Constrained Transform Coding and Surface Fitting

A constrained transform coding procedure is developed which is a combination of transform coding with differential pulse code modulation. The algorithm avoids block boundary mismatch errors, yet retains the coding efficiency of transform coding. A general theory of constrained transform coding is developed which includes the discrete cosine transformation and tensor products of splines as special cases. Results using the cosines and spines are given for two images. A complete discussion of the necessary linear algebra background is also given.