IMAGE COMPRESSION USING MULTIWAVELET

Abstract

There are many methods for digital image compression that have been the subject of much study over the past decade & their success depends on how well the basic functions represent the signal features. Discrete wavelet transform (DWT) performs a multiresolution analysis of a signal enabling an efficient representation of smooth and detailed signal regions. Computationally efficient algorithms exist for computing the DWT. Also changes in wavelet transforms and quantization methods produced algorithms that overcome the existing image compression standards like the JPEG (joint photographic expert group) algorithm. To have the best performance in image compression, wavelet transforms require filters that combine a number of desirable properties, such as orthogonality and symmetry. It is also known that because of the limited design properties, the scalar wavelet transform does not possess both properties simultaneously. The new field of multiwavelets overcomes this limitation, which allows orthogonality and symmetry to co-exist. Still, recently reported image compression results indicate that the scalar wavelets still outperform the multiwavelets in terms of peak signal-to-noise ratio (PSNR). Using a SPIHT (set partitioning in hierarchal tree) quantization scheme modified to better match the unique decomposition properties of multiwavelets, it is shown that the latest multiwavelet filters can give performance equal/superior to, the current wavelet filters. In a multiwavelet transform, the balancing orcbr of the multiwavelet is indicative of its energy compaction efficiency, since higher balancing order implies lower MSE (mean square error), in the compressed image. The characteristics of different balanced multiwavelets along with unbalanced multiwavelets were studied and their image compression performance for grayscale images with scalar wavelets were compared by using the well-known SPIHT quantizer in the compression scheme and utilizing the PSNR to assess performance. Moreover, the PSNR results depict similar performance for the best scalar wavelets and multiwavelets. The wavelet and multiwavelet filter banks are tested on a much wider range of images, providing a better analysis of the benefits and drawbacks of each.