Related papers: Generalized sampling: stable reconstructions, inve…
The problem of compressing a real-valued sparse source using compressive sensing techniques is studied. The rate distortion optimality of a coding scheme in which compressively sensed signals are quantized and then reconstructed is…
Compressed Sensing (CS) is an appealing framework for applications such as Magnetic Resonance Imaging (MRI). However, up-to-date, the sensing schemes suggested by CS theories are made of random isolated measurements, which are usually…
Recently efforts have been made to use generalized sinc functions to perfectly reconstruct various kinds of non-bandlimited signals. As a consequence, perfect reconstruction sampling formulas have been established using such generalized…
Numerous applications in signal processing have benefited from the theory of compressed sensing which shows that it is possible to reconstruct signals sampled below the Nyquist rate when certain conditions are satisfied. One of these…
Compressive sensing achieves effective dimensionality reduction of signals, under a sparsity constraint, by means of a small number of random measurements acquired through a sensing matrix. In a signal processing system, the problem arises…
Magnetic Resonance Imaging (MRI) is a kind of medical imaging technology used for diagnostic imaging of diseases, but its image quality may be suffered by the long acquisition time. The compressive sensing (CS) based strategy may decrease…
Compressive sensing is a signal acquisition framework based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable recovery. In this paper we introduce a new theory for…
With the development of numbers of high resolution data acquisition systems and the global requirement to lower the energy consumption, the development of efficient sensing techniques becomes critical. Recently, Compressed Sampling (CS)…
Generative models have emerged as powerful priors for solving inverse problems. These models typically represent a class of natural signals using a single fixed complexity or dimensionality. This can be limiting: depending on the problem, a…
We consider the problem of reconstructing signals and images from periodic nonlinearities. For such problems, we design a measurement scheme that supports efficient reconstruction; moreover, our method can be adapted to extend to…
Compressed sensing is a paradigm within signal processing that provides the means for recovering structured signals from linear measurements in a highly efficient manner. Originally devised for the recovery of sparse signals, it has become…
Existing convex relaxation-based approaches to reconstruction in compressed sensing assume that noise in the measurements is independent of the signal of interest. We consider the case of noise being linearly correlated with the signal and…
The problem of high-dimensional and large-scale representation of visual data is addressed from an unsupervised learning perspective. The emphasis is put on discrete representations, where the description length can be measured in bits and…
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 is a new methodology for constructing sensors which allow sparse signals to be efficiently recovered using only a small number of observations. The recovery problem can often be stated as the one of finding the solution…
Measurement samples are often taken in various monitoring applications. To reduce the sensing cost, it is desirable to achieve better sensing quality while using fewer samples. Compressive Sensing (CS) technique finds its role when the…
Compressive sensing(CS) has drawn much attention in recent years due to its low sampling rate as well as high recovery accuracy. As an important procedure, reconstructing a sparse signal from few measurement data has been intensively…
We present a general sample reweighting scheme and its underlying theory for the integration of an unknown function with low dimensionality. Our method produces better results than standard weighting schemes for common sampling strategies,…
Compressive Sensing theory says that it is possible to reconstruct a measured signal if an enough sparse representation of this signal exists in comparison to the number of random measurements. This theory was applied to reconstruct signals…
In many linear inverse problems, we want to estimate an unknown vector belonging to a high-dimensional (or infinite-dimensional) space from few linear measurements. To overcome the ill-posed nature of such problems, we use a low-dimension…