Relaxed Linearized Algorithms for Faster X-Ray CT Image Reconstruction

Abstract

Statistical image reconstruction (SIR) methods are studied extensively for X-ray computed tomography (CT) due to the potential of acquiring CT scans with reduced X-ray dose while maintaining image quality. However, the longer reconstruction time of SIR methods hinders their use in X-ray CT in practice. To accelerate statistical methods, many optimization techniques have been investigated. Over-relaxation is a common technique to speed up convergence of iterative algorithms. For instance, using a relaxation parameter that is close to two in alternating direction method of multipliers (ADMM) has been shown to speed up convergence significantly. This paper proposes a relaxed linearized augmented Lagrangian (AL) method that shows theoretical faster convergence rate with over-relaxation and applies the proposed relaxed linearized AL method to X-ray CT image reconstruction problems. Experimental results with both simulated and real CT scan data show that the proposed relaxed algorithm (with ordered-subsets [OS] acceleration) is about twice as fast as the existing unrelaxed fast algorithms, with negligible computation and memory overhead.

A separable quadratic surrogate total variation minimization algorithm for accelerating accurate CT reconstruction from few‐views and limited‐angle data

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Low dose CT image reconstruction with learned sparsifying transform

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“…[·] C is an operator that projects the input vector onto the convex set C, M is the number of ordered subsets, and A m , W m , and the vector y m are sub-matrices of A, W, and sub-vector of y, respectively, for the mth subset. 1 ≤ α < 2 is the (over-)relaxation parameter, and ρ > 0 is the AL penalty parameter decreasing gradually as iterations progress [10], i.e.,…”

Reduced anatomical clutter in digital breast tomosynthesis with statistical iterative reconstruction

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