Multiresolution analysis of emission tomography images in the wavelet domain

This article develops a theoretical framework for the use of the wavelet tr ansform in the estimation of emission tomography images. The solution of th e problem of estimation addresses the equivalent problems of optimal filter ing, maximum compression, and statistical testing. In particular, new theor y and algorithms are presented that allow current wavelet methodology to de al with the two main characteristics of nuclear medicine images: low signal -to-noise ratios and correlated noise. The technique is applied to syntheti c images, phantom studies, and clinical images. Results show the ability of wavelets to model images and to estimate the signal generated by cameras o f different resolutions in a wide variety of noise conditions. Moreover, th e same methodology can be used for the multiscale analysis of statistical m aps. The relationship of the wavelet approach to current hypothesis-testing methods is shown with an example and discussed. The wavelet transform is s hown to be a valuable tool for the numerical treatment of images in nuclear medicine. It is envisaged that the methods described here may be a startin g point for further developments in image reconstruction and image processi ng.