Spiral Fractal Compression in Transform Domains for Underwater Communication

Abstract

This paper presents a simplified fractal image compression algorithm, which is implemented on a block-by-block basis. This algorithm achieves a Compression Ratio (CR) of up to 10 with a Peak Signal-to-Noise Ratio (PSNR) as high as 35 dB. Hence, it is very appropriate for the new applications of underwater communication. The idea of the proposed algorithm is based on the segmentation of the image, first, into blocks to setup reference blocks. The image is then decomposed again into block ranges, and a search process is carried out to find the reference blocks with the best match. The transmitted or stored values, after compression, are the reference block values and the indices of the reference block that achieves the best match. If there is no match, the average value of the block range is transmitted or stored instead. The effect of the spiral architecture instead of square block decomposition is studied. A comparison between different algorithms, including the conventional square search, the proposed simplified fractal compression algorithm and the standard JPEG compression algorithm, is introduced. We applied the types of fractal compression on a video sequence. In addition, the effect of using the fractal image compression algorithms in transform domain is investigated. The image is transferred firstly to a transform domain. The Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT) are used. After transformation takes place, the fractal algorithm is applied. A comparison between three fractal algorithms, namely conventional square, spiral, and simplified fractal compression, is presented. The comparison is repeated in the two cases of transformation. The DWT is used also in this paper to increase the CR of the block domain pool. We decompose the block domain by wavelet decomposition to two levels. This process gives a CR for block domain transmission as high as 16. The advantage of the proposed implementation is the simplicity of computation. We found that with the spiral architecture in fractal compression, the video sequence visual quality is better than those produced with conventional square fractal compression and the proposed simplified algorithm at the same CR, but with longer time consumed. We found also that all types of fractal compression give better quality than that of the standard JPEG. In addition, the decoded images, in case of using the wavelet transform, are the best. On the other hand, in case of using DCT, the decoded images have poor quality.