Optimal pyramidal and subband decompositions for hierarchical coding of noisy and quantized images

Optimal hierarchical coding is sought, for progressive or scalable image transmission, by minimizing the variance of the error difference between the original image and its lower resolution renditions. The optimal, according to the above criterion, pyramidal and subband image coders are determined for images subject to corruption by quantization or transmission noise. Given arbitrary analysis filters and assuming adequate knowledge of the noise statistics, optimal synthesis filters are found. The optimal analysis filters are subsequently determined, leading to formulas for globally optimal structures for pyramidal and subband image decompositions. Experimental results illustrate the implementation and performance of the optimal coders.