Fourier transform resampling: Theory and application

Conference · Tue Dec 31 04:00:00 EST 1996

OSTI ID:513238

Hawkins, W G ^[1]

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1. Univ. of Nebraska Medical Center, Omaha, NE (United States)

One of the most challenging problems in medical imaging is the development of reconstruction algorithms for nonstandard geometries. This work focuses on the application of Fourier analysis to the problem of resampling or rebinning. Conventional resampling methods utilizing some form of interpolation almost always result in a loss of resolution in the tomographic image. Fourier Transform Resampling (FTRS) offers potential improvement because the Modulation Transfer Function (MTF) of the process behaves like an ideal low pass filter. The MTF, however, is nonstationary if the coordinate transformation is nonlinear. FTRS may be viewed as a generalization of the linear coordinate transformations of standard Fourier analysis. Simulated MTF`s were obtained by projecting point sources at different transverse positions in the flat fan beam detector geometry. These MTF`s were compared to the closed form expression for FIRS. Excellent agreement was obtained for frequencies at or below the estimated cutoff frequency. The resulting FTRS algorithm is applied to simulations with symmetric fan beam geometry, an elliptical orbit and uniform attenuation, with a normalized root mean square error (NRME) of 0.036. Also, a Tc-99m point source study (1 cm dia., placed in air 10 cm from the COR) for a circular fan beam acquisition was reconstructed with a hybrid resampling method. The FWHM of the hybrid resampling method was 11.28 mm and compares favorably with a direct reconstruction (FWHM: 11.03 mm).

• OSTI ID: 513238
• Report Number(s): CONF-961123--
• Country of Publication: United States
• Language: English

Related Subjects

44 INSTRUMENTATION
INCLUDING NUCLEAR AND PARTICLE DETECTORS
55 BIOLOGY AND MEDICINE
BASIC STUDIES
99 GENERAL AND MISCELLANEOUS
ALGORITHMS
FOURIER ANALYSIS
IMAGE PROCESSING
KERNELS
SAMPLING
SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY