This article develops a theoretical framework for the use of the wavelet transform in the estimation of emission tomography images. The solution of the problem of estimation addresses the equivalent problems of optimal filtering, maximum compression, and statistical testing. In particular, new theory and algorithms are presented that allow current wavelet methodology to deal with the two main characteristics of nuclear medicine images: low signal-to-noise ratios and correlated noise. The technique is applied to synthetic images, phantom studies, and clinical images. Results show the ability of wavelets to model images and to estimate the signal generated by cameras of different resolutions in a wide variety of noise conditions. Moreover, the same methodology can be used for the multiscale analysis of statistical maps. The relationship of the wavelet approach to current hypothesis-testing methods is shown with an example and discussed. The wavelet transform is shown 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 starting point for further developments in image reconstruction and image processing.