SVD inversion for the bi-dimensional Conical Radon Transform

Abstract

Abstract.In nuclear medicine, the Conical Radon Transforms family includes 2D and 3D models for scatter radiation imaging. The underlying idea is taking advantage of Comptom effect in order to provide image reconstruction without rotating the detector system. Several techniques currently applied for the classical Radon transform may also be useful in this new context. Nevertheless, since the physical model is rather different, it is necessary to assess the performance of each method. In previous works, we have studied inversion by filtered-backprojection and adaptive algebraic reconstruction techniques. In this paper we study the performance of a method based in the factorization of the projection matrix in order to invert the projections. Particularly, we test our algorithms on the bi-dimensional Conical Radon Transform, a simple member of the Conical Radon family. We obtain useful results on the performance of the three methods which should be valuable in the more realistic 3D context.

Real-Time 3D PET Image with Pseudoinverse Reconstruction

“…The singular value decomposition (SVD) [44][45][46][47][48] was used here to compute the pseudoinverse of the matrix. In this method, matrix A is first decomposed into the product of two orthonormal matrices U and V and a diagonal matrix S containing the singular values (s ≥ 0) of A:…”