Spatial resolution analysis of iterative image reconstruction with separate regularization of real and imaginary parts

A common method of improving the conditioning in iterative image reconstruction is to include regularization in the reconstruction algorithm. One such regularization is the roughness penalty, which when used in the algorithm encourages smoother images. For complex valued images, the roughness penalty typically penalizes equally the real and imaginary parts. The desired resolution of the reconstructed image can then be evaluated using the local impulse response. A fast algorithm to calculate it was developed for the typical roughness penalty, used for matching the regularization parameter expediently to the desired resolution. For some cases its advantageous to penalize independently the real and imaginary parts. This paper proposes a fast algorithm to calculate the local impulse response for that penalty and applies it to an fMRI reconstruction problem