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

Abstract

Medical CT imaging often encounters metallic implants or some metal interventional therapy apparatus. These metallic objects can produce metal artifacts in reconstruction images, which severely degrade image quality. In this paper, we analyze the difference between polychromatic projection data and Radon transform data and develop an analytical method to reduce metal artifacts. Approximate features of metal artifacts can be obtained by a simplified energy spectrum function of x-ray beam. The developed method can reduce most artifacts, and preserve more original details. It does not require prior knowledge of x-ray energy spectrum and original projection data, avoiding iterative calculation and saving reconstruction time. Simulation experimental results show that the method can greatly remove metal artifacts.

Region stability of linear stochastic discrete systems with time-delays

“…If system (5) is D(q, r)-stable then there exist two constants C 1 > 0,C 2 > 0 such that C 2 x 0 2 ( q + ε) t ≤ E x(t) 2 ≤ C 1 x 0 2 (( q + r)ε) t . If system (5) is D(r, θ )-stable then there exists a constant C > 0 such that E x(t) 2 ≤ C x 0 2 (rε) t .Remark 3.3 From Theorem 3.5 and Corollaries 3.2-3.4, region stabilities defined in this paper imply mean square stability of system(5).…”

“…Stability is one of essential concepts in dynamical system theory, which has been considered by the researchers in many fields, such as [1][2][3][4][5][6][7][8], and [9][10][11][12]. For a linear system without delays, as is well known, the stability is related to the system matrix root-clustering in subregions of the complex plane.…”

Hybrid variational model based on alternating direction method for image restoration

“…Image restoration mainly includes image deblurring and image denoising, which is one of the most fundamental problems in imaging science. It plays an important role in many mid-level and high-level image-processing areas such as medical imaging, remote sensing, machine identification, and astronomy [1][2][3][4]. The image restoration problem usually can be expressed in the following form:…”

“…The Tikhonov regularization method has a disadvantage, which tends to make images overly smooth and often fails to adequately preserve important image attributes such as sharp edges. The total variation regularization method has the ability to preserve edges well and remove noise at the same time, which was first introduced by Rudin et al [6] as follows: min f Hfg 2 2 + α f TV , (1.2) where • 2 denotes the Euclidean norm, • TV is the discrete total variation regularization term, and α is a positive regularization parameter that controls the tradeoff between these two terms. To define the discrete TV norm, we first introduce the discrete gradient ∇f :…”

“…where α 1 , α 2 are positive regularization parameters. Model (1.3) adds a term fu 2 2 , compared with model (1.2). The experimental results show that the modified TV minimization model can preserve edges very well in the image restoration processing.…”