Related papers: On Finite Alphabet Compressive Sensing
Grammar-based compression is a popular and powerful approach to compressing repetitive texts but until recently its relatively poor time-space trade-offs during real-life construction made it impractical for truly massive datasets such as…
Modern scientific instruments produce vast amounts of data, which can overwhelm the processing ability of computer systems. Lossy compression of data is an intriguing solution, but comes with its own drawbacks, such as potential signal…
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…
The Compressive Sensing framework maintains relevance even when the available measurements are subject to extreme quantization, as is exemplified by the so-called one-bit compressed sensing framework which aims to recover a signal from…
Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…
Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…
We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution…
Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding…
We introduce the broad subclass of algebraic compressed sensing problems, where structured signals are modeled either explicitly or implicitly via polynomials. This includes, for instance, low-rank matrix and tensor recovery. We employ…
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…
A new variant of the Compressed Sensing problem is investigated when the number of measurements corrupted by errors is upper bounded by some value l but there are no more restrictions on errors. We prove that in this case it is enough to…
What learning algorithms can be run directly on compressively-sensed data? In this work, we consider the question of accurately and efficiently computing low-rank matrix or tensor factorizations given data compressed via random projections.…
This work addresses the problem of extracting deeply learned features directly from compressive measurements. There has been no work in this area. Existing deep learning tools only give good results when applied on the full signal, that too…
Machine learning at the edge offers great benefits such as increased privacy and security, low latency, and more autonomy. However, a major challenge is that many devices, in particular edge devices, have very limited memory, weak…
The problem of storing a set of strings --- a string dictionary --- in compact form appears naturally in many cases. While classically it has represented a small part of the whole data to be processed (e.g., for Natural Language processing…
This paper investigates the problem of recovering the support of structured signals via adaptive compressive sensing. We examine several classes of structured support sets, and characterize the fundamental limits of accurately recovering…
In this paper we develop a general theory of compressed sensing for analog signals, in close similarity to prior results for vectors in finite dimensional spaces that are sparse in a given orthonormal basis. The signals are modeled by…
In this paper we consider Basis Pursuit De-Noising (BPDN) problems in which the sparse original signal is drawn from a finite alphabet. To solve this problem we propose an iterative message passing algorithm, which capitalises not only on…
The sparse signal recovery in the standard compressed sensing (CS) problem requires that the sensing matrix be known a priori. Such an ideal assumption may not be met in practical applications where various errors and fluctuations exist in…
Is it possible to detect a feature in an image without ever looking at it? Images are known to have sparser representation in Wavelets and other similar transforms. Compressed Sensing is a technique which proposes simultaneous acquisition…