Wavelet based multiresolution expectation maximization image reconstruction algorithm for positron emission tomography

Maximum Likelihood (ML) estimation based Expectation Maximization (EM) [IEEE Trans Med Imag, MI-1 (2) (1982) 113] reconstruction algorithm has shown to provide good quality reconstruction for positron emission tomography (PET). Our previous work [IEEE Trans Med Imag, 7(4) (1988) 273; Proc IEEE EMBS Conf, 20(2/6) (1998) 759] introduced the multigrid (MG) and multiresolution (MR) concept for PET image reconstruction using EM. This work transforms the MGEM and MREM algorithm to a Wavelet based Multiresolution EM (WMREM) algorithm by extending the concept of switching resolutions in both image and data spaces. The MR data space is generated by performing a 2D-wavelet transform on the acquired tube data that is used to reconstruct images at different spatial resolutions. Wavelet transform is used for MR reconstruction as well as adapted in the criterion for switching resolution levels. The advantage of the wavelet transform is that it provides very good frequency and spatial (time) localization and allows the use of these coarse resolution data spaces in the EM estimation process. The MR algorithm recovers low-frequency components of the reconstructed image at coarser resolutions in fewer iterations, reducing the number of iterations required at finer resolution to recover high-frequency components. This paper also presents the design of customized biorthogonal wavelet filters using the lifting method that are used for data decomposition and image reconstruction and compares them to other commonly known wavelets.