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A new reconstruction approach for reflection mode diffraction tomography
IEEE Transactions on Image Processing, 2000
Reflection mode diffraction tomography (RM DT) is an inversion scheme used to reconstruct the acoustical refractive index distribution of a scattering object. In this work, we reveal the existence of statistically complementary information inherent in the back scattered data and propose reconstruction algorithms that exploit this information for achieving a bias-free reduction of image variance in RM DT images. Such a reduction of image variance can potentially enhance the detectability of subtle image features when the signal-to-noise ratio of the measured scattered data is low in RM DT. The proposed reconstruction algorithms are mathematically identical, but they propagate noise and numerical errors differently. We investigate theoretically, and validate numerically, the noise properties of images reconstructed using one of the reconstruction algorithms for several different multifrequency sources and uncorrelated data noise.
A generalized diffraction tomography algorithm
The Journal of the Acoustical Society of America, 1991
Available diffraction tomography algorithms are based on Fourier transform techniques and require either plane-wave illumination in a uniform background medium or far-field illumination combined with paraxial approximations. In this paper a generalized diffraction tomography algorithm is introduced that can handle both irregularly spaced measurement data, nonuniform background models, and general acquisition geometries. Using data from water tank experiments, the method's ability to yield high-quality reconstructions of geometry and velocity, as long as the weak-scattering assumption is satisfied, is demonstrated.
Computational inverse coherent wave field imaging
2009 16th IEEE International Conference on Image Processing (ICIP), 2009
We consider reconstruction of a wave eld distribution in an input/object plane from data in an output/diffraction (sensor) plane. For the forward propagation the matrix form of the discrete diffraction transform (DDT) originated in [1] and [2] is used. This "matrix DDT " is aliasing free and precise for pixel-wise invariant object and sensor plane distributions. A contribution of this paper concerns a study of the backward wave eld propagation as an inverse problem for the diffraction kernel. The analysis of the conditioning of the transfer DDT matrices is presented in order to nd when the perfect reconstruction of the object wave eld distribution is possible. This condition number can be used as an indicator of the accuracy of the wave eld reconstruction. Simulation experiments show that the developed inverse propagation algorithm demonstrates an improved accuracy as compared with the standard convolutional and discrete Fresnel transform algorithms.
Physical Review A, 2019
We present an alternative numerical reconstruction algorithm for direct tomographic reconstruction of a sample's refractive indices from the measured intensities of its far-field coherent diffraction patterns. We formulate the well-known phase-retrieval problem in ptychography in a tomographic framework which allows for simultaneous reconstruction of the illumination function and the sample's refractive indices in three dimensions. Our iterative reconstruction algorithm is based on the Levenberg-Marquardt algorithm and we demonstrate the performance of our proposed method with simulated and real datasets.
IEEE Transactions on Instrumentation and Measurement, 2000
In this paper, a three-dimensional (3-D) extension of the well-known filtered-backpropagation (FBP) algorithm is presented with the aim of taking into account scattered-field-data measurements obtained using incident directions not restricted in a single plane. The FBP algorithm has been extensively used to solve the two-dimensional inverse-scattering problem under the first-order Born and Rytov approximations for weak scatterers. The extension of this algorithm in three dimensions is not straightforward, because the task of collecting the data needed to obtain a low-pass filtered version of the scattering object, taking into account all spatial frequencies within a radius of √ 2k 0 , and of incorporating these data to the FBP algorithm, needs to be addressed. A simple extension using incident field directions restricted to a single plane (illumination plane) leaves a region of spatial frequencies of the sphere of radius √ 2k 0 undetermined. The locus of these spatial frequencies may be crucial for the accurate reconstruction of objects which do not vary slowly along the axis perpendicular to the illumination plane. The proposed 3-D FBP algorithm presented here is able to incorporate the data collected from more than one illumination plane and to ensure the reliability of the reconstruction results.
Image Reconstructions in Diffraction Tomography from Limited Transmitted Field Data Sets
Applied Optics, 2000
Diffraction tomography reconstructions of objects from limited transmitted field data sets are discussed together with theoretical analyses and results of numerical experiments. It is shown that limited data sets, representing only a small part of the complete data sets, can be used for reconstructions in diffraction tomography with satisfactory accuracy. We also find that, in diffraction tomography based on the hybrid filtered backpropagation and the first-Rytov approximation, the use of limited data sets can provide a larger range of validity than the use of complete data sets, the reason being that limited data sets pose less-severe phase-unwrapping problems.
Nonlinear diffraction tomography: The use of inverse scattering for imaging
International Journal of Imaging Systems and Technology, 1996
Our recent inverse scattering work has been to derive inverse scattering theory and algorithms that can be used to process practical experimental data. The theory makes use of computation of the forward scattering solution. Therefore, an e cient forward solver is instrumental to the rapid solution of the inverse scattering problem. The advantage of the more sophisticated theory over a linear theory is that it accounts for multiple scattering e ects within the scatterers which often give rise to distortions in an image. A new method to invert strong scatterers, such as metallic scatterers, is presented.
Simplified approach to diffraction tomography in optical microscopy
Optics Express, 2009
We present a novel microscopy technique to measure the scattered wavefront emitted from an optically transparent microscopic object. The complex amplitude is decoded via phase stepping in a commonpath interferometer, enabling high mechanical stability. We demonstrate theoretically and practically that the incoherent summation of multiple illumination directions into a single image increases the resolving power and facilitates image reconstruction in diffraction tomography. We propose a slice-by-slice object-scatter extraction algorithm entirely based in real space in combination with ordinary z-stepping. Thereby the computational complexity affiliated with tomographic methods is significantly reduced. Using the first order Born approximation for weakly scattering objects it is possible to obtain estimates of the scattering density from the exitwaves.
International Journal of Imaging Systems and Technology, 1999
In diffraction tomography (DT), the measured scattered data are unavoidably contaminated by noise. Because the detectability of an object in a noisy image relies strongly on the signal-to-noise ratio, it is important in certain applications to reduce the statistical variation in the reconstructed image. Recently, we revealed the existence of statistically complementary information inherent in the scattered data and proposed a linear strategy that makes use of this information to achieve a bias-free reduction of the image variance in two-dimensional (2D) DT. This strategy leads to the development of an infinite class of estimation methods, that from the measured scattered data, can estimate the Radon transform of the scattering object function. From the estimated Radon transforms, one can readily reconstruct the object function by using a variety of existing reconstruction algorithms. The estimation methods in the class are mathematically equivalent, but they respond to noise differently. We investigated the noise properties of these estimation methods by use of computer simulation studies. The results of our simulation studies demonstrate quantitatively that it is possible to achieve a bias-free variance reduction in the reconstructed scattering object by utilizing complementary statistical information that is inherent in the scattered data.