On the problem of simultaneous encoding of magnitude and location information

Modern image coders balance bitrate used for encoding the location of significant transform coefficients, and bitrate used for coding their values. The importance of balancing location and value information in practical coders raises fundamental open questions about how to code even simple processes with joint uncertainty in coefficient location and magnitude. The most basic example of such a process is studied: a 2-D process studied earlier by Weidmann and Vetterli that combines Gaussian magnitude information with Bernoulli location uncertainty. An insight into the coding of this process by investigating several new coding strategies based on more general approaches to lossy compression of location is presented. Extending these ideas to practical coding, a trellis-coded quantization algorithm with performance matching the published theoretical bounds is developed. Finally, the quality of the strategies is evaluated by deriving a rate-distortion bound using Blahut's algorithm for discrete sources.