signals are…
In compressed sensing, we wish to reconstruct a sparse signal $x$ from observed data $y$. In sparse coding, on the other hand, we wish to find a representation of an observed signal $y$ as a sparse linear combination, with coefficients $x$,…
Spectroscopy sampling along delay time is typically performed with uniform delay spacing, which has to be low enough to satisfy the Nyquist-Shannon sampling theorem. The sampling theorem puts the lower bound for the sampling rate to ensure…
In compressed sensing, one wishes to acquire an approximately sparse high-dimensional signal $x\in\mathbb{R}^n$ via $m\ll n$ noisy linear measurements, then later approximately recover $x$ given only those measurement outcomes. Various…
We discuss the applicability of compressed sensing theory. We take a genuine look at both experimental results and theoretical works. We answer the following questions: 1) What can compressed sensing really do? 2) More importantly, why?
An intriguing phenomenon in many instances of compressed sensing is that the reconstruction quality is governed not just by the overall sparsity of the signal, but also on its structure. This paper is about understanding this phenomenon,…
A range of efficient wireless processes and enabling techniques are put under a magnifier glass in the quest for exploring different manifestations of correlated processes, where sub-Nyquist sampling may be invoked as an explicit benefit of…
Compressed Sensing decoding algorithms can efficiently recover an N dimensional real-valued vector x to within a factor of its best k-term approximation by taking m = 2klog(N/k) measurements y = Phi x. If the sparsity or approximate…
The theory of Compressed Sensing, the emerging sampling paradigm 'that goes against the common wisdom', asserts that 'one can recover signals in Rn from far fewer samples or measurements, if the signal has a sparse representation in some…