The focus of this paper is to consider the compressed sensing problem. It is stated that the compressed sensing theory, under certain conditions, helps relax the Nyquist sampling theory and takes smaller samples. One of the important tasks in this theory is to carefully design measurement matrix (sampling operator). Most existing methods in the literature attempt to optimize a randomly initiali...

the focus of this paper is to consider the compressed sensing problem. it is stated that the compressed sensing theory, under certain conditions, helps relax the nyquist sampling theory and takes smaller samples. one of the important tasks in this theory is to carefully design measurement matrix (sampling operator). most existing methods in the literature attempt to optimize a randomly initiali...

Compressed sensing and magnetic resonance imaging are hot topics in the field of signal processing. In this study we introduced in Lustig’s variable density sampling method, integrated it to compressed sensing, and applied it to brain MRI acquisition. The realistic experiment shows the variable density sampling recovery better than traditional random sampling method on a 256x256 brain magnetic ...

Magnetic Resonance Imaging (MRI) is a noninvasive imaging method widely used in medical diagnosis. Data in MRI are obtained line-by-line within the K-space, where there are usually a great number of such lines. For this reason, magnetic resonance imaging is slow. MRI can be accelerated through several methods such as parallel imaging and compressed sensing, where a fraction of the K-space lines...

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 sampling with subsequent data compression is prohibitive, there is at least one more efficient, in terms of data compression capability, and more simple and ...