1,277 research outputs found

    Graph- and finite element-based total variation models for the inverse problem in diffuse optical tomography

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    Total variation (TV) is a powerful regularization method that has been widely applied in different imaging applications, but is difficult to apply to diffuse optical tomography (DOT) image reconstruction (inverse problem) due to complex and unstructured geometries, non-linearity of the data fitting and regularization terms, and non-differentiability of the regularization term. We develop several approaches to overcome these difficulties by: i) defining discrete differential operators for unstructured geometries using both finite element and graph representations; ii) developing an optimization algorithm based on the alternating direction method of multipliers (ADMM) for the non-differentiable and non-linear minimization problem; iii) investigating isotropic and anisotropic variants of TV regularization, and comparing their finite element- and graph-based implementations. These approaches are evaluated on experiments on simulated data and real data acquired from a tissue phantom. Our results show that both FEM and graph-based TV regularization is able to accurately reconstruct both sparse and non-sparse distributions without the over-smoothing effect of Tikhonov regularization and the over-sparsifying effect of L1_1 regularization. The graph representation was found to out-perform the FEM method for low-resolution meshes, and the FEM method was found to be more accurate for high-resolution meshes.Comment: 24 pages, 11 figures. Reviced version includes revised figures and improved clarit

    Joint Total Variation ESTATICS for Robust Multi-Parameter Mapping

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    Quantitative magnetic resonance imaging (qMRI) derives tissue-specific parameters -- such as the apparent transverse relaxation rate R2*, the longitudinal relaxation rate R1 and the magnetisation transfer saturation -- that can be compared across sites and scanners and carry important information about the underlying microstructure. The multi-parameter mapping (MPM) protocol takes advantage of multi-echo acquisitions with variable flip angles to extract these parameters in a clinically acceptable scan time. In this context, ESTATICS performs a joint loglinear fit of multiple echo series to extract R2* and multiple extrapolated intercepts, thereby improving robustness to motion and decreasing the variance of the estimators. In this paper, we extend this model in two ways: (1) by introducing a joint total variation (JTV) prior on the intercepts and decay, and (2) by deriving a nonlinear maximum \emph{a posteriori} estimate. We evaluated the proposed algorithm by predicting left-out echoes in a rich single-subject dataset. In this validation, we outperformed other state-of-the-art methods and additionally showed that the proposed approach greatly reduces the variance of the estimated maps, without introducing bias.Comment: 11 pages, 2 figures, 1 table, conference paper, accepted at MICCAI 202

    Denoising of Fluorescence Image on the Surface of Quantum Dot/Nanoporous Silicon Biosensors

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    In the process of biological detection of porous silicon photonic crystals based on quantum dots, the concentration of target organisms can be indirectly measured via the change in the gray value of the fluorescence emitted from the quantum dots in the porous silicon pores before and after the biological reaction on the surface of the device. However, due to the disordered nanostructures in porous silicon and the roughness of the surface, the fluorescence images on the surface contain noise. This paper analyzes the type of noise and its influence on the gray value of fluorescent images. The change in the gray value caused by noise greatly reduces the detection sensitivity. To reduce the influence of noise on the gray value of quantum dot fluorescence images, this paper proposes a denoising method based on gray compression and nonlocal anisotropic diffusion filtering. We used the proposed method to denoise the quantum dot fluorescence image after DNA hybridization in a Bragg structure porous silicon device. The experimental results show that the sensitivity of digital image detection improved significantly after denoising

    Edge-Preserving Tomographic Reconstruction with Nonlocal Regularization

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    Tomographic image reconstruction using statistical methods can provide more accurate system modeling, statistical models, and physical constraints than the conventional filtered backprojection (FBP) method. Because of the ill posedness of the reconstruction problem, a roughness penalty is often imposed on the solution to control noise. To avoid smoothing of edges, which are important image attributes, various edge-preserving regularization methods have been proposed. Most of these schemes rely on information from local neighborhoods to determine the presence of edges. In this paper, we propose a cost function that incorporates nonlocal boundary information into the regularization method. We use an alternating minimization algorithm with deterministic annealing to minimize the proposed cost function, jointly estimating region boundaries and object pixel values. We apply variational techniques implemented using level-sets methods to update the boundary estimates; then, using the most recent boundary estimate, we minimize a space-variant quadratic cost function to update the image estimate. For the positron emission tomography transmission reconstruction application, we compare the bias-variance tradeoff of this method with that of a "conventional" penalized-likelihood algorithm with local Huber roughness penalty.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85989/1/Fessler73.pd
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