Wavelet phase filter for emission tomography
Elwood T. Olsen, Biquan Lin · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1995
The presence of a high level of noise is a characteristic in some tomographic imaging techniques such as positron emission tomography (PET). Wavelet methods can smooth out noise while preserving significant features of images. Mallat et al. proposed a wavelet based denoising scheme exploiting wavelet modulus maxima, but the scheme is sensitive to noise. In this study, we explore the properties of wavelet phase, with a focus on reconstruction of emission tomography images. Specifically, we show that the wavelet phase of regular Poisson noise under a Haar-type wavelet transform converges in distribution to a random variable uniformly distributed on (0, 2(pi) ). We then propose three wavelet-phase-based denoising schemes which exploit this property: edge tracking, local phase variance thresholding, and scale phase variation thresholding. Some numerical results are also presented. The numerical experiments indicate that wavelet phase techniques show promise for wavelet based denoising methods.