Abstract
Advances in wavelet transforms and quantization methods have produced algorithms capable of surpassing the existing image compression standards like the Joint Photographic Experts Group (JPEG) algorithm. The existing compression methods for JPEG standards are using DCT with arithmetic coding and DWT with Huffman coding. The DCT uses a single kernel where as wavelet offers more number of filters depends on the applications. The wavelet based Set Partitioning In Hierarchical Trees (SPIHT) algorithm gives better compression. For best performance in image compression, wavelet transforms require filters that combine a number of desirable properties, such as orthogonality and symmetry, but they cannot simultaneously possess all of these properties. The relatively new field of multiwavelets offer more design options and can combine all desirable transform features. But there are some limitations in using the SPIHT algorithm for multiwavelets coefficients. This paper presents a new method for encoding the multiwavelet decomposed images by defining coefficients suitable for SPIHT algorithm which gives better compression performance over the existing methods in many cases.
Highlights
Generalizing the wavelet case, the multiresolution analysis is to be generated by a finite number of scaling functions> @ I0 (t),I1(t),Ir1 (t) and their integer translates
We propose a new method for making the multiwavelet structure, applicable for Set Partitioning In Hierarchical Trees (SPIHT) algorithm without mingling the bandpass coefficients with the highpass coefficients
Image compression experiments using GHM multiwavelet were conducted in both the coefficient shuffling method and the new method
Summary
Generalizing the wavelet case, the multiresolution analysis is to be generated by a finite number of scaling functions. K with the finite sequence N[k]k of r u r matrices of real coefficients coming by completion of {M[k]}k. By assuming that the scaling functions and their integer translates form an orthogonal basis of V0 , for s(t) V0. From these relations, the multi input multi output filter bank can be constructed. The 4 coefficient symmetric multiwavelet filter bank is given in (10). This filter is given by four 2×2 matrices c[k]. 2,n and their coarse approximation (component in V ) is computed with the low pass part of the multiwavelet filter bank V04V1 are computed with the high pass part d[k]
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