The problem of minimization of the number of measurements needed for digital image acquisition and reconstruction with a given accuracy is addressed. Basics of the sampling theory are outlined to show that the lower bound of signal sampling rate sufficient for signal reconstruction with a given accuracy is equal to the spectrum sparsity of the signal sparse approximation that has this accuracy....

Interharmonics frequencies are not integer multiple of the fundamental frequency, and interharmonics amplitudes are far less than fundamental amplitude and harmonics amplitudes, which mean high sensitivity to desynchronization problems, so it’s dificult to estimate interharmonics. In this paper, a new method based on random sparse sampling and compressed sensing (CS) Bregman technique was propo...

Compressed Sensing (CS) is a novel sampling paradigm that tries to take data-compression concepts down to the sampling layer of a sensory system. It states that discrete compressible signals are recoverable from sub-sampled data, when the data vector is acquired by a special linear transform of the original discrete signal vector. Distributed sampling problems especially in Wireless Sensor Netw...

In order to solve storage and computation cost problems for the traditional whole sampling image fusion algorithms, a new method of infrared and visible light image fusion is put forward based on compressed sensing (CS) theory. Nonsubsampled shearlet transform (NSST) is introduced as the sparse transform. Compressed sensing is applied to fuse the high frequency subbands decomposed by NSST. The ...

We developed a novel method to accelerate diffusion spectrum imaging using compressed sensing. The method can be applied to either reduce acquisition time of diffusion spectrum imaging acquisition without losing critical information or to improve the resolution in diffusion space without increasing scan time. Unlike parallel imaging, compressed sensing can be applied to reconstruct a sub-Nyquis...

Ultra-wideband (UWB) communication systems can be used as overlay over existing systems due to their large absolute bandwidth and low power spectral density. But realization of UWB systems has been obstructed due to present state of art of A/D converters that are not able to meet the high sampling rate requirement of UWB systems. Compressed sensing appears to be a natural solution to develop sy...

Methodology is presented for the design of single and double compressed limit Sequential Probability Ratio Tests (SPRT) and Cumulative Sum (CUSUM) control charts to detect one-sided mean shifts in a symmetric probability distribution. We also show how to evaluate the average run length properties with the Fast Initial Response (FIR) feature. The resulting CUSUM plans have a simple scoring proce...

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 JP...

Classical compressed sensing (CS) allows us to recover structured signals from far few linear measurements than traditionally prescribed, thereby efficiently decreasing sampling rates. However, if there exist nonlinearities in the measurements, is it still possible to recover sparse or structured signals from the nonlinear measurements? The research of nonlinear CS is devoted to answering this ...

We introduce a mathematical framework that bridges a substantial gap between compressed sensing theory and its current use in real-world applications. Although completely general, one of the principal applications for our framework is the Magnetic Resonance Imaging (MRI) problem. Our theory provides a comprehensive explanation for the abundance of numerical evidence demonstrating the advantage ...