High compression and low order linear predictor for lossless coding of grayscale images

Abstract

In this paper we propose a novel method for designing block-wise lossless image compression scheme using linear predictors. In this prediction scheme, the prediction for each pixel is formed by using a set of least-square-based linear prediction coefficients of the block to which the current pixel belongs. Predicted value of each pixel is subtracted from the actual value of the current pixel to get an error image. An error image is compressed using grayscale bit plane coding using quadtree method. Experimental results show that the compression performance of the proposed method is superior to Joint Photographics Expert Group's [1] JPEG-LS [IEEE Trans. Image Processing 9 (2000) 1309] method, and Classified Adaptive Prediction and Entropy Coding in terms of coding performance.

Introduction

Recently, lossless coding of grayscale images has attracted much research interest among the image processing community. Many techniques have been proposed to achieve better compression performance or to provide a tradeoff between compression performance and computational complexity to meet requirements from several applications such as medical imaging, remote sensing, and image archiving [2], [3], [4], [5]. Predictive coding is one of the most popular techniques in these coding schemes, since it is a simple and effective tool for removing redundancy of image signals. In general, the Minimum Mean Square Error (MMSE) is an important concept in designing of coders [6] and several kinds of lossless coding schemes actually employ predictors which are optimized on the basis of the MMSE criterion [2], [3].

In most state-of-the-art methods for lossless image compression, and one-pass sequential techniques, prediction is an essential component. A high quality predictor gives high compression performance. JPEG-LS uses three neighboring pixels to guess the values of the pixels, and is of very high quality predictor for one-pass sequential technique. In general the quality of a predictor directly affects the overall compression performance because it is the prediction error that is entropy coded. The simplest and most widely used prediction method is linear prediction. However, for a linear predictor to be able to accurately model image data which are usually non-stationary, some adaptation scheme must be developed to let the predictor change according to local characteristics. The method of least-squares (LS) has been adopted for this kind of adaptation and is shown to perform very well even in edge areas [3], [4], [5].

In this paper, we present a block-based LS linear predictor where the compression performance is improved by using quadtree method to compress the gray bit planes of the error image. This method is actually related to Bayesian model averaging (BMA) [7]—an effective solution to the problem of building the ‘best’ model from a set of possible models when there is model uncertainty.

Our experimental results show that a combination of block-based LS predictor to predict pixel value, and grayscale bit plane compression using quadtree method to compress prediction error, gives better compression performance.

A simple introduction to the LS-based prediction is presented in Section 2. The proposed method for the combination of block-based predictor and grayscale bit plane compression using quadtree method is presented in Section 3. The experimental results as well as comparison with other algorithms are presented in Section 4. Finally, conclusions are presented in Section 5.