# Biblio

Compressed sensing (CS) or compressive sampling deals with reconstruction of signals from limited observations/ measurements far below the Nyquist rate requirement. This is essential in many practical imaging system as sampling at Nyquist rate may not always be possible due to limited storage facility, slow sampling rate or the measurements are extremely expensive e.g. magnetic resonance imaging (MRI). Mathematically, CS addresses the problem for finding out the root of an unknown distribution comprises of unknown as well as known observations. Robbins-Monro (RM) stochastic approximation, a non-parametric approach, is explored here as a solution to CS reconstruction problem. A distance based linear prediction using the observed measurements is done to obtain the unobserved samples followed by random noise addition to act as residual (prediction error). A spatial domain adaptive Wiener filter is then used to diminish the noise and to reveal the new features from the degraded observations. Extensive simulation results highlight the relative performance gain over the existing work.

Compressed Sensing or Compressive Sampling is the process of signal reconstruction from the samples obtained at a rate far below the Nyquist rate. In this work, Differential Pulse Coded Modulation (DPCM) is coupled with Block Based Compressed Sensing (CS) reconstruction with Robbins Monro (RM) approach. RM is a parametric iterative CS reconstruction technique. In this work extensive simulation is done to report that RM gives better performance than the existing DPCM Block Based Smoothed Projected Landweber (SPL) reconstruction technique. The noise seen in Block SPL algorithm is not much evident in this non-parametric approach. To achieve further compression of data, Lempel-Ziv-Welch channel coding technique is proposed.

This paper addresses the issue of magnetic resonance (MR) Image reconstruction at compressive sampling (or compressed sensing) paradigm followed by its segmentation. To improve image reconstruction problem at low measurement space, weighted linear prediction and random noise injection at unobserved space are done first, followed by spatial domain de-noising through adaptive recursive filtering. Reconstructed image, however, suffers from imprecise and/or missing edges, boundaries, lines, curvatures etc. and residual noise. Curvelet transform is purposely used for removal of noise and edge enhancement through hard thresholding and suppression of approximate sub-bands, respectively. Finally Genetic algorithms (GAs) based clustering is done for segmentation of sharpen MR Image using weighted contribution of variance and entropy values. Extensive simulation results are shown to highlight performance improvement of both image reconstruction and segmentation problems.