Edge preserving reconstruction using adaptive smoothing in wavelet domain

An edge preserving image reconstruction approach for emission tomography is presented, in which the image x is modeled by a space-variant prior distribution P(x) based on anisotropic diffusion. By adaptively smoothing pixels in regions with small intensity fluctuations while preserving sharp edges, anisotropic diffusion works well in extracting boundaries for images which comprise smooth regions separated by discontinuities. This boundary information is incorporated into the reconstruction algorithm by means of space-variant simultaneous autoregressive (SAR) processes. To further reduce the noise effect and to improve boundary extraction, P(a) is defined in the wavelet domain. Wavelet transform (WT) decomposes x into subbands with distinctive characteristics, and each subband is modeled by a SAR process whose coefficients are determined according to the spatial features of the subband for a more accurate prior description. An iterative algorithm similar to the EM algorithm is proposed to solve the formulated image reconstruction problem. This algorithm is stable and converges in all the experiments performed so far, and its convergence has been proven for the case where the SAR coefficients are fixed