GB2192120A

GB2192120A - Reconstructing objects from limited-angle scannings in computerized tomography

Info

Publication number: GB2192120A
Application number: GB08714563A
Authority: GB
Inventors: Kwok Cheong Tam
Original assignee: General Electric Co
Current assignee: General Electric Co
Priority date: 1986-06-23
Filing date: 1987-06-22
Publication date: 1987-12-31
Anticipated expiration: 2007-06-22
Also published as: IT1204649B; GB8714563D0; FR2600442A1; DE3716988A1; JPS6325538A; IT8720631A0; GB2192120B

Description

1 GB 2 192 120 A 1

SPECIFICATION with embedded flaws, contains a medium that

Reconstructing objects.from limited-angle occupies most of the crosssectional area whose scannings in computerized tomography density is known. In the reconstruction procedure the idea is to eliminate the contribution of that This invention relates to imaging objects with a 70 medium, and reconstruct the image which is the computerized tomography system when the difference between the original object and a angular coverage is restricted, and especially to a hypothetical object made up of only that medium method incorporating the a priori information of the which has the same exterior boundary as the dominant component of the object into limited- original object.

angle reconstruction procedures. 75 The method of limited-angle imaging and X-ray CTtechniques are being applied to the reconstructing flaws in such an object, according to nondestructive inspection of industrial products and the illustrative embodiment, comprises scanning equipment. Standard CT reconstruction techniques the object with x-rays or another imaging agent at calculate the density distribution within a cross- many angles and generating a measured projection section of the inspected objectfrom the attenuation 80 at each scan angle. Projections are calculated of the measurements of the cross-section at all angles. hypothetical object just described. The calculated However, in some situations the object can be projection is subtracted from the measured scanned only in a restricted angular range. For projection at the corresponding scan angle to example, the object may be very long in one produce a difference projection resulting from the dimension, and therefore the measurements at 85 presence of a flaw. The difference projections at the small angles to the longitudinal direction are several angles are backprojected to yield image attenuated too much to serve any useful purpose. strips inside the boundary to which the flaws are Also, measurements in some angular range may be confined, and a region or regions enclosing the obstructed by other objects. The images flaws is constructed by overlapping all the image constructed from such restricted data usually 90 strips. Using the flaw- enclosing region and the contain artifacts. difference projections, the shape of the flaws and Limited-angle reconstruction techniques have density values are reconstructed by means of been developed to remove the artifacts due to the limited-angle reconstruction algorithms.

missing information; one reference is the published Another aspect of the method is that the paper by the inventor and V. Perez-Mendez, 95 backprojected image strips have non-zero values "Tomographical Imaging with Limited-Angle while all other image portions inside the boundary Input", J. Opt. Soc. Am., 71 (May 1981) 582-592. are assigned a zero value.

Typically the limited-angle image reconstruction Yet another aspect is that the limited-angle techniques make use of the available a priori reconstruction procedure is iterative and the information of the object to compensate for the 100 reconstructed image is transformed back and forth missing scanning information. The most readily between object space by filtered backprojection, available a priori information include the external and projection spaces by projection, and repeatedly boundary of the object, and the known upper and corrected by a priori information about the flaw lower bounds of the density values. The more enclosing region in object space (extent and precise these a priori information are known, the 105 location of that region, upper and lower bounds of better the quality of the reconstructed images. Still, the density values) and by the difference projections the images reconstructed in this way are usually not in projection space. - as good as those reconstructed from complete An embodiment of the present invention, given by angular scanning information. way of non-limitative example, will now be A method to improve further the images 110 described with reference to the accompanying reconstructed from limited-angle information drawings, in which:

makes use of multiple energy x-ray scanning as Fig. 1 is a representation of a typical industrial taught in the US patent 4,506,327. The method is for object composed of a medium containing a number composite objects which are made up of a small of flaws.

number of substances. Industrial products and 115 Fig. 2 is a diagram showing determination of a equipment usuallyfulfill this condition. The object is difference projection from a measured projection scanned several times by x-rays at different and the calculated projection of a hypothetical energies. By suitably combining the scanning data object having no flaw.

the different components within the object can be Fig. 3 illustrates backprojecting each difference reconstructed individually, which results in much 120 projection.

better image quality. Of course, this method cannot Fig. 4 illustrates constructing a region that be applied if it is impractical to perform multiple encloses all the flaws in the object.

energy x-ray scannings. Fig. 5 shows diagrammatically using the In an aspect of the present invention limited-angle constructed flaw- enclosing region and difference imaging of certain objects is improved by 125 projections to reconstruct the flaws by means of incorporating additional a priori information of limited-angle reconstruction algorithms.

those objects other than the usual a priori Fig. 6 is a flow chart of one limited-angle information such as the external boundary, and reconstruction technique.

upper and lower bounds of the density values. In Fig. 7 shows an x-ray computerized tomography many cases the object, such as a volume of metal 130 system for industrial inspection when the angular 2 GB 2 192 120 A 2 coverage is restricted. projections c1l, the flaw or flaws 11 are reconstructed Object 10 in Fig. 1 is composed of a medium m by means of known limited- angle reconstruction that occupies most of the region but contains one or algrothims. To start with, it was known that all the more flaws 11. The density prn of the medium is other component substances or flaws are located known and the exterior boundary S of the object is 70 somewhere inside the boundary S. After the step known. Such is the case in, but not restricted to, illustrated in Fig. 4 the region of their occurrence is industrial non-destructive testing in which the narrowed down from S to the much smaller region object may consist of a metal medium with some D. Since there is now a much more precise flaws embedded inside, and the flaws are often knowledge of the region of occurrence for the flaws, either voids or inclusions. The term "flaws" is 75 the limited-angle reconstruction of the flaws using sometimes used is a broader sense to denote flaw the flaw-enclosing region D as a priori information component substances in the object other than the will yield much better results than if the much medium m. bigger region S were used.

The reconstruction procedures are illustrated in One suitable limitedangle reconstruction Figs. 2-5. A single flaw is shown butthe method is 80 technique which is developed in the previously equally applicable to the reconstruction and mentioned published technical paper is sketched in imaging of multiple flaws. The original object A, Fig. 6. This is an iterative algorithm: the Fig. 2, is scanned with an imaging agent such as x- reconstructed image is transformed back and forth rays and from the detected data a measured between the object space by filtered backprojection, projection Pi is generated. This is done at many scan 85 and the projection space by projection, being angles overthe limited angular range that is repeatedly corrected by the a priori information available. Let P1, P21... Pn denote the measured aboutthe object in the object space and by the projections at the n angles 01, 02-.. On respectively. known projections in the projection space. The A hypothetical object B is utilized which is made up known information on the object, i.e. flaw-enclosing entirely of the medium m and which has the same 90 region, are the extent and location of that region, the exterior boundary S as the original object. An image upper bound of the density value, and the lower is reconstructed which is the difference between the bound of the density value. The density value here original object A and the hypothetical object B; this referred to is the density of the reconstructed eliminates the contribution of the medium m. The difference image of the difference between the reconstruction proceeds by calculating projections 95 original object A and the hypothetical object B. The qi of the hypothetical object B from the knowledge upper and lower bounds of the density value can be of the exterior boundary S and the value pm. The derived from the upper and lower bounds of the projections q1, q2... qn of the hypothetical object B density value of the original object A and the density are calculated at the n angles. At each scan angle the of the medium m.

calculated projection qj is subtracted at 12 from the 100 The estimated object density is determined, measured projection pi, yielding a difference corrected by resetting to zero those pixels outside projection di resulting from the presence of a flaw. the known extent of the object, resetting to the The several projections q, are subtracted from the upper bound those pixels with density exceeding corresponding projections pi and the difference of the upper bound, and resetting to the lower bound the projections is denoted by d, = pi - q1. If there 105 pixels with density below the lower bound. The are multiple flaws the difference projection will difference projections d, to d. of the object in the contain more than one non-zero region at most of limited angular range are provided, and the other the scan angles. missing projections to make up a complete 1800 Referring to Fig. 3, the next step in the angular range are setto zero initially. From the reconstruction procedure is to backproject the 110 initial set of projections the first estimate of the difference projections to derive image strips inside object density is made which is corrected by the the boundary S to which the flaws are confined. foregoing a priori information about the object.

Each difference projection di is backprojected at the From this second estimate of the object density the respective scan angle Oi. Denote by D, the portion of projections in the supplementary, missing angles the backprojected image inside the boundary that 115 are calculated. The calculated projections of the has non-zero value. The portions Di' correspond to supplementary angles are combined with the the region in the original object A that is occupied known difference projections at other angles to yield entirely by the medium m. All the flaws are confined a new estimate of object density, and the process is to the portion Di, i.e. to the image strip. repeated. The shape of the flaw or flaws as well as As shown in Fig. 4, all of the backprojected image 120 an indication of their density are calculated. The strips D1 are overlapped to construct a flaw difference between the flaw density and the enclosing region D. In this figure the difference medium density is actually computed.

projections at five scan angles which cover less than Fig. 7 shows one practical implementation of the 180'are identified as d, to the d5. The region D atthe invention, an x- ray CT system to image internal intersection of the five image strips encloses all the 125 flaws in an otherwise homogeneous object. An x flaws in the object. The region D does not need to be ray beam emitted by a source 13 is collimated into a single connected region; it may consist of a parallel rays by a collimator 14, passes through the number of separate convex regions. object 15 and is detected by x-ray detector 16. The The next step is illustrated in Fig. 5. Using the object is scanned linearly in the direction illustrated, flaw-enclosing region D and the difference 130 then successively turned to scan at other angles 3 GB 2 192 120 A 3 over the available range. The detected signals, measured projection at each said scan angle to which are the projections pl, are fed into the generate a difference projection resulting from the processing computer 17 togetherwith the values of presence of a flaw; Oi. The a priori information on the boundary S of the constructing a flaw- enclosing region by object and the known density p,,, of the medium m 70 backprojecting the difference projections and making up most of the object are also input to determining the intersection of image strips inside computer 17. Given S and p,,, and the scan angles 01, the boundary of the object to which the flaw is the calculated projections qi of the hypothetical confined; and object B at the corresponding scan angles (Fig. 2) using the difference projections and flaw- are computed at 18. The difference projections d, at 75 enclosing region, reconstructing the flaw by means the respective angles Oi are obtained at 19 by of limited-angle reconstruction algorithms.

Claims

subtracting the calculated projections qi from the
2. The method of Claim

1 wherein the image strips measured projections pi. By backprojecting at 20 the have a non-zero value and all other image regions difference projections di at the corresponding inside the boundary have a zero value.

angles and determining the intersection of image 80
3. The method of Claim 1 or Claim 2 wherein the strips Di (Fig. 3) the boundary of region D which imaging agent is x-rays.

encloses the flaw or flaws is obtained (Fig. 4).
4. The method of any of Claims 1 to 3 wherein the Finally, using the flaw-enclosing region D, the limited-angle reconstruction algorithm is iterative difference projections di, and the values of the scan and the reconstructed image is transformed back angles E)i in limited-angle reconstructions, the flaws 85 and forth between object space by filtered are reconstructed at 21 and displayed at 22. The backprojection, and projection space by projection, shape of the flaw or flaws and an indication of their and repeatedly corrected by a priori information density are displayed, and the boundary S of the about the flaw-enclosing region in the object space object if desired. and by the difference projections in the projection The application of x-ray CT to industrial non- 90 space.

destructive evaluation has been growing in recent
5. The method of Claim 4 wherein the a priori years. Limited-angle x-ray imaging frequently information aboutthe flaw- enclosing region is the occurs in industrial inspection. Some circumstances extent and location of that region, and upper and to which the invention is applicable are where lower bounds of the density value of the difference measurements over 180'or a complete 3600 are 95 image.

obstructed by other objects, or where the object is
6. A method of imaging, in a computerized long and narrow so that measurements at angles tomography system, flaws in an object whose close to the longitudinal direction do not yield useful exterior boundary is known and which contains a information. medium occupying most of the cross-sectional area The number of angles from which the object is 100 whose density is known, comprising:

scanned will depend on the circumstances of the scanning the object with x-rays at a plurality of individual case. However, it is preferred that the angles over a limited angular range and generating number of angles N is determined in the following a measured projection at every scan angle; manner from the available scanning angular range calculating projections of a hypothetical object R and the angle spacing interval AE):- 105 made up entirely of the medium and having the AE) (in radians) is selected to be no greater than same exterior boundary as the original object; s/S where S is the diameter of the object A and s is subtracting the calculated projection from the the linear dimension of a pixel; measured projection at each scan angle to yield a N is then given by N = R/AG. difference projection resulting from the presence of While the invention has been shown and 110 a flaw; described with reference to a preferred backprojecting the difference projections to derive embodiment, it will be understood by those skilled image strips inside the boundary to which the flaws in the art that various changes in form and details are confined; may be made without departing from the scope of overlapping the backprojected image strips to the invention. 115 construct one or more flaw-enclosing regions; using the difference projections and flaw CLAIMS enclosing regions, reconstructing the flaws by 1. A limited-angle imaging method to reconstruct means of limited-angle reconstruction procedures; flaws embedded inside an object in a computerized and tomography system when a known medium 120 displaying the shape of the reconstructed flaws occupies most of the cross-sectional area of the and an indication of their density.

object, the method comprising:
7. The method of Claim 6 wherein the scanning the object with an imaging agent at a backprojected image strips have a non-zero value plurality of angles over a limited angular range and and all other image portions inside the boundary generating a measured projection at every said scan 125 have a zero value.

angle;
8. The method of Claim 6 or Claim 7 wherein the calculating projections of a hypothetical object limited-angle reconstruction procedure is iterative made up entirely of the known medium and having and the reconstructed image is transformed back the same exterior boundary as the original object; and forth between object space by filtered subtracting the calculated projection from the 130 backprojection, and projection space by projection, NOW. IIIIIIIIIIE-1, - 4 GB 2 192 120 A 4 and repeatedly corrected by a priori information plurality of angles within a limited angular range aboutthe flaw-enclosing regions in the object space and generates a measured projection at every said and by the difference projections in the projection 25 scan angle; space. calculates projections of a hypothetical object
9. The method of Claim 8 wherein the a priori made up entirely of the known medium and having information about the flaw-enclosing regions is the the same exterior boundary as the original object; extent and location of those regions, and upper and subtracts the calculated projection from the lower bounds of the density value of the difference 30 measured projection at every said scan angle to image. generate a difference projection;
10. The method of any preceding claim in which constructs a flaw- enclosing region by the number N of said scan angles meets the backprojecting the difference projections and criterion N = R/AG where R is the available determines the intersection of image strips inside scanning angular range and AG is the angle spacing 35 the boundary of the object to which the flaw is interval, and AG (in radians) <_ s/S where S is the confined; and diameter of the object and s isthe width of a pixel of using the difference projections and the flaw a projection. enclosing region, reconstructs the flaw by means of
11. Computerized tomography apparatus for a limited-angle reconstruction algorithm.

reconstructing flaws embedded inside an object by 40
12. A limited-angle imaging method of limited angle imaging, when a known medium reconstructing flaws in an object by computerised occupies most of the cross-sectional area of the tomography substantially as herein described with object, which apparatus: reference to the accompanying drawings.

scans the object with an imaging agent at a Printed for Her Majesty's Stationery Office by Courier Press, Leamington Spa, 12/87. Demand No. 8991685. Published by the Patent Office, 25 Southampton Buildings, London, WC2A 1AY, from which copies may be obtained.