The high-resolution rate-distortion function under the structural similarity index
EURASIP Journal on Advances in Signal Processing - Special issue on theory and application of general linear image processing
| Hi-index | 754.84 |
The problem of asymptotic (i,e., low-distortion) behavior of the rate-distortion function of a random vector is investigated for a class of non-difference distortion measures. The main result is an asymptotically tight expression which parallels the Shannon lower bound for difference distortion measures. For example, for an input-weighted squared error distortion measure d(x,y)=||W(x)(y-x)||2,y,x∈Rn, the asymptotic expression for the rate-distortion function of X∈Rn at distortion level D equals h(X)-2 /nlog(2πeD/n)+Elog|detW(X)| where h(X) is the differential entropy of X. Extensions to stationary sources and to high-resolution remote (“noisy”) source coding are also given