An accurate iterative reconstruction algorithm for sparse objects: application to 3D blood vessel reconstruction from a limited number of projections.
Based on the duality of nonlinear programming, this paper proposes an accurate row-action type iterative algorithm which is appropriate to reconstruct sparse objects from a limited number of projections. The cost function we use is the Lp norm with p approximately 1.1. This norm allows us to pick up a sparse solution from a set of feasible solutions to the measurement equation. Furthermore, since it is both strictly convex and differentiable, we can use the duality of nonlinear programming to construct a row-action type iterative algorithm to find a solution. We also impose the bound constraint on pixel values to pick up a better solution. We demonstrate that this method works well in three-dimensional blood vessel reconstruction from a limited number of cone beam projections.
Li
Meihua
M
University of Tsukuba, Tsukuba 305-8573, Japan. limeihua@imagelab.is.tsukuba.ac.jp
Yang
Haiquan
H
Kudo
Hiroyuki
H
D000465:Algorithms; D000792:Angiography / Q000379:methods*; D006801:Humans; D021621:Imaging, Three-Dimensional / Q000379:methods*; D019047:Phantoms, Imaging; D011856:Radiographic Image Enhancement / Q000379:methods*; D014054:Tomography / Q000295:instrumentation / Q000379:methods; D014057:Tomography, X-Ray Computed / Q000295:instrumentation / Q000379:methods*