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Register a new userGENFIRE: A generalized Fourier iterative reconstruction algorithm for high-resolution 3D imaging
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Tomography has made a radical impact on diverse fields ranging from the study of 3D atomic arrangements in matter to the study of human health in medicine. Despite its very diverse applications, the core of tomography remains the same, that is, a mathematical method must be implemented to reconstruct the 3D structure of an object from a number of 2D projections. In many scientific applications, however, the number of projections that can be measured is limited due to geometric constraints, tolerable radiation dose and/or acquisition speed. Thus it becomes an important problem to obtain the best-possible reconstruction from a limited number of projections. Here, we present the mathematical implementation of a tomographic algorithm, termed GENeralized Fourier Iterative REconstruction (GENFIRE). By iterating between real and reciprocal space, GENFIRE searches for a global solution that is concurrently consistent with the measured data and general physical constraints. The algorithm requires minimal human intervention and also incorporates angular refinement to reduce the tilt angle error. We demonstrate that GENFIRE can produce superior results relative to several other popular tomographic reconstruction techniques by numerical simulations, and by experimentally by reconstructing the 3D structure of a porous material and a frozen-hydrated marine cyanobacterium. Equipped with a graphical user interface, GENFIRE is freely available from our website and is expected to find broad applications across different disciplines.
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In this study, the neuronal current in the brain is represented using Helmholtz decomposition. It was shown in earlier work that data obtained via electroencephalography (EEG) are affected only by the irrotational component of the current. The irrotational component is denoted by $Psi$ and has support in the cerebrum. This inverse problem is severely ill-posed and requires that additional constraints are imposed. Here, we impose the requirement of the minimization of the $L_2$ norm of the current (energy). The function $Psi$ is expanded in terms of inverse multiquadric radial basis functions (RBF) on a uniform Cartesian grid inside the cerebrum. The minimal energy constraint in conjunction with the RBF parametrization of $Psi$ results in a Tikhonov regularized solution of $Psi$. The RBF shape parameter (regularization parameter), is computed by solving a 1-D non-linear maximization problem. Reconstructions are presented using synthetic data with a signal to noise ratio (SNR) of $20$ dB. The root mean square error (RMSE) between the exact and the reconstructed $Psi$ is RMSE=$0.1122$. The proposed reconstruction algorithm is computationally efficient and can be vectorized in MATLAB.
Faraday tomography offers crucial information on the magnetized astronomical objects, such as quasars, galaxies, or galaxy clusters, by observing its magnetoionic media. The observed linear polarization spectrum is inverse Fourier transformed to obtain the Faraday dispersion function (FDF), providing us a tomographic distribution of the magnetoionic media along the line of sight. However, this transform gives a poor reconstruction of the FDF because of the instruments limited wavelength coverage. The current Faraday tomography techniques inability to reliably solve the above inverse problem has noticeably plagued cosmic magnetism studies. We propose a new algorithm inspired by the well-studied area of signal restoration, called the Constraining and Restoring iterative Algorithm for Faraday Tomography (CRAFT). This iterative model-independent algorithm is computationally inexpensive and only requires weak physically-motivated assumptions to produce high fidelity FDF reconstructions. We demonstrate an application for a realistic synthetic model FDF of the Milky Way, where CRAFT shows greater potential over other popular model-independent techniques. The dependence of observational frequency coverage on the various techniques reconstruction performance is also demonstrated for a simpler FDF. CRAFT exhibits improvements even over model-dependent techniques (i.e., QU-fitting) by capturing complex multi-scale features of the FDF amplitude and polarization angle variations within a source. The proposed approach will be of utmost importance for future cosmic magnetism studies, especially with broadband polarization data from the Square Kilometre Array and its precursors. We make the CRAFT code publicly available.
Improving the image resolution and acquisition speed of magnetic resonance imaging (MRI) is a challenging problem. There are mainly two strategies dealing with the speed-resolution trade-off: (1) $k$-space undersampling with high-resolution acquisition, and (2) a pipeline of lower resolution image reconstruction and image super-resolution. However, these approaches either have limited performance at certain high acceleration factor or suffer from the error accumulation of two-step structure. In this paper, we combine the idea of MR reconstruction and image super-resolution, and work on recovering HR images from low-resolution under-sampled $k$-space data directly. Particularly, the SR-involved reconstruction can be formulated as a variational problem, and a learnable network unrolled from its solution algorithm is proposed. A discriminator was introduced to enhance the detail refining performance. Experiment results using in-vivo HR multi-coil brain data indicate that the proposed SRR-Net is capable of recovering high-resolution brain images with both good visual quality and perceptual quality.
High angular resolution diffusion imaging data is the observed characteristic function for the local diffusion of water molecules in tissue. This data is used to infer structural information in brain imaging. Nonparametric scalar measures are proposed to summarize such data, and to locally characterize spatial features of the diffusion probability density function (PDF), relying on the geometry of the characteristic function. Summary statistics are defined so that their distributions are, to first-order, both independent of nuisance parameters and also analytically tractable. The dominant direction of the diffusion at a spatial location (voxel) is determined, and a new set of axes are introduced in Fourier space. Variation quantified in these axes determines the local spatial properties of the diffusion density. Nonparametric hypothesis tests for determining whether the diffusion is unimodal, isotropic or multi-modal are proposed. More subtle characteristics of white-matter microstructure, such as the degree of anisotropy of the PDF and symmetry compared with a variety of asymmetric PDF alternatives, may be ascertained directly in the Fourier domain without parametric assumptions on the form of the diffusion PDF. We simulate a set of diffusion processes and characterize their local properties using the newly introduced summaries. We show how complex white-matter structures across multiple voxels exhibit clear ellipsoidal and asymmetric structure in simulation, and assess the performance of the statistics in clinically-acquired magnetic resonance imaging data.
PET image reconstruction is challenging due to the ill-poseness of the inverse problem and limited number of detected photons. Recently deep neural networks have been widely and successfully used in computer vision tasks and attracted growing interests in medical imaging. In this work, we trained a deep residual convolutional neural network to improve PET image quality by using the existing inter-patient information. An innovative feature of the proposed method is that we embed the neural network in the iterative reconstruction framework for image representation, rather than using it as a post-processing tool. We formulate the objective function as a constraint optimization problem and solve it using the alternating direction method of multipliers (ADMM) algorithm. Both simulation data and hybrid real data are used to evaluate the proposed method. Quantification results show that our proposed iterative neural network method can outperform the neural network denoising and conventional penalized maximum likelihood methods.
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