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 signal space, a geometric parameter independent of the specific signal and measurement, and logarithmic in the ambient dimension where the signal is pres...

The most popular lossy image compression method used on the Internet is the JPEG standard. JPEG's good compression performance and low computational and memory complexity make it an attractive method for natural image compression. Nevertheless, as we go to low bit rates that imply lower quality, JPEG introduces disturbing artifacts. It is known that, at low bit rates, a down-sampled image, when...

A problem is addressed of minimization of the number of measurements needed for image acquisition and reconstruction with a given accuracy. In last several years, the compressed sensing approach to solving this problem was advanced, which promises reducing the number of required measurements by means of obtaining sparse approximations of images. However, the number of measurements required by c...

Mathematical approaches refer to make quantitative descriptions, deductions and calculations through the use of mathematics concepts, approaches and techniques, then draw some new conclusions and foresee by mathematical analysis and judgement. In recent years, Compressed Sensing theory (CS) provides solutions in alleviating the huge amount of information demand in the pressure of signal samplin...

Recent developments of new medical treatment techniques put challenging demands on ultrasound imaging systems in terms of both image quality and raw data size. Traditional sampling methods result in very large amounts of data, thus, increasing demands on processing hardware and limiting the flexibility in the postprocessing stages. In this paper, we apply Compressed Sensing (CS) techniques to a...

Distributed compressed sensing is the extension of compressed sampling (CS) to sensor networks. The idea is to design a CS joint decoding scheme at the base station which exploits the inter-sensor correlations, in order to recover the whole observations from very few number of random measurements per node. Here, the questions are about modeling the correlations, design of the joint recovery alg...

In compressive sensing (CS) theory, as the number of samples is decreased below a minimum threshold, the average error of the recovery increases. Sufficient sampling is either required for quality reconstruction or the error is resignedly accepted. However, most CS work has not taken advantage of the inherent structure in a variety of signals relevant to engineering applications. Hence, this pa...

Compressed sensing is a new approach for acquiring signals. It captures and represents signals and images at a rate significantly below Nyquist rate. In certain areas like magnetic resonance imaging (MRI), it is urgent to reduce the time of the patients’ exposure in the electromagnetic radiation. Compressed sensing breaks the canonical rules and effectively reduces the sampling rate without los...

When the number of projections does not satisfy the Shannon/Nyquist sampling requirement, streaking artifacts are inevitable in x-ray computed tomography (CT) images reconstructed using filtered backprojection algorithms. In this letter, the spatial-temporal correlations in dynamic CT imaging have been exploited to sparsify dynamic CT image sequences and the newly proposed compressed sensing (C...

§ This work was supported by a Joint Research Grant of the British Council and the GSRT and by the EU ACTS project SCALAR (AC077). ABSTRACT An efficient down-sampling algorithm of DCT (discrete cosine transform) compressed images is presented in this communication. The algorithm operates directly on the compressed data, thus avoiding the need for decompressing, down-sampling in the spatial doma...