On compressed sensing image reconstruction using linear prediction in adaptive filtering

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.