This paper is intended as a tutorial review of certain digital image processing transform techniques utilizing the notion of outer product expansions. Examples from Fourier, Walsh, Haar, and other well known transforms are reviewed in the notation of matrix-vector outer products; and implementation of the singular value decomposition (SVD) of large sized images is presented. The use of the SVD as an aid in image restoration utilizing the pseudoinverses is presented. Conditions on the point spread matrix are investigated in the light of singular value decomposition, Kronecker products, and general imaging conditions.

This correspondence presents results concerning the display of interpolated images for cosmetically pleasing effects. Replication, bilinear interpolation, and various cubic spline function interpolators are investigated as to numeric computational difficulty and psychovisually pleasing results. A degree of freedom analysis is provided to demonstrate the fact that apparent image improvement does not necessarily increase the inherent quantitative information within an image.

The numerical techniques of transform image coding are well known in the image bandwidth compression literature. This concise paper presents a new transform method in which the singular values and singular vectors of an image are computed and transmitted instead of transform coefficients. The singular value decomposition (SVD) method is known to be the deterministically optimal transform for energy compaction [2]. A systems implementation is hypothesized, and a variety of coding strategies is developed. Statistical properties of the SVD are discussed and a self adaptive set of experimental results is presented, Imagery compressed to 1, 1.5, and 2.5 bits per pixel with less than 1.6, 1, and 1/3 percent, respective mean-square error is displayed. Finally, additional image coding scenarios are postulated for further consideration.