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A RECURSIVE ALGORITHM FOR COMPUTING CRAMER-RAO-TYPE BOUNDS ON ESTIMATOR COVARIANCE

IEEE TRANSACTIONS ON INFORMATION THEORY 1994年第4期40卷 1205-1210页

作者： HERO, A FESSLER, JA UNIV MICHIGAN DIV NUCL MEDANN ARBORMI 48109

We give a recursive algorithm to calculate submatrices of the Cramer-Rao (CR) matrix bound on the covariance of any unbiased estimator of a vector parameter theta. Our algorithm computes a sequence of lower bounds that converges monotonically to the CR bound with exponential speed of convergence. The recursive algorithm uses an invertible ''splitting matrix'' to successively approximate the inverse Fisher information matrix. We present a statistical approach to selecting the splitting matrix based on a ''complete-data-incomplete-data'' formulation similar to that of the well-known EM parameter estimation algorithm. As a concrete illustration we consider image reconstruction from projections for emission computed tomography.

关键词： MULTIDIMENSIONAL PARAMETER ESTIMATION ESTIMATOR COVARIANCE BOUNDS COMPLETE incomplete data PROBLEM image reconstruction

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Complex-valued image reconstruction from spectral phase or magnitude

Complex-valued image reconstruction from spectral phase or m...

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2nd Conference on image reconstruction from incomplete data

作者： Tang, XQ Porat, M Univ Auckland Dept Elect & Elect Engn Auckland 1 New Zealand

ISBN: (纸本)0819445592

Many significant features of images are represented in their Fourier transform. The spectral phase of an image can often be measured more precisely than magnitude for frequencies of up to a few GHz. However, spectral magnitude is the only measurable data in many imaging applications. In this paper, the reconstruction of complex-valued images from either the phases or magnitudes of their Fourier transform is addressed. Conditions for unique representation of a complex-valued image by its spectral magnitude combined with additional spatial information is investigated and presented. reconstruction algorithms of complex-valued images are developed and introduced. Three types of reconstruction algorithms are presented. (1) Algorithms that reconstruct a complex-valued image from the magnitude of its discrete Fourier transform and part of its spatial samples based on the autocorrelation function. (2) Iterative algorithms based on the Gerchberg and Saxton approach. (3) Algorithms that reconstruct a complex-valued image from its localized Fourier transform magnitude. The advantages of the proposed algorithms over the presently available approaches are presented and discussed.

关键词： complex-valued image unique representation image reconstruction Fourier magnitude Fourier phase

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image reconstruction based on compressed sensing for sparse-data endoscopic photoacoustic tomography

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COMPUTERS IN BIOLOGY AND MEDICINE 2020年 116卷 103587-103587页

作者： Sun Zheng Yan Xiangyang North China Elect Power Univ Dept Elect & Commun Engn Baoding 071003 Peoples R China

Endoscopic photoacoustic tomography (EPAT) is an interventional application of photoacoustic tomography (PAT) to visualize anatomical features and functional components of biological cavity structures such as nasal cavity, digestive tract or coronary arterial vessels. One of the main challenges in clinical applicability of EPAT is the incomplete acoustic measurements due to the limited detectors or the limited-view acoustic detection enclosed in the cavity. In this case, conventional image reconstruction methodologies suffer from significantly degraded image quality. This work introduces a compressed-sensing (CS)-based method to reconstruct a high-quality image that represents the initial pressure distribution on a luminal cross-section from incomplete discrete acoustic measurements. The method constructs and trains a complete dictionary for the sparse representation of the photoacoustically-induced acoustic measurements. The sparse representation of the complete acoustic signals is then optimally obtained based on the sparse measurements and a sensing matrix. The complete acoustic signals are recovered from the sparse representation by inverse sparse transformation. The image of the initial pressure distribution is finally reconstructed from the recovered complete signals by using the time reversal (TR) algorithm. It was shown with numerical experiments that high-quality images with reduced under-sampling artifacts can be reconstructed from sparse measurements. The comparison results suggest that the proposed method outperforms the standard TR reconstruction by 40% in terms of the structural similarity of the reconstructed images.

关键词： Endoscopic photoacoustic tomography (EPAT) image reconstruction Sparse measurement Compressed sensing (CS) Time reversal (TR)

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Compressible Latent-Space Invertible Networks for Generative Model-Constrained image reconstruction

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IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING 2021年 7卷 209-223页

作者： Kelkar, Varun A. Bhadra, Sayantan Anastasio, Mark A. Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA Washington Univ St Louis Dept Comp Sci & Engn St Louis MO USA Univ Illinois Dept Bioengn Urbana IL 61801 USA

There remains an important need for the development of image reconstruction methods that can produce diagnostically useful images from undersampled measurements. In magnetic resonance imaging (MRI), for example, such methods can facilitate reductions in data-acquisition times. Deep learning-based methods hold potential for learning object priors or constraints that can serve to mitigate the effects of data-incompleteness on image reconstruction. One line of emerging research involves formulating an optimization-based reconstruction method in the latent space of a generative deep neural network. However, when generative adversarial networks (GANs) are employed, such methods can result in image reconstruction errors if the sought-after solution does not reside within the range of the GAN. To circumvent this problem, in this work, a framework for reconstructing images from incomplete measurements is proposed that is formulated in the latent space of invertible neural network-based generative models. A novel regularization strategy is introduced that takes advantage of the multiscale architecture of certain invertible neural networks, which can result in improved reconstruction performance over classical methods in terms of traditional metrics. The proposed method is investigated for reconstructing images from undersampled MRI data. The method is shown to achieve comparable performance to a state-of-the-art generative model-based reconstruction method while benefiting from a deterministic reconstruction procedure and easier control over regularization parameters.

关键词： image reconstruction Imaging Magnetic resonance imaging reconstruction algorithms Neural networks Noise measurement Gallium nitride image reconstruction compressive sensing generative neural networks invertible neural networks

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Improving Sparse Compressed Sensing Medical CT image reconstruction

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AUTOMATIC CONTROL AND COMPUTER SCIENCES 2019年第3期53卷 281-289页

作者： Zhang, Jingyu Teng, Jianfu Bai, Yu Tianjin Univ Sch Elect Informat Engn Tianjin 300072 Peoples R China

For the incomplete scanning data, the traditional algorithms cannot guarantee that the medical CT reconstruction image meets the diagnostic requirements. In this case, a medical CT image reconstruction method with the limited angle projection is proposed. According to the theory of compressed sensing, medical CT images with a sparse representation can be reconstructed from the incomplete scanning data and provide reliable information for the diagnosis. The sparse representation of CT images is performed by the sparse patch-ordering wavelet-tree transform, and the digital features of sparse coefficients are used as regularization terms to ensure the validity of the solution. Meantime, the weighting term is added into the fidelity item to reduce the influence of noise on the reconstruction results. The extended Lagrange method is used to solve the constrained objective function iteratively so as to realize the reconstruction of low dose medical CT images. Simulation results demonstrate that the reconstructed image can not only satisfy the completeness condition of projection data, but also can reconstruct the high quality image and effectively improve the mean square error and the structural similarity index.

关键词： CT image reconstruction sparse compressed sensing patch-ordering wavelet-tree transform extended Lagrangian method high quality image structural similarity index

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Edge Information Diffusion-Based reconstruction for Cone Beam Computed Laminography

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IEEE TRANSACTIONS ON image PROCESSING 2018年第9期27卷 4663-4675页

作者： Zhao, Yunsong Xu, Jinqiu Li, Hongwei Zhang, Peng Capital Normal Univ Sch Math Sci Beijing 100048 Peoples R China Capital Normal Univ Beijing Adv Innovat Ctr Imaging Technol Beijing 100048 Peoples R China

Computed laminography (CL) is a prospective nondestructive testing technique for flat object inspection in industrial applications. However, CL image reconstruction is a challenging task, because incomplete projection data are acquired from the CL scan. When a conventional computed tomography (CT) reconstruction method is applied to cone beam CL data, the vertical edges (singularities in the z-direction) in the reconstructed image would be blurred. On the contrary, the horizontal edges (singularities within slices) can be quite accurately reconstructed. Based on this key observation, an edge information diffusion method is developed, which fixes the horizontal edges and propagates their values within the slices. An effective CL reconstruction method is then proposed for flat object inspection by combining the edge information diffusion procedure, which plays the role of regularization, with conventional CT image reconstruction algorithms. Experiments on both simulated data and real data are performed to verify the effectiveness of the proposed method. The results show that the proposed method can effectively suppress the inter-slice aliasing and blurring caused by the incompleteness of the CL scan data and that it outperforms the other state-of-the-art methods.

关键词： Computed laminography image reconstruction edge information diffusion

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reconstruction of seismic data using adaptive regularization

Reconstruction of seismic data using adaptive regularization

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2nd Conference on image reconstruction from incomplete data

作者： Liu, B Sacchi, MD Univ Alberta Dept Phys Edmonton AB T6G 2J1 Canada

ISBN: (纸本)0819445592

In seismic data processing, we often need to interpolate/extrapolate missing spatial locations in a domain of interest. The reconstruction problem can be posed as an inverse problem where from inadequate and incomplete data one attempts to recover the complete band-limited seismic wavefield. However, the problem is often ill posed due to factors such as inaccurate knowledge of bandwidth and noise. In this case, regularization can be used to help to obtain a unique and stable solution. In this paper, we formulate band-limited data reconstruction as a minimum norm least squares type problem where an adaptive DFT-weighted norm regularization term is used to constrain the solution. In particular, the regularization term is iteratively updated through using the modified periodogram of the estimated data. The technique allows for adaptive incorporation of prior knowledge of the data such as the spectrum support and the shape of the spectrum. The adaptive regularization can be accelerated using FFTs and an iterative solver like preconditioned conjugate gradient algorithm. Examples on synthetic and real seismic data illustrate improvement of the new method over damped least squares estimation.

关键词： band-limited signal reconstruction DFT-weighted norm regularization FFT preconditioning

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Geometric Bayesian inpainting and applications

Geometric Bayesian inpainting and applications

引用

2nd Conference on image reconstruction from incomplete data

作者： Shen, JH Univ Minnesota Sch Math Computat & Appl Math Minneapolis MN 55455 USA

ISBN: (纸本)0819445592

Inpainting is an image interpolation problem, with broad applications in image processing andthe digital technology. This paper presents our recent efforts in developing inpainting models based on the Bayesian and variational principles. We discuss several geometric image (prior) models, their role in the construction of variational inpainting models, the resulting Euler-Lagrange differential equations, and their numerical implementation.

关键词： inpainting interpolation Bayesian image model Euler's elastica computational PDE

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Progressive EPR imaging with adaptive projection acquisition

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JOURNAL OF MAGNETIC RESONANCE 2005年第2期174卷 177-187页

作者： Deng, YM Kuppusamy, P Zweier, JL Ohio State Univ Coll Med Ctr Biomed EPR Spect & Imaging Davis Heart & Lung Res InstDiv Cardiovasc MedDe Columbus OH 43210 USA

Continuous wave electron paramagnetic resonance imaging (EPRI) of living biological systems requires rapid acquisition and visualization of free radical images. in the commonly used multiple-stage back-projection image reconstruction algorithm, the EPR image cannot be reconstructed until a complete set of projections is collected. If the data acquisition is incomplete, the previously acquired incomplete data set is no longer useful. In this work, a 3-dimensional progressive EPRI technique was implemented based on inverse Radon transform in which a 3-dimensional EPR image is acquired and reconstructed gradually from low resolution to high resolution. An adaptive data acquisition strategy is proposed to determine the significance of projections and acquire them in an order from the most significant to the least significant. The image acquisition can be terminated at any time if further collection of projections does not improve the image resolution distinctly, providing flexibility to trade image quality with imaging time. The progressive imaging technique was validated using computer simulations as well as imaging experiments. The adaptive acquisition uses 50-70 % less projections as compared to the regular acquisition. In conclusion, adaptive data acquisition with progressive image reconstruction should be very useful for the accelerated acquisition and visualization of free radical distribution. (c) 2005 Elsevier Inc. All rights reserved.

关键词： EPR imaging image reconstruction radon transform adaptive acquisition simulation free radical

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SINOGRAM RECOVERY WITH THE METHOD OF CONVEX PROJECTIONS FOR LIMITED-data reconstruction IN COMPUTED-TOMOGRAPHY

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS image SCIENCE AND VISION 1991年第7期8卷 1148-1160页

作者： KUDO, H SAITO, T UNIV TSUKUBA INST INFORMAT SCI & ELECTRTSUKUBA 305JAPAN

image reconstruction from incomplete 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.

关键词： Beam fanning Computed tomography Fourier transforms image display image reconstruction Industrial inspection

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