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A fast method to emulate an iterative POCS image reconstruction algorithm
Author(s) -
Zeng Gengsheng L.
Publication year - 2017
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1002/mp.12169
Subject(s) - algorithm , iterative method , iterative reconstruction , smoothing , noise reduction , projection (relational algebra) , computer science , mathematical optimization , noise (video) , filter (signal processing) , penalty method , nonlinear system , image (mathematics) , mathematics , computer vision , physics , quantum mechanics
Purpose Iterative image reconstruction algorithms are commonly used to optimize an objective function, especially when the objective function is nonquadratic. Generally speaking, the iterative algorithms are computationally inefficient. This paper presents a fast algorithm that has one backprojection and no forward projection. Methods This paper derives a new method to solve an optimization problem. The nonquadratic constraint, for example, an edge‐preserving denoising constraint is implemented as a nonlinear filter. The algorithm is derived based on the POCS (projections onto projections onto convex sets) approach. A windowed FBP (filtered backprojection) algorithm enforces the data fidelity. An iterative procedure, divided into segments, enforces edge‐enhancement denoising. Each segment performs nonlinear filtering. Results The derived iterative algorithm is computationally efficient. It contains only one backprojection and no forward projection. Low‐dose CT data are used for algorithm feasibility studies. The nonlinearity is implemented as an edge‐enhancing noise‐smoothing filter. Conclusions The patient studies results demonstrate its effectiveness in processing low‐dose x ray CT data. This fast algorithm can be used to replace many iterative algorithms.