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.

<title>Segmentation, noise suppression, and compression of multispectral image sequences</title>

“…Each scene element may have its own spectral characteristics and occupy only a portion of the pixel area. The resulting gray-scale value of that pixel can be modeled by (2).…”

“…White noise (with zero mean and zero interpixel correlation) is one model for this type of image degradation. Designating the pixel noise as n(i,j ,k) the model given in (2) can be expanded to g(ij,k) = •J5m(J)Sm(k) + n(ij,k) (5) or, using vector notation, g(ij) = >.m(J)Sm + n(ij).…”

“…From them and the process signature vectors s., the image sequence can be reconstructed using (2). If the total number p of processes is less than the number n of images in the image sequence, then compression is possible.…”

“…In this case, estimates of the gray-scale maps for each of the p-b desired process can be calculated, reducing the number of images from n to p-b. A new image sequence can then be generated using only the p-b selected processes according to (2).…”

Eigenimage filtering in MR imaging: An application in the abnormal chest wall

“…Linear filters have been used in a variety of image techniques to enhance contrast between one or more features in an image sequence (4)(5)(6). Linear filters produce a single composite image from a weighted summation of the images in an image sequence of the same anatomical site, i.e., where S, is the gray level of the ijth pixel in the composite image, puk is the gray level of the 0th pixel in the kth image in the sequence, and ek is the kth weighting factor.…”