Since scattered radiation in cone-beam volume CT implies severe degradation of CTimages by quantification errors, artifacts, and noise increase, scatter suppression is one of the main issues related to image quality in CBCTimaging. The aim of this review is to structurize the variety of scatter suppression methods, to analyze the common structure, and to develop a general framework for scatter correction procedures. In general, scatter suppression combines hardware techniques of scatter rejection and software methods of scatter correction. The authors emphasize that scatter correction procedures consist of the main components scatter estimation (by measurement or mathematical modeling) and scatter compensation (deterministic or statistical methods). The framework comprises most scatter correction approaches and its validity also goes beyond transmission CT. Before the advent of cone-beam CT, a lot of papers on scatter correction approaches in x-ray radiography, mammography, emission tomography, and in Megavolt CT had been published. The opportunity to avail from research in those other fields of medical imaging has not yet been sufficiently exploited. Therefore additional references are included when ever it seems pertinent. Scatter estimation and scatter compensation are typically intertwined in iterative procedures. It makes sense to recognize iterative approaches in the light of the concept of self-consistency. The importance of incorporating scatter compensation approaches into a statistical framework for noise minimization has to be underscored. Signal and noise propagation analysis is presented. A main result is the preservation of differential-signal-to-noise-ratio (dSNR) in CT projection data by ideal scatter correction. The objective of scatter compensation methods is the restoration of quantitative accuracy and a balance between low-contrast restoration and noise reduction. In a synopsis section, the different deterministic and statistical methods are discussed with respect to their properties and applications. The current paper is focused on scatter compensation algorithms. The multitude of scatter estimation models will be dealt with in a separate paper.
The authors have to appreciate additional references by Jan Boese, critical comments by Bernhard Scholz, discussions with M. Petersilka and Karl Stierstorfer, and assistance in Latex handling by Frank Dennerlein and Christopher Rohkohl.
Last not least the first author acknowledges the early encouragement of mathematical generalizations and emphasizing of consistency principles by his former boss and colleague Guenter Schwierz (now retired).
I.A. Review of scatter relevance in CT
I.B. Organization and aim of the article
I.C. Mathematical notations
II. HARDWARE TECHNIQUES OF SCATTER SUPPRESSION
II.B. Beam shaper (Bow-tie filter)
II.D. Antiscatter grid
III. STRUCTURE OF SCATTER CORRECTION METHODS
III.A. Image-basedscatter correction
III.B. Projection-based scatter correction
III.C. Mixed strategies
IV. IMAGE RECONSTRUCTION BASED SCATTER COMPENSATION APPROACHES
IV.A. Iterative improvement reconstruction
IV.A.1. Iterative improvement in data space
IV.A.2. Iterative improvement in object image space
IV.C. Postprocessing image corrections
V. PROJECTION-BASED DETERMINISTIC SCATTER COMPENSATION APPROACHES
V.A. Matrix inversion and deconvolution approaches
V.B. Fixed-point equation and iterative subtractive algorithms
V.C. Iterative multiplicative algorithm
VI. PROJECTION-BASED STATISTICAL SCATTER COMPENSATION APPROACHES
VI.A. Gaussian maximum likelihood
VI.B. Poisson maximum likelihood approach
VI.B.1. Poisson MLEM in emission tomography
VI.B.2. Poisson MLEM for Scatter Correction
VI.C. Bayesian maximum a posteriori probability or penalized likelihood method
VI.D. Penalized weighted least squares method
VI.E. Split and smooth method
VII. ERROR ANALYSIS AND IMAGE QUALITY ISSUES
VII.A. Deterministic error analysis of scatter propagation in CT
VII.A.1. Deterministic CT projection error due to scatter
VII.A.2. Cupping and shadow artifacts in CTimages
VII.A.3. “Contrast” degradation due to scatter
VII.B. Statistical error analysis of scatter in CT
VII.B.1. Differential-signal-to-noise-ratio dSNR
VII.B.2. Contrast recovery, noise amplification and dSNR preservation by scatter correction
VII.B.3. dSNR propagation via backprojection
VII.B.4. Note on DQE analysis
VIII.A. Synopsis of scatter compensation approaches
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