Deblurring in the presence of non-Gaussian noise is a hard problem, specially in ultrasonic and CT images. In this paper, a new method of image restoration, using complex wavelet transform, has been devised and applied to deblur in the presence of high speckle noise. It has been shown that the new method outperforms the Weiner filtering and Fourier-wavelet regularized deconvolution (ForWaRD) methods for both ultrasonic and CT images. Unlike Fourier and real wavelet transforms, complex wavelet transform is nearly shift-invariant. This gives complex wavelet transform an edge over other traditional methods when applied simultaneously for deblurring as well as denoising. The proposed method is independent of any assumption about the degradation process. It is adaptive, as it uses shrinkage function based on median and mean of absolute wavelet coefficient as well as standard deviation of wavelet coefficients. Its application on real spiral CT images of inner ear has shown a clear improvement over other methods.
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