The wide-sense stationary-uncorrelated scattering (WSSUS) channel model is a commonly employed model for the multipath channel experienced in mobile communications. The second-order statistics of these channels are described by the delay cross-power density h (;1t) or by its 1t-Fourier transform, the scattering function S h (;). This paper presents an analysis of the delay cross-power density and scattering functions for mobile communications channels. We assume an arbitrary spatially uncorrelated scattering (US) field with arbitrary propagation-loss factors. Our first result is a general integral expression for h (;1t) that holds with both transmitter and receiver being mobile. We then derive more detailed results for the case of a stationary base station. We derive an infinite Bessel series for h (;1t) and a closed-form expression for S h (;). These results generalize the well-known classical approximation for the time-correlation function h (1t) def = h (;1t)d J 0 (2 m 1t), which corresponds to the zeroth term of our Bessel series.
We propose a new compressed sensing MRI approach that uses the discrete nonseparable shearlet transform (DNST) as a sparsifying transform and the fast iterative soft thresholding algorithm (FISTA) for reconstruction. FISTA has a simple design and has shown good convergence behavior. The DNST transform has excellent localization properties within the space domain and excellent directional selectivity. We utilize the frequency representation of the DNST canonical dual filters to obtain a memory efficient modified FISTA based algorithm with a simple and efficient way of calculating the update, tuned to the non tight frame DNST transform. The proposed approach shows improved performance and similar execution time when compared with other state of the art reconstruction approaches.Index Terms-Compressed sensing, discrete nonseparable shearlet transform (DNST), FISTA, MRI.
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