Recently

the modern imaging techniques of positron emission tomography and of single photon emission computed tomography are two of the most important tools for studying the functional characteristics of the brain

and they now play a vital role in several areas of clinical medicine

including nuclear medicine emission imaging. The basic mathematical problems associated with these techniques are the reconstruction of the Radon transform and the so-called generalized Radon transform

respectively. The singular value decomposition of the generalized Radon transform is developed by means of operator theory of function spaces

which are square integrable on

R

n

with known weight functions. Furthermore

the inversion formula and characteristics of its range are also obtained.