The maximum likelihood method is applied to the problem of extracting the correct sequence of spatial patterns from the corresponding sequence of measurement frames corrupted by background noise. Each measurement frame is modeled as the sum of a pattern matrix and a background noise matrix. The model proposed for the statistics of the sequence of background matrices results in jointly Gaussian elements whose correlations are product separable in row, column, and frame indices. The logarithm of the likelihood function is computed and involves a matched filtering operation on the measurement frames, which acts to suppress the background relative to the pattern. Because of the product separability in the back-ground element correlations, this matched filtering operation is accomplished by pre- and post-multiplying the measurement frames by the inverses of the background row and column correlation matrices, respectively. Thus, the measurement frames are operated on in their original matrix format without resorting to stacking. Applications include the detection of targets in background noise.