Implementation a new Technique of Slantlet Transform on Gray Image Using Two-Scale Iteration of Filter Bank


The slantlet transform (SLT) is an orthogonal discrete wavelet transform (DWT) with two zero moments and with improved time localization. It also retains the basic characteristic of the usual filterbank such as octave band characteristic, a scale dilation factor of two and efficient implementation. However, the SLT is based on the principle of designing different filters for different scales unlike iterated filterbank approaches for the DWT. Therefore the discrete wavelet transform (DWT) is usually carried out by filterbank iteration; however, for a fixed number of zero moments, this does not yield a discrete-time basis that is optimal with respect to time localization. This paper discusses the implementation and properties of an orthogonal DWT, with two zero moments and with improved time localization. The basis is not based on filterbank iteration; instead, different filters are used for each scale. For coarse scales, the support of the discrete-time basis functions approaches two thirds that of the corresponding functions obtained by filterbank iteration. This basis, which is a special case of a class of bases described by Alpert, retains the octave-band characteristic and is piecewise linear (but discontinuous). Closed-form expressions for the filters are given, an efficient implementation of the transform is described, and improvement in a denoising example is shown. This basis, being piecewise linear, is reminiscent of the slant transform, to which it is compared.Keywords: SLT Slantlet transform DWT discrete wavelet transform.


Gray Image