Design of optimal statistical filter for the discrete convolution backprojection method

A statistically optimal convolving function (fllter) is derived for discrete implementation of the convolution backproject method. The method of derivation simultaneously takes into account (i) ‘the process’ generating the object images, (ii) the data collection geometry, (iii) the discretization scheme used, (iv) various interpolations used, and (v) the data noise. The proposed filter minimizes the expected weighted sum of squared errors in pixel reconstructions. The performance of this optimal filter, in reconstructing discretized images by convolution backprojection method, is compared with that of some of the commonly used filters.