Related papers: Can compressed sensing beat the Nyquist sampling r…
Lossy compressors are increasingly adopted in scientific research, tackling volumes of data from experiments or parallel numerical simulations and facilitating data storage and movement. In contrast with the notion of entropy in lossless…
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…
The task of compressed sensing is to recover a sparse vector from a small number of linear and non-adaptive measurements, and the problem of finding a suitable measurement matrix is very important in this field. While most recent works…
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…
Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling…
Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…
The theory of Compressed Sensing (CS) asserts that an unknown signal $x\in\mathbb{R}^p$ can be accurately recovered from an underdetermined set of $n$ linear measurements with $n\ll p$, provided that $x$ is sufficiently sparse. However, in…
Recently, sparsity has become a key concept in various areas of applied mathematics, computer science, and electrical engineering. One application of this novel methodology is the separation of data, which is composed of two (or more)…
Algorithms for rare event complex systems simulations are proposed. Compressed Sensing (CS) has {\it revolutionized} our understanding of limits in signal recovery and has forced us to re-define Shannon-Nyquist sampling theorem for sparse…
Deep neural network pruning and quantization techniques have demonstrated it is possible to achieve high levels of compression with surprisingly little degradation to test set accuracy. However, this measure of performance conceals…
The recently introduced theory of compressive sensing (CS) enables the reconstruction of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be…
The recovery of structured signals from a few linear measurements is a central point in both compressed sensing (CS) and discrete tomography. In CS the signal structure is described by means of a low complexity model e.g. co-/sparsity. The…
We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of…
The linear inverse source and scattering problems are studied from the perspective of compressed sensing, in particular the idea that sufficient incoherence and sparsity guarantee uniqueness of the solution. By introducing the sensor as…
Ultrashort time-domain spectroscopy and field-resolved spectroscopy of molecular fingerprints are gold standards for detecting samples' constituents and internal dynamics. However, they are hindered by the Nyquist criterion, leading to…
Compressed sensing is a promising technique that attempts to faithfully recover sparse signal with as few linear and nonadaptive measurements as possible. Its performance is largely determined by the characteristic of sensing matrix.…
Can compression algorithms be employed for recovering signals from their underdetermined set of linear measurements? Addressing this question is the first step towards applying compression algorithms for compressed sensing (CS). In this…
In the light of the progress in quantum technologies, the task of verifying the correct functioning of processes and obtaining accurate tomographic information about quantum states becomes increasingly important. Compressed sensing, a…
Sampling theories lie at the heart of signal processing devices and communication systems. To accommodate high operating rates while retaining low computational cost, efficient analog-to digital (ADC) converters must be developed. Many of…
Compressive Sensing (CS) theory shows that a signal can be decoded from many fewer measurements than suggested by the Nyquist sampling theory, when the signal is sparse in some domain. Most of conventional CS recovery approaches, however,…