Section 3 provides a brief outline of the mathematical aspect related to compression using wavelet technology and various parameters to examine the quality of compressed image.
With wavelet as the main ingredient, we enter into a dynamic contemporary research environment, what is now referred to as image compression and pattern recognition in medical imaging.
In this study, a novel adaptive speckle noise reduction algorithm using anisotropic diffusion filter based on Haar wavelet transform and the median absolute deviation was proposed.
Haar wavelet transform is a kind of discrete wavelet transform.
In terms of signal processing, the following methods can be used: embedded signal identification technique (ESIT) [10], the wavelet packet method [11], the Hilbert transform method [12], and so on.
As a comparatively new and powerful mathematical tool for time series analysis, multiresolution decomposition (MRD) is one of the basic tools of wavelet theory.
The quantitative properties of any wavelet method strongly depends on the used wavelet basis, namely on its condition number, the length of the support of the wavelets, the number of vanishing wavelet moments, and the smoothness of the basis functions.