Reduced pyramids, i.e pyramids without analysis flters are known to produce excellent results when used for losslesssignal nad image compression. The present paper introduces a novel methos for the construction of extended reduced pyramids with rational decimation ratios form stage to stage. It is shown that this construction produces more accurte interpolation than conventional reduced pyramids. The synthesis filters are selectedso as to minimize the error variance at each stage ofthe pyramid. This establishes optimally efficient interpolative lossless ocmpresion. It also has the added advntage of producing lossy replicas of the original, which, at lower resolutions retain as much similarity to the original as possible. This is highly useful for the progressive coding of signals or images, needed in many applications such as fast browsing through image databases or hybrid lossless/lossy medical image coding. Experimental evaluatin shows that the resulting method produces better results than other known algorithms for progressive lossless image coding.
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