Optimal Filtering of Radiographic Image Sequences Using Simultaneous Diagonalization

Abstract

A method is presented for the processing of temporal image sequences to enhance a desired process and suppress an undesired (interfering) process and random noise. Furthermore, the processed information is contained in a single frame which is easily interpreted. The method consists of collecting information about the desired and interfering processes from the frames of the given image sequence. The information is in the form of vectors that characterize the temporal properties of the processes. Matrices are formed by performing outer product expansions on these vectors and an eigenvector matrix is found which will simultaneously diagonalize these matrices. By calculating the inner product of a selected eigenvector from this matrix with the image sequence, an enhanced image of the desired process is obtained. A parameter can be adjusted which will increase the amount of suppression for either random noise or the interfering process. At one limit setting of this parameter, a matched filter for the desired process results, while at the other extreme, very high attenuation of the interfering process will occur. Simulations which demonstrate the effectiveness of this technique are presented along with results obtained by processing a radiographic temporal image sequence.