Noise removal for degraded images by IBS shrink method in multiwavelet domain

The wavelet transform has been used for image compression, image restoration, signal processing, and pattern recognition. In most cases, processing is performed with a scalar wavelet using one scaling function. However, the scalar wavelet has the deficiency that the properties of shortness of support, regularity, orthogonality, and high vanishing moment are not shared at the same time. Recently, the multiwavelet, consisting of several scaling functions and several wavelet functions, has been proposed. Since several input data are obtained by preprocessing in the multiwavelet transform, many studies of applications of the multiwavelet in the fields of signal processing and image processing are being carried out. Many engineering achievements have been reported. However, little has been reported on the use of multiwavelets for restoration of degraded images. This is a research field with prospects for future growth. In the present research, a threshold shrinking method is proposed in which different threshold values are used for the horizontal, vertical, and diagonal directions at each level and also within the same level in the multiwavelet domain for degraded images with superimposed Gaussian noise. The effectiveness of the proposed method is demonstrated by a computer simulation. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(7): 15– 24, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20295