Reconstruction Algorithm For Diffraction Tomography Research Articles

Numerically robust minimal‐scan reconstruction algorithms for diffraction tomography via radon transform inversion

AbstractIt is widely believed that measurements from a full angular range of 2π are generally required to exactly reconstruct a complex‐valued refractive index distribution in diffraction tomography (DT). In this work, we developed a new class of minimal‐scan reconstruction algorithms for DT that utilizes measurements only over the angular range 0 ≤ ϕ ≤ 3π/2 to perform an exact reconstruction. These algorithms, referred to as minimal‐scan estimate‐combination (MS‐E‐C) reconstruction algorithms, effectively operate by transforming the DT reconstruction problem into a conventional x‐ray CT reconstruction problem that requires inversion of the Radon transform. We performed computer simulations to compare the noise and numerical properties of the MS‐E‐C algorithms against existing filtered backpropagation‐based algorithms. © 2002 Wiley Periodicals, Inc. Int J Imaging Syst Technol 12, 84–91, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.10014

Reconstruction algorithm for diffraction tomography of diffuse photon density waves in a random medium

With applications in medical diagnosis in mind we apply the theory of diffraction tomography to diffuse photon density waves in a random medium. We consider the two-and-a-half-dimensional (2.5D) problem in which a two-dimensional (2D) object is illuminated by diffuse photon density waves from a point source. Both the forward problem and the inverse problem are discussed, and a reconstruction algorithm based on the weak-scattering approximation is presented together with computer simulations.

Conjugate gradient method applied to inverse scattering problem

A new reconstruction algorithm for diffraction tomography is presented. The algorithm is based on the minimization of a functional which is defined as the norm of the discrepancy between the measured scattering amplitude and the calculated one for an estimated object function. By using the conjugate gradient method to minimize the functional, one can derive an iterative formula for getting the object function. Numerical results for some two-dimensional scatterers show that the algorithm is very effective in reconstructing refractive index distributions to which the first-order Born approximation can not be applied. In addition, the number of iterations is reduced by using a priori information about the outer boundary of the objects. Furthermore, the method is not so sensitive to the presence of noise in the scattered field data. >

On a simple diffraction tomography technique based on a modified newton‐kantorovich method

AbstractA study of a simple reconstruction algorithm for diffraction tomography based on the modified Newton‐Kantorovich method is presented. In situations where the Born approximation fails, the algorithm provides high‐quality reconstructed images without employing the usual regularization technique. Computer simulations demonstrate fast convergence properties of the iterative procedure.

A computational study of reconstruction algorithms for diffraction tomography: Interpolation versus filtered-backpropagation

From the standpoint of reporting a new contribution, this paper shows that by using bilinear interpolation followed by direct two-dimensional Fourier inversion, one can obtain reconstructions of quality which is comparable to that produced by the filtered-backpropagation algorithm proposed recently by Devaney. For an N × N image reconstructed from N diffracted projections, the former approach requires approximately 4N FFT's, whereas the backpropagation technique requires approximately N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> FFT's. We have also taken this opportunity to present the reader with a tutorial introduction to diffraction tomography, an area that is becoming increasingly important not only in medical imaging, but also in underwater and seismic mapping with microwaves and sound. The main feature of the tutorial part is the statement of the Fourier diffraction projection theorem, which is an extension of the traditional Fourier slice theorem to the case of image formation with diffracting illumination.