The problem of signal recovery fromincompletedata is investigated in the context of phase-space tomography. Particular emphasis is given to the case where only a limited number intensity measurements can be performe...
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ISBN:
(纸本)0819455008
The problem of signal recovery fromincompletedata is investigated in the context of phase-space tomography. Particular emphasis is given to the case where only a limited number intensity measurements can be performed, which corresponds to partial coverage of the ambiguity function of the signal. Based on numerical simulations the impact of incomplete knowledge of the ambiguity function on the performance of phase-space tomography is illustrated. Several schemes to address the limited data problem are evaluated. This includes the use of prior information about the phase retrieval problem. In addition, the redundancy of phase-space representations is investigated as the means to recover the signal from partial knowledge of phase space. A generalization of deterministic phase retrieval is introduced which allows one to obtain a model based phase estimate for bandlimited functions. This allows one to use prior information for improving the phase estimate in the presence of noise.
A hybrid method is presented which allows the acceleration of parallel MR imaging through combining the ideas of compressed sensing with inversion of the imaging matrix. A novel data reordering is employed to enhance ...
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ISBN:
(纸本)9780819472960
A hybrid method is presented which allows the acceleration of parallel MR imaging through combining the ideas of compressed sensing with inversion of the imaging matrix. A novel data reordering is employed to enhance the sparsity inherent in the image transform. Simulation results with actual head scan data, are presented.
imagereconstructionfromincomplete projection data is strongly required in widespread applications of computed tomography. This problem can be formulated as a sinogram-recovery problem. The sinogram-recovery problem...
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imagereconstructionfromincomplete projection data is strongly required in widespread applications of computed tomography. This problem can be formulated as a sinogram-recovery problem. The sinogram-recovery problem is to find a complete sinogram that is compatible with the Helgason-Ludwig consistency condition, the measured incomplete sinogram, and other a priori knowledge about the sinogram in question. The direct use of the Helgason-Ludwig consistency condition considerably reduces computational requirements and the accumulation of digital-prcessing errors over the conventional iterative reconstruction-reprojection method. Most research for solving the sinogram-recovery problem is based on directly inverting systems of linear equations associated with the Helgason-Ludwig consistency condition. However, these noniterative techniques cannot be applied to various different types of limited-data situations in a unified way. Moreover, nonlinear a priori constraints such as the nonnegativity and the amplitude limit are not easily incorporated. We solve the sinogram-recovery problem by using an iterative signal-recovery technique known as the method of projection onto convex sets. Once an estimation of the complete sinogram is obtained, the conventional convolution-backprojection method can be utilized to reconstruct an image. The performance of the proposed method is investigated both with numerical phantoms and with actual x-ray data.
A Bayesian optimization scheme is presented for reconstructing fluorescent yield and lifetime, the absorption coefficient, and-the scattering coefficient in turbid media, such as biological tissue. The method utilizes...
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ISBN:
(纸本)0819445592
A Bayesian optimization scheme is presented for reconstructing fluorescent yield and lifetime, the absorption coefficient, and-the scattering coefficient in turbid media, such as biological tissue. The method utilizes measurements at both the excitation and emission wavelengths for reconstructing all unknown parameters. The effectiveness of the reconstruction algorithm is demonstrated by simulation and by application to experimental datafrom a tissue phantom containing a fluorescent agent.
We describe how the number of degrees of freedom associated with a scattering experiment provides a guide to the minimum number of source and receiver locations required to image the scattering target. Since the numbe...
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ISBN:
(纸本)9780819492173
We describe how the number of degrees of freedom associated with a scattering experiment provides a guide to the minimum number of source and receiver locations required to image the scattering target. Since the number of degrees of freedom is approximately fixed, additional measurements do not necessarily improve the image fidelity in the absence of any prior knowledge. We illustrate these observations using a fast nonlinear inverse scattering method.
The conjugate gradient method incorporating the object-extent constraint is applied to imagereconstruction of a three-dimensional object using an incomplete projection-data set. The missing information is recovered b...
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The conjugate gradient method incorporating the object-extent constraint is applied to imagereconstruction of a three-dimensional object using an incomplete projection-data set. The missing information is recovered by constraining the solution with the knowledge of the outer boundary of the object-extent which may be a priori measured or known. The algorithm is derived from the least-squares criterion as an advanced version of conventional iterative reconstruction algorithms such as SIRT (Simultaneous Iterative reconstruction Technique) and ILST (Iterative Least Squares Technique). In the case of reconstructionfrom noisy projection data, a method based on the minimum mean-square error criterion is also proposed. Computer simulated reconstructionimages of a phantom using limited angle and number of views are presented. The result shows that the conjugate gradient method incorporating the object-extent constraining provides the fastest convergence and the least error.
Photoacoustic tomography is a rapidly emerging imaging technique that can benefit a wide range of biomedical applications. In this method, illumination of an object with a pulsed optical field induces an acoustic pres...
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ISBN:
(纸本)9780819482969
Photoacoustic tomography is a rapidly emerging imaging technique that can benefit a wide range of biomedical applications. In this method, illumination of an object with a pulsed optical field induces an acoustic pressure wave related to the heating of the object (optical absorption). from knowledge of the resultant pressure wave measured in a region away from the acoustic source, the object's spatially varying optical absorption properties are estimated by use of an imagereconstruction algorithm. Most existing analytic reconstruction algorithms for photoacoustic tomography assume the object of interest possesses homogeneous acoustic properties. In this work, photoacoustic tomography is considered in the case that the primary acoustic source is embedded in a planar layered medium whose speed of sound and densities are known. Exact propagation models valid for acoustic wave propagation in dispersive and absorptive layered media are presented that account for multiple reflections between the layers. Using the angular spectrum method, an inversion model is presented for acoustic data acquired on a plane parallel to the layered medium. The acquired data are shown to be simple linear combinations of plane waves generated at the source.
Biomedical photoacoustic tomography, which can provide high-resolution 3D soft tissue images based on optical absorption, has advanced to the stage at which translation from the laboratory to clinical settings is beco...
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Biomedical photoacoustic tomography, which can provide high-resolution 3D soft tissue images based on optical absorption, has advanced to the stage at which translation from the laboratory to clinical settings is becoming possible. The need for rapid image formation and the practical restrictions on data acquisition that arise from the constraints of a clinical workflow are presenting new imagereconstruction challenges. There are many classical approaches to imagereconstruction, but ameliorating the effects of incomplete or imperfect data through the incorporation of accurate priors is challenging and leads to slow algorithms. Recently, the application of deep learning (DL), or deep neural networks, to this problem has received a great deal of attention. We review the literature on learned imagereconstruction, summarizing the current trends and explain how these approaches fit within, and to some extent have arisen from, a framework that encompasses classical reconstruction methods. In particular, it shows how these techniques can be understood from a Bayesian perspective, providing useful insights. We also provide a concise tutorial demonstration of three prototypical approaches to learned imagereconstruction. The code and data sets for these demonstrations are available to researchers. It is anticipated that it is in in vivo applications-where data may be sparse, fast imaging critical, and priors difficult to construct by hand-that DL will have the most impact. With this in mind, we conclude with some indications of possible future research directions. (C) The Authors. Published by SPIE under a Creative Commons Attribution 4.0 Unported License.
3D reconstructionfrom an incompletedata set is an ill- posed problem. To overcome this drawback, an approach based on constrained optimization is introduced. This approach provides a powerful mathematical framework ...
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ISBN:
(纸本)0819422118;9780819422118
3D reconstructionfrom an incompletedata set is an ill- posed problem. To overcome this drawback, an approach based on constrained optimization is introduced. This approach provides a powerful mathematical framework for selecting a specific solution from the set of feasible solutions; this is done by minimizing some criteria depending on prior densitometric information. We propose a global optimization scheme using a deterministic relaxation algorithm based on Bregman's algorithm associated with half-quadratic minimization techniques. When used for 3D vascular reconstructionfrom 2D digital subtracted angiography data, such an approach allows reconstructing well-contrasted 3D vascular network in comparison with results obtained by using standard algorithms.
The parameters of the prior, the hyperparameters, play an important role in Bayesian image estimation, Of particular importance for the case of Gibbs priors is the global hyperparameter, beta, which multiplies the Ham...
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The parameters of the prior, the hyperparameters, play an important role in Bayesian image estimation, Of particular importance for the case of Gibbs priors is the global hyperparameter, beta, which multiplies the Hamiltonian, Here we consider maximum likelihood (ML) estimation of beta fromincompletedata, i.e., problems in which the image, which is drawn from a Gibbs prior, is observed indirectly through some degradation or blurring process, Important applications include image restoration and imagereconstructionfrom projections. Exact ML estimation of beta fromincompletedata is intractable for most image processing, Here we present an approximate ML estimator that is computed simultaneously with a maximum a posteriori (MAP) image estimate, The algorithm is based on a mean field approximation technique through which multidimensional Gibbs distributions are approximated by a separable function equal to a product of one-dimensional (1-D) densities, We show how this approach can be used to simplify the ML estimation problem. We also show how the Gibbs-Bogoliubov-Feynman (GBF) bound can be used to optimize the approximation for a restricted class of problems, We present the results of a Monte Carlo study that examines the bias and variance of this estimator when applied to image restoration.
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