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Manuscript received December 18, 1978;revised March 15,1979. The author is with the School of Electrical Engineering, Purdue University, West Lafayette, IN 47907. 'The low contrast resolution dependa upon the signal-to-noise ratio in the reconstructed image and, therefore, is a function of radiation dosage.
I . ample DiChiro et Q(461 comparedthetomogramsofaheadfor a slice taken
near the apex (where the beam hardening effects are the greatest) with a slice takenatalower level. Theyshowedthatthe attenuation value computed for cerebrospinal fluid was 30 (CT units) in the former case and 11 in the latter. Apparently, the severe beam hardening caused this large change in the computed CT number. The often quoted 1-percent sensitivity onlyrefers to the ability of a CT scanner to distinguish between tissues(over a few square millimeters area) whose attenuation coefficients may differ by only 1 percent.
0018-9219/79/0900-1245$00.75 1979 IEEE 0
Authorized licensed use limited to: Illinois Institute of Technology. Downloaded on January 30, 2010 at 11:33 from IEEE Xplore. Restrictions apply.
1246
PROCEEDINGS OF THE IEEE. VOL. 67, NO. 9, SEPTEMBER 1979
goal here is the same as with X-rays, namely, to obtain quantitative crosssectional images depicting morphological detail of the humanbody. However, incontrastwith X-rays,CT imagingwith ultrasound is madedifficultby thefactthat rays of sound'.energy do not necessarily travel along straight lines intissue,andmayundergoseriousrefraction at interfaces between soft and hard tissues. On account of this,a p plications of ultrasound CT appear t o be limited for the foreseeable future to tho& parts of human body that are free of hard tissues such as bone.Thusmost of thecurrenteffort in t i area is focused on the clinically important problem of hs tumor detection in the female breast. Common to all threedifferent CTimaging modalities described above are the computer algorithms for reconstructing tomograms projection from data. Al reconstruction algol rithms are based on the assumption that the projections are line integrals of the quantity of interest. The extent to which ti assumption is violated determines the magnitude of artihs facts visible in the tomogram. Examples of such artifacts include those caused by beam hardening in the case of X-ray C T, those caused byinadequate or inaccurateattenuation compensation for emission CT, and those caused by refractive effects in ultrasound CT. Study of artifacts and ways to minimize them has assumed importance during the last threeyears, and a number articles hasbeen published on this subject. of Our aim in this paper isto do a review of the major develop mentsthat have taken place in CT imaging during the last three years. We have focused on this period for two reasons: i) the relevant science and engineering have grown enormously during this period; and ii) review papers by other authorshave morethanadequately covered thetime period before1976 (excepting ultrasound CT which has not been reviewed so far). The review article by Brooks and DiChiro[ 141 surveys X-ray CT for work published till 1976. Emission CT hasbeenreviewedbyTer-Pogossian[ 1131, Phelps[ 991, and Budinger[271. Because of space limitations there had to be some selection in the topicspresentedhere. In emission CT the biggest development of the last three years is the great
interest that has developed inpositrontomography. While have we reviewed most of the recent advances in single photon emission CT, our treatment of positron emission CT is essentially introductory. Positron emission CT presents aseries of unique technical problemsthat are not addressed here. In what follows, Section I1 deals with recent developments in reconstruction algorithms. Section 111 is on X-ray CT and examines the degree to which the projection data generated on CT scanners conform to the assumptions made in the development of algorithms. Section IV is on emission CT and includes positron both tomography tomography and using single gamma-ray counting. Section V is on ultrasound CT.
where tl is the perpendicular distance of the linefrom the origin. The integral of the function f(x, ) along this line may y be expressed as
1=
ray AB
I
f(x,y)ds
where 6(*) the Dirac delta function. The function P e ( t ) as is a function of t (for a given value of 0) defines theparallel projection of f (~y, ) for angle 8. The two dimensional function P e ( t ) is also called the Radon transform of f(x, y ) . One may also generate projections by integrating a function along a set of lines emanating from a point source as shown in Fig. 2. Such projections are called fan-beam projections. A reconstructionalgorithm tells us how to reconstructa function f(x, y ) from its projections. Over the past few years many such algorithms have been developed[ 141. The algorithms that are currently being used on most if not all CT scanners are of the filtered-backprojection type. We will now present and discuss the steps involved in the implementation of these algorithms. We will assume that the projections are uniformly sampled, which is the case most often encountered in practice. For the case of nonuniform sampling the reader is referredto[681.A . Filtered-Backprojection Algorithm for Parallel Projection Data T i algorithm is based on following relationships[ 121,1791, hs 11021,[lo71