Optimisation of quantisation based on rth-power distortion measures

Quantisation is an important technique for data compression, and quantisation distortion is usually an unavoidable error in signal processing. An efficient algorithm is presented for the design of minimum-mean-rth-power distortion, scalar quantisers with a fixed number of reconstruction levels. The properties of this design algorithm are discussed and demonstrated by numerical examples. For minimum-mean-absolute-error quantisation, simple explicit design formulas for Laplace-distributed signals are also derived. The method provided in the paper is applicable to quite general distributed signals.