104 research outputs found
A Reconstruction Algorithm for Photoacoustic Imaging based on the Nonuniform FFT
Fourier reconstruction algorithms significantly outperform conventional
back-projection algorithms in terms of computation time. In photoacoustic
imaging, these methods require interpolation in the Fourier space domain, which
creates artifacts in reconstructed images. We propose a novel reconstruction
algorithm that applies the one-dimensional nonuniform fast Fourier transform to
photoacoustic imaging. It is shown theoretically and numerically that our
algorithm avoids artifacts while preserving the computational effectiveness of
Fourier reconstruction.Comment: 22 pages, 8 figure
Compressed sensing and sparsity in photoacoustic tomography
Increasing the imaging speed is a central aim in photoacoustic tomography. This issue is especially important in the case of sequential scanning approaches as applied for most existing optical detection schemes. In this work we address this issue using techniques of compressed sensing. We demonstrate, that the number of measurements can significantly be reduced by allowing general linear measurements instead of point-wise pressure values. A main requirement in compressed sensing is the sparsity of the unknowns to be recovered. For that purpose, we develop the concept of sparsifying temporal transforms for three-dimensional photoacoustic tomography. We establish a two-stage algorithm that recovers the complete pressure signals in a first step and then apply a standard reconstruction algorithm such as back-projection. This yields a novel reconstruction method with much lower complexity than existing compressed sensing approaches for photoacoustic tomography. Reconstruction results for simulated and for experimental data verify that the proposed compressed sensing scheme allows for reducing the number of spatial measurements without reducing the spatial resolution.ope
Analysis of existing mathematics textbooks for use in secondary schools.
Thesis (Ed.M.)--Boston University
Thesis (M.A.)--Boston Universit
On regularization methods of EM-Kaczmarz type
We consider regularization methods of Kaczmarz type in connection with the
expectation-maximization (EM) algorithm for solving ill-posed equations. For
noisy data, our methods are stabilized extensions of the well established
ordered-subsets expectation-maximization iteration (OS-EM). We show
monotonicity properties of the methods and present a numerical experiment which
indicates that the extended OS-EM methods we propose are much faster than the
standard EM algorithm.Comment: 18 pages, 6 figures; On regularization methods of EM-Kaczmarz typ
Neural networks-based regularization for large-scale medical image reconstruction
In this paper we present a generalized Deep Learning-based approach for solving ill-posed large-scale inverse problems occuring in medical image reconstruction. Recently, Deep Learning methods using iterative neural networks (NNs) and cascaded NNs have been reported to achieve state-of-the-art results with respect to various quantitative quality measures as PSNR, NRMSE and SSIM across different imaging modalities. However, the fact that these approaches employ the application of the forward and adjoint operators repeatedly in the network architecture requires the network to process the whole images or volumes at once, which for some applications is computationally infeasible. In this work, we follow a different reconstruction strategy by strictly separating the application of the NN, the regularization of the solution and the consistency with the measured data. The regularization is given in the form of an image prior obtained by the output of a previously trained NN which is used in a Tikhonov regularization framework. By doing so, more complex and sophisticated network architectures can be used for the removal of the artefacts or noise than it is usually the case in iterative NNs. Due to the large scale of the considered problems and the resulting computational complexity of the employed networks, the priors are obtained by processing the images or volumes as patches or slices. We evaluated the method for the cases of 3D cone-beam low dose CT and undersampled 2D radial cine MRI and compared it to a total variation-minimization-based reconstruction algorithm as well as to a method with regularization based on learned overcomplete dictionaries. The proposed method outperformed all the reported methods with respect to all chosen quantitative measures and further accelerates the regularization step in the reconstruction by several orders of magnitude
Quantitative Photo-acoustic Tomography with Partial Data
Photo-acoustic tomography is a newly developed hybrid imaging modality that
combines a high-resolution modality with a high-contrast modality. We analyze
the reconstruction of diffusion and absorption parameters in an elliptic
equation and improve an earlier result of Bal and Uhlmann to the partial date
case. We show that the reconstruction can be uniquely determined by the
knowledge of 4 internal data based on well-chosen partial boundary conditions.
Stability of this reconstruction is ensured if a convexity condition is
satisfied. Similar stability result is obtained without this geometric
constraint if 4n well-chosen partial boundary conditions are available, where
is the spatial dimension. The set of well-chosen boundary measurements is
characterized by some complex geometric optics (CGO) solutions vanishing on a
part of the boundary.Comment: arXiv admin note: text overlap with arXiv:0910.250
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