Biblio

Signals get sampled using Nyquist rate in conventional sampling method, but in compressive sensing the signals sampled below Nyquist rate by randomly taking the signal projections and reconstructing it out of very few estimations. But in case of recovering the image by utilizing compressive measurements with the help of multi-resolution grid where the image has certain region of interest (RoI) that is more important than the rest, it is not efficient. The conventional Cartesian sampling cannot give good result in motion image sensing recovery and is limited to stationary image sensing process. The proposed work gives improved results by using Radial sampling (a type of compression sensing). This paper discusses the approach of Radial sampling along with the application of Sparse Fourier Transform algorithms that helps in reducing acquisition cost and input/output overhead.

This paper proposes a fast and robust procedure for sensing and reconstruction of sparse or compressible magnetic resonance images based on the compressive sampling theory. The algorithm starts with incoherent undersampling of the k-space data of the image using a random matrix. The undersampled data is sparsified using Haar transformation. The Haar transform coefficients of the k-space data are then reconstructed using the orthogonal matching Pursuit algorithm. The reconstructed coefficients are inverse transformed into k-space data and then into the image in spatial domain. Finally, a median filter is used to suppress the recovery noise artifacts. Experimental results show that the proposed procedure greatly reduces the image data acquisition time without significantly reducing the image quality. The results also show that the error in the reconstructed image is reduced by median 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.