HIGH-SPEED TOMOGRAPHIC RECONSTRUCTION EMPLOYING FOURIER METHODS

Direct Fourier methods (DFM) of tomographic reconstruction have been i nvestigated since the introduction of the technique in the early 1970s , although computerized tomograms employ the convoluted back projectio n method (CBPM) as the means of computing the reconstruction. The main difficulty with DFM is the required interpolation of radially sampled data to the Cartesian grid in order to allow a 2D Fourier transform t o be performed on the frequency plane data, and is at least part of th e reason for the preference for CBPM. However, CBPM is difficult to im plement quickly on even highly specialized hardware, In contrast to th is, the main computational components of the DFM are a series of 1D Fo urier transforms on the projection data followed by a 2D Fourier trans form subsequent to a radial-to-Cartesian coordinate conversion, The Fo urier transforms can be computed very efficiently using a fast Fourier transform (FFT) algorithm implemented in digital signal processing ha rdware. This paper describes the development of a DFM reconstruction m ethod, The issue of the frequency plane interpolation is addressed and the effect of the accuracy with which this is performed on image reco nstruction quality is examined, It was found that good reconstruction quality could be obtained with a combination of zero-padding the proje ction data and simple bilinear interpolation of the frequency plane da ta array from radial to Cartesian coordinates, Hardware was developed based around the Sharp LH9124 FFT DSP chipset that is capable of compu ting a 2D 512 x 512 resolution complex to complex Fourier transform in 32 ms, Thus, by implementing the DFM with this hardware it is possibl e to compute tomographic reconstructions in several tens of millisecon ds, some two orders of magnitude faster than currently achieved with C BPM, This would be of value in a number of medical and industrial appl ications that require dynamic processes to be examined in real-time. ( C) 1997 Academic Press Limited.