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The celebrated Radon transform [1, 2] of a two-dimensional function is defined as the set of all its line integrals [3]. There exists a certain generalization of the Radon transform, the so-called attenuated Radon transform, defined as the set of all line integrals of a two-dimensional function attenuated with respect to an attenuation function. The non-attenuated and attenuated versions of the Radon transform provide the mathematical foundation of two of the most important medical imaging techniques, referred to as positron emission tomography (PET)[4], and single-photon emission computed tomography (SPECT)[5], respectively. The non-attenuated Radon transform gives rise to an associated inverse problem, namely to “reconstruct” a function from its line integrals. The main task in PET imaging is the numerical implementation of the inversion of the non-attenuated Radon transform. Similarly, in the case of the attenuated Radon transform, the corresponding inverse problem is to reconstruct a function from its attenuated line integrals. The main task in SPECT imaging is the inversion of the attenuated Radon transform. In [6], Novikov and Fokas rederived the well-known inversion of the Radon transform by performing the so-called spectral analysis of the following eigenvalue equation: