The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-IPI-510

“The Role of Phase in Adaptive Image Coding”

by Andrew G. Tescher

December 1973

Results of a comprehensive research program to develop efficient transform image coding algorithms are reported in this dissertation. The objective is to develop algorithms that outperform the conventional block-encoding procedures, i.e., achieve data rates below the one bit/picture element which is the approximate lower limit for conventional transform coders.

The dissertation includes a detailed analysis of image modeling aspects of the transform coding problem. Two alternate prediction algorithms are analyzed for the transform sample variance estimation; the first technique uses a two-dimensional polynomial to model the image power spectral density; the second technique is a simple recursive approach based on previously quantized values. The actual coding algorithms utilize the latter approach.

The generalized phase concept is developed and plays a vital role in the coding algorithms. Both the Fourier and Walsh transforms are utilized, the former being demonstrated to have superior performance. A non-negative image constraint is explored via the Lukosz bound.

The experimental phase of the study includes two dimensional coding of monochrome, and three dimensional coding of color, as well as interframe images with coding at 0.38, 0.55, and 0.25 bits per pixel, respectively. It is ascertained that decoded and reconstructed images are not significantly degraded. It is also demonstrated that adaptive transform domain modeling is important, and that large-size transforms, in conjunction with the proper image model, can significantly outperform block-encoding techniques.

A requirement for large-size transforms can easily discourage hardware usage. Techniques can be developed, however, that could advantageously be employed for computer-to-computer image transfer.

Although the new coding-decoding methods are sensitive to channel errors, it is demonstrated that they produce data which are statistically equivalent to discrete memoryless source. Thus, conventional channel coding techniques can be used.

To download the report in PDF format click here: USC-IPI-510.pdf (11.5Mb)