Region-of-Interest CT Reconstruction Using Object Extent and Singular Value Decomposition

In computed tomography, a whole scan of the object may be impossible, generally because the object is larger than the scanner field of view. Such a set up leads to truncated projections. Using differentiated backprojection, the reconstruction problem can be reduced to a set of 1-D problems consisting of the inversion of the Hilbert transform. When the object partly overlaps the scanner field of view, this problem is commonly referred to as the “one-sided truncated Hilbert transform.” Our work investigates this situation and proposes a novel approach to address it. Using differentiated backprojection, and the object extent supposedly known
a priori
, a pseudoinverse of the truncated Hilbert transform is computed by truncated singular value decomposition, and its truncated singular values are replaced by a simple estimation. The estimation is calculated using the singular value decomposition of the known convex hull filled with a constant value per line computed from the corresponding projection in the direction of the Hilbert transform. The experiments illustrate the image quality improvements resulting from this approach compared to a simple truncation of the singular values and the reconstruction speed improvement compared to 2-D iterative reconstruction solving penalized least squares with the conjugate gradient algorithm.