[OPTICAL REVIEW Vol. 13, No. 3 (2006) 129-137]

© 2006 The Optical Society of Japan

## Wavelet Denoising for Tomographically Reconstructed Image

Susumu KUWAMURA^{*}

Department of Computer Sciences, Kitami Institute of Technology, 165 Koen-cho, Kitami, Hokkaido 090-8507, Japan

(Received September 9, 2005; Accepted March 3, 2006)

We have developed a wavelet denoising (thresholding) method for a tomographically reconstructed image to which the conventional wavelet methods are not necessarily applicable because of their limitation of applicable noise models. The basic idea of our new method is that noise variance is, in general, spatially varying and the threshold must be adapted to it. Specifically, our algorithm includes two key steps: The first is to estimate local variances in image space to produce a “σ-map”. The second is to calculate the standard deviations of individual wavelet coefficients from the σ-map by a formula of “covariance propagation”. Spatially adaptive thresholds are then given as those proportional to the standard deviations. Our method is applicable to a wider range of noise models, and numerical experiments have shown that it can yield a denoised image with 10% less residual error than that in the boxcar smoothing or the median filtering.

Key words: tomographic image, image reconstruction, wavelet transform, wavelet denoising, threshold, covariance propagation, σ-map, nonconstant variance, expectation maximization (EM)

^{*}E-mail address: kuwamura@cs.kitami-it.ac.jp