Object dependency of resolution and convergence rate in OSEM with filtering

It is well known that the convergence properties of the maximum likelihood expectation maximisation (MLEM) algorithm depend on the activity distribution in the field of view. We study resolution properties for MLEM/ordered subsets EM (OSEM) with different types of regularisation. It will be shown that although different parts of the image converge at different rates, pure and post filtered MLEM/OSEM achieve reasonably uniform resolution. By contrast, inter-iteration filtering (IF OSEM) with smoothing filters, such as a Gaussian, produces images with varying spatial resolution that is dependent on the surrounding activity. We conclude that the resolution non-uniformity is entirely due to the filtering. We propose a spatially varying filter to overcome this problem and to obtain images with nearly uniform resolution. Experimental evidence of the performance of these filters on noiseless data is also shown.