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Absolute values of attenuation coefficients in computed tomography
This content has been downloaded from IOPscience. Please scroll down to see the full text. 1979 Phys. Med. Biol. 24 828 (http://iopscience.iop.org/0031-9155/24/4/017) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 160.36.178.25 This content was downloaded on 01/10/2015 at 20:03
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828
Correspondence
Absolute Values of Attenuation Coefficient in Computed Tomography THE EDITOR, Sir, Gore and Tofts(1978)in theirScientific Note dispute the claim of Rutherford, Pullan, Goddard and Isherwood (1976) that ‘the convolution method does not provide an absolutevalue of absorption coefficient’. The following (hypothetical) experiment may shed light on the dispute. A reconstruction is made of the water box of a water box scanner; identical measurements result a t each sampling position (ignoring quantum noise); zero values emerge after convolution and their back-projection sum is also zero. The water boxis then filled with any otheruniform medium and theprocedure repeated. The result is always zero; therefore the absolute values cannot be recovered. I n effect, the scanners determine the departure of the local attenuation from the attenuation of the medium in which the object is immersed (typically air or water) which is presumably known and remains constant, and values can only be expressed on an absolute scale where this value is given. On a related point, it is sometimes argued that referencing to the medium is produced by expressing measurements (Ip)as lnIo/Ipwhere Io is the measurement of the reference medium at the edge of the scan field or some similar constant. However, any constant multiplier for theintensity readings of a single projection vanishes during the convolution step since it may be separated out as In Io Cfp where fp are the filter elements, which have a zero sum. Thus normalisation of readings serves only as a scaling operation for computational purposes and has no impact on the value (or meaning) of the reconstructed values, and referencing to themedium is inherent in theconvolution procedure. It is important to note that changes in attenuation values are observed for objectsinwaterboxscanners if thewater is sufficiently contaminated or heated. Even larger changes would occur for air scanners if the units were immersed in water-but the experiment is not to be encouraged!
5 January 1979
C. H. MARSHALL, Radiological Research Laboratory, New York University Medical Center, 560 First Avenue, New York, NY 10016, U.S.A.
THEEDITOR, Sir, The above letter raises some interesting points regarding our assertion(Gore and Tofts 1978) that the method of filtered back-projectionis capable of reconstructingabsolutevalues of an objectdensityfunction.Thismethod
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My IOPscience
Absolute values of attenuation coefficients in computed tomography
This content has been downloaded from IOPscience. Please scroll down to see the full text. 1979 Phys. Med. Biol. 24 828 (http://iopscience.iop.org/0031-9155/24/4/017) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 160.36.178.25 This content was downloaded on 01/10/2015 at 20:03
Please note that terms and conditions apply.
828
Correspondence
Absolute Values of Attenuation Coefficient in Computed Tomography THE EDITOR, Sir, Gore and Tofts(1978)in theirScientific Note dispute the claim of Rutherford, Pullan, Goddard and Isherwood (1976) that ‘the convolution method does not provide an absolutevalue of absorption coefficient’. The following (hypothetical) experiment may shed light on the dispute. A reconstruction is made of the water box of a water box scanner; identical measurements result a t each sampling position (ignoring quantum noise); zero values emerge after convolution and their back-projection sum is also zero. The water boxis then filled with any otheruniform medium and theprocedure repeated. The result is always zero; therefore the absolute values cannot be recovered. I n effect, the scanners determine the departure of the local attenuation from the attenuation of the medium in which the object is immersed (typically air or water) which is presumably known and remains constant, and values can only be expressed on an absolute scale where this value is given. On a related point, it is sometimes argued that referencing to the medium is produced by expressing measurements (Ip)as lnIo/Ipwhere Io is the measurement of the reference medium at the edge of the scan field or some similar constant. However, any constant multiplier for theintensity readings of a single projection vanishes during the convolution step since it may be separated out as In Io Cfp where fp are the filter elements, which have a zero sum. Thus normalisation of readings serves only as a scaling operation for computational purposes and has no impact on the value (or meaning) of the reconstructed values, and referencing to themedium is inherent in theconvolution procedure. It is important to note that changes in attenuation values are observed for objectsinwaterboxscanners if thewater is sufficiently contaminated or heated. Even larger changes would occur for air scanners if the units were immersed in water-but the experiment is not to be encouraged!
5 January 1979
C. H. MARSHALL, Radiological Research Laboratory, New York University Medical Center, 560 First Avenue, New York, NY 10016, U.S.A.
THEEDITOR, Sir, The above letter raises some interesting points regarding our assertion(Gore and Tofts 1978) that the method of filtered back-projectionis capable of reconstructingabsolutevalues of an objectdensityfunction.Thismethod
