Fast Compressed Sensing Reconstruction Using a Direct Fourier-Wavelet Transform

KyungHyun Sung¹, Brian Andrew Hargreaves²

High computational complexity is one major issue for compressed sensing (CS) reconstruction. We present a new way to reduce the computational complexity for the CS reconstruction by directly transforming between k-space and wavelet domains. This replaces FIR filtering in the image domain with a multiplication in k-space and can reduce computational complexity. This efficient computation can benefit almost all CS methods that exploit the wavelet sparsity, and we have shown the actual CS reconstruction time can be reduced by 46% on MATLAB.