We investigate the use of direct-Fourier (DF) image reconstruction in computerized tomography and synthetic aperture radar (SAR). One of our aims is to determine why the convolutionbackprojection (CBP) method is favored over DF methods in tomography, while DF methods are virtually always used in SAR. We show that the CBP algorithm is equivalent to DF reconstruction using a Jacobian-weighted 2-D periodic sinc-kernel interpolator. This interpolation is not optimal in any sense, which suggests that DF algorithms utilizing optimal interpolators may surpass CBP in image quality. We consider use of two types of DF interpolation: a windowed sinc kernel, and the least-squares optimal Yen interpolator. Simulations show that reconstructions using the Yen interpolator do not possess the expected visual quality, because of regularization needed to preserve numerical stability. Next, we show that with a concentric-squares sampling scheme, DF interpolation can be performed accurately and efficiently...

The Fast Factorised Back-Projection (FFBP) algorithm has received considerable attention recently for SAS image reconstruction. The FFBP algorithm provides a means of trading image quality and/or resolution for a reduction in computational cost over standard Back-Projection. In this paper we describe FFBP for SAS image reconstruction and compare it to the Wavenumber algorithm in terms of computational cost and image quality.

This paper also proposed another reconstruction method based on a direct approximation of the Fourier inversion formula using a twodimensional (2-D) trapezoidal rule. In addition, the possibility of reconstruction from a concentric-squares raster was discussed. Numerous simple interpolators have been tried in DF reconstruction with the results compared with CBP [33]. In [34] and [35], the concept of angular bandlimiting was used to interpolate the polar data onto a Cartesian grid. In [36], a DF reconstruction using bilinear interpolation for diffraction tomography provided image quality that was comparable to that produced by the CBP algorithm. Very good reconstruction quality was obtained in [37] and [38] using a spline interpolator, or a hybrid type of spline interpolator. The notion of "gridding" was introduced in [39] as a method of obtaining optimal inversion of Fourier data. An optimal gridding function was proposed, and successful results were obtained when applied to the tomographic reconstruction problem. In [40], several different gridding functions were tried for DF reconstruction, and the performances were compared. In [41, 42], the linogram reconstruction method was proposed as a form of DF reconstruction. The data collection grid in the linogram method is the same as in the concentric-squares sampling scheme. The inversion of the Fourier data in [41, 42] was accomplished by first applying the chirp-z transform in one direction and then computing FFTs in the other direction. In CT, many of these attempts at DF reconstruction have given a poorer result than the CBP algorithm, due to the error incurred in the process of the polar-to-Cartesian interpolation. The attraction of DF reconstruction, however, is that it is thought to require less computation than ...

Thesis to the dissertation examination

Supervisor: doc. Ing. Miloˇs Drutarovsk´y, CSc. ”If we save even one life, we have been cost effective.”

A number of imaging technologies reconstruct an image function from its Radon projection using the convolution backprojection method. The convolution is an O(N² log N ) algorithm, where the image consists of N x N pixels, while the backprojection is an O(N³) algorithm, thus constituting the major computational burden of the convolution backprojection method. An O(N² log N ) multilevel backprojection method is presented here. When implemented with a Fourier-domain postprocessing technique, also presented here, the resulting image quality is similar to or superior than the image quality of the classical backprojection technique.

This paper presents a design for the parallel processing of synthetic aperture radar data using one or more Field Programmable Gate Arrays (FPGAs). Our design supports real-time computation of a two-dimensional image from a matrix of echo pulses and their corresponding response values. Components of this design include: (a) central processing pipeline to perform back projection calculations, (b) pre-fetch cache to minimize external memory access latency, (c) memory bridge that serves as the primary on-chip storage for pulse data, and (d) a pixel queue to direct image data in and out of the pipeline. Design parameters may be adjusted to achieve optimum performance, and multiple instances of this design may be replicated on-chip to achieve prespecified performance objectives. We provide a complexity analysis as a function of the input and output parameters. Simulation results based on an implementation of this design show that our design achieves 160 GOPs per instance on a simulated Altera Stratix III EP3SL150 FPGA, and scales well for output image size ranging from 500 x 500 pixels to 5,000 x 5,000 pixels.

Abstract not found

In this paper, we introduce a new synthetic aperture radar (SAR) imaging modality which can provide a high-resolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms. This new imaging scheme, requires no new hardware components and allows the aperture to be compressed. It also presents many new applications and advantages which include strong resistance to countermesasures and interception, imaging much wider swaths and reduced on-board storage requirements.