A splitting algorithm for MR image reconstruction from sparse sampling

Here b is the observed data in k-space, Fp is a Fourier transform evaluated only at a subset of frequency domain samples (corresponding to one of the k-space undersampling schemes), βi(i = 1, 2) is the regularization parameter, ∇ is the discrete gradient operator defined by

with (∇xu)r,s = ur+1,s − ur,s and (∇yu)r,s = ur,s+1 − ur,s. and W is an orthogonal wavelet transform matrix.