In this paper, the properties of the exponential Radon transform and its dual are discussed. Furthermore, the analytical reconstruction formulas of exponential Radon transform with two different methods are developed.
In this work,the image reconstruction inπ-scheme short-scan single-photon emission computed tomography(SPECT)with nonuniform attenuation is derived in its most general form whenπ-scheme short-scan SPECT entails data acquisition over disjoint angular intervals without conjugate views totaling toπradians.The reconstruction results are based on decomposition of Novikov’s inversion operator into three parts bounded in the L2 sense.The first part involves the measured partial data;the second part is a skewsymmetric operator;the third part is a symmetric and compact contribution.It is showed firstly that the operators involved belong to L(L2(B)).Furthermore numerical simulations are conducted to demonstrate the efectiveness of the developed method.
The loping OS-EM iteration is a numerically efficient regularization method for solving ill-posed problems. In this article we investigate the loping OS-EM iterative method in connection with the circular Radon transform. We show that the proposed method converges weakly for the noisy data. Numerical tests are presented for a linear problem related to photoacoustic tomography.
