A Wavelet Phase Filter for Emission Tomography

The presence of a high level of noise is a characteristic in some tomographic imaging techniques such as positron emission tomography. Wavelet methods can smooth out noise while preserving signiicant 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. Speciically, 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). We then propose three wavelet-phase-based denoising schemes which exploit this property: edge tracking, local phase variance thresholding, and scale phase variation thresholding. Numerical results are also presented. The numerical experiments indicate that wavelet-phase techniques show promise for wavelet based denoising methods.