<title>Lossless and progressive image coding using optimal pyramidal analysis</title>

Abstract

Pyramidal decomposition is known to be highly useful for progressive and lossless image coding. The present paper presents a methodology for the optimal construction of pyramids by selecting the analysis prefilters and interpolation synthesis postfilters so as to minimize the error variance at each level of the pyramid. This establishes optimally efficient pyramidal lossless compression. It also has the added advantage of producing lossy replicas of the original which, at lower resolutions retain as much similarity to the original as possible. Thus, optimal progressive coding of signals or images is produced, as is needed for many applications such as fast browsing through image databases or hybrid lossless/lossy medical image coding. To achieve efficient lossless coding a scheme is utilized for the reduction of the number of data needed to be transmitted to reconstruct the original from the low resolution image and the errors produced at the various pyramid stages. This scheme in effect renders the pyramid into a `reduced' pyramid without sacrificing, however, the optimal analysis prefilters of the pyramid. Experimental application of this methodology shows that is outperforms existing methods for lossless and progressive image coding.