Adaptive compressed MRI sampling based on wavelet encoding

Introduction: The main idea of Compressed Sensing is to exploit the fact that there is some structure and redundancy in most signals of interest. Clearly, the more we known about the signal and the more the information we encode into the signal processing algorithm, the better performance we can achieve. In this paper, we propose an adaptive compressed MRI sensing scheme that combined wavelet encoding with compressed sensing which originated from the optic image data acquisition [1]. Our approach exploits not only the fact that most of the wavelet coefficients of MR images are small but also the fact that values and locations of the large coefficients have a particular structure [2,3]. Exploiting the structure of the wavelet coefficients of MR images is achieved by replacing the pseudo-random measurements with a direct and fast method of adaptive wavelet coefficient acquisition. Theory: Given a low-pass scaling function and band-pass wavelet function ψ,