Design and evaluation of minimum‐rate predictors for lossless image coding

Abstract

SUMMARYIn this paper, the authors propose a new method for designing predictors suitable for lossless image coding. In recent years, lossless coding systems based on optimal design of predictors for each image have been studied. In these systems, the linear prediction coefficients are determined so as to minimize the mean squared prediction errors. In lossless image coding, however, where the ultimate goal is to reduce the coding rate, minimizing the mean squared prediction errors does not necessarily yield the best results. Therefore, in order to reduce the coding rate directly, the authors attempted to formulate the amount of information on the prediction errors and design the predictors so as to minimize that value. Moreover, the image is divided into blocks, and these blocks are classified into multiple classes; multiple predictors for adaptive prediction are optimized at the same time by repeatedly executing the design of the predictor for each class and updating the class for each block, based on the cost representing the amount of information. In the results from a coding simulation, this system demonstrated superior coding efficiency compared to the conventional method for minimizing the mean squared prediction errors, and was confirmed to achieve a coding rate of 0.37 bit/pel lower than JPEG-LS which is an international standard for lossless image coding.

A lossless coding scheme using adaptive predictors and arithmetic code optimized for each image

“…In Ref. 8, the conditional probability density functions P(e|n) of the prediction errors e that were observed separately in each context (n = 1, 2, . .…”

“…, 16) were assumed to follow a Gaussian distribution with a variance of σ n 2 . Based on this assumption, the data length of the prediction errors can be approximated by the sum of the squares of e weighted by the reciprocal of the variance σ n 2 (i.e., the sum of e 2 /σ n 2 ), and the set of prediction coefficients that minimize this value can easily be determined [8] by solving a normal equation in the same way as for an MMSE predictor [5]. In real images, however, the above assumption may not necessarily hold true, and a problem arises in that the efficiency of the entropy encoder is reduced due to mismatches in the probability density function.…”

“…If the P(n|e) obtained in this way is utilized as a model of the probability density function, with the exception of c n = 2, the data length of the prediction errors can no longer be approximated by the sum of weighted squares of errors as is done in Ref. 8. We therefore consider ways to directly calculate the data length of prediction errors based on an actual entropy coding procedure.…”

“…The initial values of each of the parameters are predetermined using the method in Ref. 8. The steps in Sections 4.1 to 4.4 are a single iteration of processing which is executed repeatedly until the value of the cost function J that evaluates the entire image stops decreasing or the iteration count reaches some predefined iteration limit (which is set to 100 iterations in this paper).…”

“…In consideration of these points, the authors have previously proposed a method in which the linear predictors that are used in the lossless coding are reconfigured for each image [8]. This method presumes block adaptive prediction [5] that can switch between multiple different predictors at the block level, and the coding is optimized by repeatedly alternating between optimizing the predictor configurations and selecting the optimal predictors for each block.…”