<title>Computer tomographic (CT) image reconstruction from limited information</title>

Abstract

A new reconstruction algorithm is introduced to obtain high quality computerized tomography image from limited information.There are many practical cases that only limited projection data can be collected due to the physical constraints of hardware system and the object structure. In these cases , conventional reconstruction algorithms which require complete projections are often unacceptable because it causes severe streak artifacts and distortions. So image reconstruction from limited information is very important and many authors have contributed to it. But the methods presented are often time consuming , less efficient and some algorithm's convergency can not be guaranteed. For iterative algorithms , it is more important to guarantee the convergency and accelcrate the convergency speed.In this paper , an CT image reconstruction method which exploits the Helgason -Ludwig consistency condition is designed to consider obtainable information content about object and reconstruction error in the situation of finite number of projection. Based on the consideration , we developed a new iterative algorithm which can reconstruct high quality artifactiess CT image from limited information , and we design a new histOgram constraint obtained from apriori knowledge to guarantee the convergency and to acquire high convergency speed. The results of simulated tests show the great advantages of this new method.

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

“…It is important to note that, this time, the verification has gone through the testing with projection data acquired by clinical MDCT. Both HLCC (Natterer 1986, Li and Wang 1995, Basu and Bresler 2000, Wang and Sze 2001, Clackdoyle 2013, Clackdoyle and Desbat 2015 and DIIC (Wei et al 2006, Tang et al 2012 are data consistency constraints, but they are established under parallel beam geometry and fan beam geometry, respectively. The primary advantage of DIIC over HLCC lies in the fact that the former only requires the engagement of one pair of projection views acquired at any angle under the fan beam geometry, whereas the latter demands the engagement of a large number of neighboring projection views acquired at relatively high and uniform sampling rate in the angulation.…”

“…A quadratic objective function based on the HLCC has been defined in Tang et al (2011) to determine the scaling factor λ 0 that is optimal for equation (9). However, the HLCC, either in its original form defined under parallel beam geometry (Natterer 1986, Li and Wang 1995, Basu and Bresler 2000, Wang and Sze 2001, Clackdoyle 2013, Clackdoyle and Desbat 2015 or its derivative under fan beam geometry (Yu et al 2006, Yu and Wang 2007, Tang et al 2011 demands the engagement of a large number of neighboring projection views and thus limits it applications over situations where projection data can only be acquired at sparse or non-uniform angular sampling rate. To address this drawback, we propose a method based on DIIC (Wei et al 2006, Tang et al 2012.…”

“…As demonstrated in our previous work (Tang et al 2011), the correction of bone-induced beam-hardening artifacts in CT can be accomplished by turning the calibration-oriented iterative operation into solving an optim ization problem, in which a quadratic objective function based on the Helgasson-Ludwig consistency constraint (HLCC) (Natterer 1986, Li and Wang 1995, Basu and Bresler 2000, Wang and Sze 2001, Yu and Wang 2007, Xu et al 2010, Clackdoyle 2013, Clackdoyle and Desbat 2015 is defined. In principle, the optimization based beam-hardening correction (BHC) using data consistency constraint (DCC) (John 1938, Patch 2002a, 2002b, Defrise et al 2003, Chen and Leng 2005, Leng et al 2007, Tang et al 2012 is sustained by projection data, and thus, its performance can be maintained over all scenarios while the tedious calibration process that is prone to errors can be avoided.…”

Data consistency condition–based beam-hardening correction

“…7,8 Meanwhile, the projection data consistency conditions have been utilized to solve several XCT problems. [30][31][32][33][34][35][36][37][38][39] Particularly, it was demonstrated that the beam-hardening correction based on the physical model of x ray imaging, and the H-L consistency condition, is feasible. 25 Inspired by previous investigations, in this article we will construct an objective function by combining the bone-correction formula with the H-L consistency condition, and optimize the objective function to automatically and stably determine the scaling factor and corresponding coefficient vector for beam hardening correction in polychromatic XCT imaging.…”