A Three-Component Hybrid Image Compression Method

ABSTRACT In this paper we present a case study of a three-component hybrid image compression algorithm combining the widely familiar, DCT-based JPEG algorithm with the Wavelet-based JPEG 2000 algorithm and a searchless fractal image compression algorithm capable of unusually deep quadtree spanning. Comparison of the relationship between compression rate and peak signal to noise ratio for each component algorithm and the same relationship for the hybrid algorithm is presented. The hybrid algorithm is capable of providing superior performance in terms of compression rate and reconstructed image quality compared to any of the component methods alone. Keywords: image compression, fractal, JPEG, JPEG 2000 1. INTRODUCTION The growing ubiquity of digital images leads to a widespread interest in techniques for reducing the space needed to store these images and bandwidth needed to transmit them. For all but the most sensitive applications, such as medical imaging, it is acceptable to use compression methods which only approximate an original image after storage. For lossy compression methods, it is typical to be able to control the amount of error introduced by compression by selecting the rate of compression. In general, more compression correlates to more error. Compression rate (CR) is simply calculated as the ratio of the size of the original image file to that of the compressed image file. The error introduced by compression is calculated using the peak signal-to-noise ratio (PSNR). The relationship between PSNR and CR is a measure of the usefulness of an image compression technique. Perhaps the most widely used lossy image compression method is the Joint Photograpic Expert’s Group (JPEG) File Interchange Format (JFIF) algorithm which is based on a quantized Discrete Cosine Transform (DCT) [1,2]. This algorithm is more commonly referred to simply as the JPEG algorithm and this convention will be followed hereafter. The compression and, consequently, error levels for JPEG are controlled by adjusting the degree of quantization of the DCT components. This does lead to a potential weakness for the JPEG algorithm. The JPEG quantization scheme typically attenuates the highest-frequency DCT components most heavily. When the quantization levels are set for high overall compression, noticeable distortion can occur. Individual image elements that exhibit very high contrast are also likely to exhibit this distortion even when using moderate overall compression levels. A newer algorithm from JPEG, called JPEG 2000, is based on a quantized Wavelet transform rather than DCT [3]. While JPEG 2000 offers a generally better PSNR to CR relationship compared to JPEG, it has not been as widely accepted. The use of a different transform as the basis for JPEG 2000 means that different image components will be compressed with high fidelity than are handled well by JPEG. Fractal image compression methods exploit the self-similarity among image elements at varying scales to implement compression through formation of a partitioned iterated function system (PIFS) [4-8]. The ability of fractal methods to reproduce image elements is related to the availability of suitable self-similarity instead of the frequency component distribution. So long as sufficient self-similarity exists, fractal image compression can reproduce image elements with high CR. Traditional fractal methods are computationally intensive limited in maximum CR and PSNR. Recent development of a significantly lower complexity and higher PSNR fractal method has made its performance comparable with JPEG and JPEG 2000 [9]. In this paper, we describe an implementation of a hybrid image compression algorithm incorporating the best features of a searchless fractal algorithm with the quantized DCT algorithm used by JPEG and quantized Wavelet algorithm used by JPEG 2000. This builds upon a fractal/JPEG hybrid algorithm the authors previously introduced [10-12]. The 3-way hybrid