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Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming…
Compressed sensing (CS) is a powerful method routinely employed to accelerate image acquisition. It is particularly suited to situations when the image under consideration is sparse but can be sampled in a basis where it is non-sparse. Here…
As a paradigm to recover the sparse signal from a small set of linear measurements, compressed sensing (CS) has stimulated a great deal of interest in recent years. In order to apply the CS techniques to wireless communication systems,…
Compressed sensing is a novel research area, which was introduced in 2006, and since then has already become a key concept in various areas of applied mathematics, computer science, and electrical engineering. It surprisingly predicts that…
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…
Compressive sensing (CS) combines data acquisition with compression coding to reduce the number of measurements required to reconstruct a sparse signal. In optics, this usually takes the form of projecting the field onto sequences of random…
Wideband spectrum sensing is an essential part of cognitive radio systems. Exact spectrum estimation is usually inefficient as it requires sampling rates at or above the Nyquist rate. Using prior information on the structure of the signal…
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…
Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…
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 (CS) is well-known for its unique functionalities of sensing, compressing, and security (i.e. CS measurements are equally important). However, there is a tradeoff. Improving sensing and compressing efficiency with prior…
Compressed sensing (CS) provides an elegant framework for recovering sparse signals from compressed measurements. For example, CS can exploit the structure of natural images and recover an image from only a few random measurements. CS is…
Wideband spectrum sensing is a critical component of a functioning cognitive radio system. Its major challenge is the too high sampling rate requirement. Compressive sensing (CS) promises to be able to deal with it. Nearly all the current…
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…
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…
Recent advances in signal processing have focused on the use of sparse representations in various applications. A new field of interest based on sparsity has recently emerged: compressed sensing. This theory is a new sampling framework that…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
This paper describes performance bounds for compressed sensing (CS) where the underlying sparse or compressible (sparsely approximable) signal is a vector of nonnegative intensities whose measurements are corrupted by Poisson noise. In this…
In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is,…
Influence of the finite-length registers and quantization effects on the reconstruction of sparse and approximately sparse signals is analyzed in this paper. For the nonquantized measurements, the compressive sensing (CS) framework provides…