Optimization based beam-hardening correction in CT under data integral invariant constraint

Abstract

In computed tomography (CT), the polychromatic characteristics of x-ray photons, which are emitted from a source, interact with materials and are absorbed by a detector, may lead to beam-hardening effect in signal detection and image formation, especially in situations where materials of high attenuation (e.g. the bone or metal implants) are in the x-ray beam. Usually, a beam-hardening correction (BHC) method is used to suppress the artifacts induced by bone or other objects of high attenuation, in which a calibration-oriented iterative operation is carried out to determine a set of parameters for all situations. Based on the Helgasson-Ludwig consistency condition (HLCC), an optimization based method has been proposed by turning the calibration-oriented iterative operation of BHC into solving an optimization problem sustained by projection data. However, the optimization based HLCC-BHC method demands the engagement of a large number of neighboring projection views acquired at relatively high and uniform angular sampling rate, hindering its application in situations where the angular sampling in projection view is sparse or non-uniform. By defining an objective function based on the data integral invariant constraint (DIIC), we again turn BHC into solving an optimization problem sustained by projection data. As it only needs a pair of projection views at any view angle, the proposed BHC method can be applicable in the challenging scenarios mentioned above. Using the projection data simulated by computer, we evaluate and verify the proposed optimization based DIIC-BHC method's performance. Moreover, with the projection data of a head scan by a multi-detector row MDCT, we show the proposed DIIC-BHC method's utility in clinical applications.

Cone-Beam Pair-Wise Data Consistency Conditions in Helical CT

“…The correction of artifacts in CT using the DCC is based on the minimization of a cost function derived from the DCC. Past examples include the completion of missing projections in limited angle tomography [4], the correction of ring artifacts due to malfunctioning detectors [5], the correction of beam hardening in polychromatic CT [6]- [9], the calibration of geometric parameters such as the detector position and orientation [10]- [12], or the detection and the compensation of rigid patient motion [13]- [17].…”

“…(9) and by using the relation b λ,λ ′ = −c τ ×n τ . The derivative of ϕ with respect to γ can be calculated by differentiating the expression of cos ϕ with respect to γ using the chain rule sin ϕ can be obtained in the same way as cos ϕ:sin ϕ = (p λ (γ, v τ ) − s λ ) cos(γ − λ) + c 1 sin(γ − λ) n 3 ,(36)this time using c τ = b λ,λ ′ ×n τ .…”

An Analytical Method for Reducing Metal Artifacts in X‐Ray CT Images

“…Although many metal artifact reduction (MAR) methods were developed, their applications in clinical settings are not totally successful because of the complexity of their forming cause and characteristics. Currently there is no standard solution [4,5]. Therefore, how to reduce metal artifacts still remain a challenging problem in x-ray medical CT imaging.…”