A wavelet-based multiresolution regularized least squares reconstruction approach for optical tomography. 1997

W Zhu, and Y Wang, and Y Deng, and Y Yao, and R L Barbour
Department of Electrical Engineering, Polytechnic University, Brooklyn, NY 11203, USA.

In this paper, we present a wavelet-based multigrid approach to solve the perturbation equation encountered in optical tomography. With this scheme, the unknown image, the data, as well as the weight matrix are all represented by wavelet expansions, thus yielding a multiresolution representation of the original perturbation equation in the wavelet domain. This transformed equation is then solved using a multigrid scheme, by which an increasing portion of wavelet coefficients of the unknown image are solved in successive approximations. One can also quickly identify regions of interest (ROI's) from a coarse level reconstruction and restrict the reconstruction in the following fine resolutions to those regions. At each resolution level a regularized least squares solution is obtained using the conjugate gradient descent method. This approach has been applied to continuous wave data calculated based on the diffusion approximation of several two-dimensional (2-D) test media. Compared to a previously reported one grid algorithm, the multigrid method requires substantially shorter computation time under the same reconstruction quality criterion.

UI MeSH Term Description Entries
D007091 Image Processing, Computer-Assisted A technique of inputting two-dimensional or three-dimensional images into a computer and then enhancing or analyzing the imagery into a form that is more useful to the human observer. Biomedical Image Processing,Computer-Assisted Image Processing,Digital Image Processing,Image Analysis, Computer-Assisted,Image Reconstruction,Medical Image Processing,Analysis, Computer-Assisted Image,Computer-Assisted Image Analysis,Computer Assisted Image Analysis,Computer Assisted Image Processing,Computer-Assisted Image Analyses,Image Analyses, Computer-Assisted,Image Analysis, Computer Assisted,Image Processing, Biomedical,Image Processing, Computer Assisted,Image Processing, Digital,Image Processing, Medical,Image Processings, Medical,Image Reconstructions,Medical Image Processings,Processing, Biomedical Image,Processing, Digital Image,Processing, Medical Image,Processings, Digital Image,Processings, Medical Image,Reconstruction, Image,Reconstructions, Image
D008279 Magnetic Resonance Imaging Non-invasive method of demonstrating internal anatomy based on the principle that atomic nuclei in a strong magnetic field absorb pulses of radiofrequency energy and emit them as radiowaves which can be reconstructed into computerized images. The concept includes proton spin tomographic techniques. Chemical Shift Imaging,MR Tomography,MRI Scans,MRI, Functional,Magnetic Resonance Image,Magnetic Resonance Imaging, Functional,Magnetization Transfer Contrast Imaging,NMR Imaging,NMR Tomography,Tomography, NMR,Tomography, Proton Spin,fMRI,Functional Magnetic Resonance Imaging,Imaging, Chemical Shift,Proton Spin Tomography,Spin Echo Imaging,Steady-State Free Precession MRI,Tomography, MR,Zeugmatography,Chemical Shift Imagings,Echo Imaging, Spin,Echo Imagings, Spin,Functional MRI,Functional MRIs,Image, Magnetic Resonance,Imaging, Magnetic Resonance,Imaging, NMR,Imaging, Spin Echo,Imagings, Chemical Shift,Imagings, Spin Echo,MRI Scan,MRIs, Functional,Magnetic Resonance Images,Resonance Image, Magnetic,Scan, MRI,Scans, MRI,Shift Imaging, Chemical,Shift Imagings, Chemical,Spin Echo Imagings,Steady State Free Precession MRI
D003198 Computer Simulation Computer-based representation of physical systems and phenomena such as chemical processes. Computational Modeling,Computational Modelling,Computer Models,In silico Modeling,In silico Models,In silico Simulation,Models, Computer,Computerized Models,Computer Model,Computer Simulations,Computerized Model,In silico Model,Model, Computer,Model, Computerized,Model, In silico,Modeling, Computational,Modeling, In silico,Modelling, Computational,Simulation, Computer,Simulation, In silico,Simulations, Computer
D006801 Humans Members of the species Homo sapiens. Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D000465 Algorithms A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task. Algorithm
D014054 Tomography Imaging methods that result in sharp images of objects located on a chosen plane and blurred images located above or below the plane. Tomographies
D016018 Least-Squares Analysis A principle of estimation in which the estimates of a set of parameters in a statistical model are those quantities minimizing the sum of squared differences between the observed values of a dependent variable and the values predicted by the model. Rietveld Refinement,Analysis, Least-Squares,Least Squares,Analyses, Least-Squares,Analysis, Least Squares,Least Squares Analysis,Least-Squares Analyses,Refinement, Rietveld
D055095 Optics and Photonics A specialized field of physics and engineering involved in studying the behavior and properties of light and the technology of analyzing, generating, transmitting, and manipulating ELECTROMAGNETIC RADIATION in the visible, infrared, and ultraviolet range. Photonics,Photonics and Optics

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