Boots – shoes – and leggings
Patent
1986-10-15
1989-04-25
Harkcom, Gary V.
Boots, shoes, and leggings
G06F 734, G06F 1535
Patent
active
048253995
DESCRIPTION:
BRIEF SUMMARY
DESCRIPTION
1. Technical Field
In image engineering, such as computerized axial tomography (CAT or CT), it is necessary to reconstruct images with high spatial resolution in order to clearly image small objects. The present invention relates to an apparatus for increasing the spatial frequency components (so-called spatial frequency multiplication) needed for such a high-resolution imaging, by making use of Fourier transform.
2. Background Art
When an image is reconstructed with high resolution by computerized axial tomography, a convolution is performed using Fourier transform. During this process, a desired number of O's are inserted into an array of data obtained by sampling. Then, the Fourier transform of the increased amount of data is taken to increase the spatial frequency components. For example, a signal is sampled, resulting in N values a.sub.0, a.sub.1, a.sub.2, . . . , a.sub.N-1, as shown in FIG. 2. Then, two O's are added to each value, increasing the number of values to 3N. Subsequently, N O's are added to this array of values to obtain 4N values. Then, the Fourier transform of the 4N values is taken to multiply the Nyquist rate by a factor of three.
Let us assume that N=1024. Then, it is necessary to add 1024 O's to 3N (=3072) values. Then, real numbers which are N' (=4096) in total must be subjected to Fourier transform. It takes a very long time to perform this mathematical operation. Now let T be the time required to take the Fourier transform of 1024 real numbers. If the number of data items is increased by a factor of 4, and if the number of loops processed increases by a factor of 1.2, then the operation time required for the mathematical operation will increase by a factor of about 5, because 4.times.1.2 T=4.8 T. In reality, the Fourier transform of 2048 complex numbers is taken to reduce the operation time, but it is not yet sufficiently short.
When a spatial frequency is multiplied by a factor of four, 3 O's are added to each of N values a.sub.0, a.sub.1, a.sub.2, . . . , a.sub.N-1 derived by sampling, s shown in FIG. 3. Then, the Fourier transform of the resulting 4N values is taken. Therefore, the time required for the transformation is the same as in the case where the spatial frequency is multiplied by a factor of three.
DISCLOSURE OF THE INVENTION
It is an object of the present invention to provide an apparatus capable of multiplying spatial frequencies by means of Fourier transform without involving an increase in the operation time.
In accordance with the invention, data obtained by sampling is stored in a memory (MM). The Fourier transform of the data is taken by Fourier transform means (ADD, MUL, HM1, HM2, TBM) without introducing O's to the data. The result is written simultaneously to a plurality of memories (M1, M2, M3, M4) at relative addresses corresponding to each other. A series of addresses is specified through these memories (M1-M4).
Brief Description of the Drawings
FIGS. 1 is a block diagram of an apparatus according to the invention;
FIGS. 2 and 3 show arrays of data processed during the conventional process of Fourier transform; and
FIG. 4 shows an array of data used by the apparatus shown in FIG. 1.
BEST MODE FOR CARRYING OUT THE INVENTION
The theory of the Fourier transform operation performed by an apparatus according to the invention is first described. N data items are obtained by sampling. We now take an example in which the maximum spatial frequency is increased by a factor of m by Fourier transform. For simplicity, it is assumed that N=2.sup..gamma. and m=2.sup..alpha., where .gamma. and .alpha. are integers. The N data items or values are written as a.sub.0, a.sub.1, a.sub.2, . . . , a.sub.N-1 Referring to FIG. 3, O's are added to N'=m.multidot.N=2.sup..gamma.+.alpha.. This includes values b.sub.0, b.sub.1, b.sub.2, . . . , b.sub.N'-1. The following relations hold regarding these values: ##EQU1## where ##EQU2## Meanwhile hN=W.sub.N.sup.ik .multidot.e.sup.-j2.pi.ih =W.sub.N.sup.ik transform contains recurrent Fourier transform of N data items a.s
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Harkcom Gary V.
Kojima Moonray
Shaw Dale M.
Yokogawa Medical Systems Limited
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