Multiscale image restoration in nuclear medicine
Ghada Jammal · Technischen Universität Darmstadt · 2008
This work develops, analyzes and validates a new multiscale restoration framework for denoising and deconvolution in photon limited imagery. Denoising means the estimation of the intensity of a Poisson process from a single observation of the counts, whereas deconvolution refers to the recovery of an object related through a linear system of equations to the intensity function of the Poisson data. The developed framework has been named DeQuant in analogy to Denoising when the noise is of Quantum nature. DeQuant works according to the following scheme. (1) It starts by testing the statistical significance of the wavelet coefficients of the Poisson process, based on the knowledge of their probability density function. (2) A regularization constraint assigns a new value to the non significant coefficients enabling therewith to reduce artifacts and incorporate realistic prior information into the estimation process. Finally, (3) the application of the inverse wavelet transform yields the restored object. The whole procedure is iterated before obtaining the final estimate. The validation of DeQuant on nuclear medicine images showed excellent results. The obtained estimates enable a greater diagnostic confidence in clinical nuclear medicine since they give the physician the access to the diagnosis relevant information with a measure of the significance of the detected structures.