This article presents a method to perform diffraction tomography in a standard microscope that includes an LED array for illumination. After acquiring a sequence of intensity-only images of a thick sample, a ptychography-based reconstruction algorithm solves for its unknown complex index of refraction across three dimensions. The experimental microscope demonstrates a spatial resolution of 0.39 @math m and an axial resolution of 3.7 @math m at the Nyquist-Shannon sampling limit (0.54 @math m and 5.0 @math m at the Sparrow limit, respectively), across a total imaging volume of 2.2 mm @math 2.2 mm @math 110 @math m. Unlike competing methods, the 3D tomograms presented in this article are continuous, quantitative, and formed without the need for interferometry or any moving parts. Wide field-of-view reconstructions of thick biological specimens demonstrate potential applications in pathology and developmental biology.
Here, we first outline a solid foundation for the application of ptychographic phase retrieval to DT. Unlike approaching the problem from a projection-based or multi-slice perspective, the framework of DT (under the first Born approximation) follows directly from the scalar wave equation. It offers a clear picture of achievable resolution in 3D, spells out sampling and data redundancy requirements for an accurate reconstruction, and presents a clear path forward for future extensions to account for multiple scattering @cite_6 . Furthermore, our method does not require the arbitrary assignment of the number slices in the 3D volume, or their location, or for us to select a particular order in which to address each slice as iterations proceed. Instead, it simply inserts the measured data into its appropriate location in 3D Fourier space and ensures phase consistency between each measurement, given a sufficient amount of data redundancy (just like ptychography). From the initial starting point of solving for the first term in the Born expansion, we aim this approach as a general framework to eventually solve the challenging problem of forming tomographic maps of volumetric samples, at sub-micrometer resolution, in the presence of significant scattering.
@cite_6
2090612612 2097769097 2003147468 2133105246
This paper presents an approach to 3-D diffusion tensor image (DTI) reconstruction from multi-slice diffusion weighted (DW) magnetic resonance imaging acquisitions of the moving fet al brain. Motion scatters the slice measurements in the spatial and spherical diffusion domain with respect to the underlying anatomy. Previous image registration techniques have been described to estimate the between slice fet al head motion, allowing the reconstruction of 3D a diffusion estimate on a regular grid using interpolation. We propose Approach to Unified Diffusion Sensitive Slice Alignment and Reconstruction (AUDiSSAR) that explicitly formulates a process for diffusion direction sensitive DW-slice-to-DTI-volume alignment. This also incorporates image resolution modeling to iteratively deconvolve the effects of the imaging point spread function using the multiple views provided by thick slices acquired in different anatomical planes. The algorithm is implemented using a multi-resolution iterative scheme and multiple real and synthetic data are used to evaluate the performance of the technique. An accuracy experiment using synthetically created motion data of an adult head and an experiment using synthetic motion added to sedated fet al monkey dataset show a significant improvement in motion-trajectory estimation compared to current state-of-the-art approaches. The performance of the method is then evaluated on challenging but clinically typical in utero fet al scans of four different human cases, showing improved rendition of cortical anatomy and extraction of white matter tracts. While the experimental work focuses on DTI reconstruction (second-order tensor model), the proposed reconstruction framework can employ any 5-D diffusion volume model that can be represented by the spatial parameterizations of an orientation distribution function. This paper addresses the problem of hallucinating the missing high-resolution (HR) details of a low-resolution (LR) video while maintaining the temporal coherence of the reconstructed HR details using dynamic texture synthesis (DTS). Most existing multiframe-based video superresolution (SR) methods suffer from the problem of limited reconstructed visual quality due to inaccurate subpixel motion estimation between frames in an LR video. To achieve high-quality reconstruction of HR details for an LR video, we propose a texture-synthesis (TS)-based video SR method, in which a novel DTS scheme is proposed to render the reconstructed HR details in a temporally coherent way, which effectively addresses the temporal incoherence problem caused by traditional TS-based image SR methods. To further reduce the complexity of the proposed method, our method only performs the TS-based SR on a set of key frames, while the HR details of the remaining nonkey frames are simply predicted using the bidirectional overlapped block motion compensation. After all frames are upscaled, the proposed DTS-SR is applied to maintain the temporal coherence in the HR video. Experimental results demonstrate that the proposed method achieves significant subjective and objective visual quality improvement over state-of-the-art video SR methods. A new method, based on an iterative procedure, for solving the two-dimensional inverse scattering problem is presented. This method employs an equivalent Neumann series solution in each iteration step. The purpose of the algorithm is to provide a general method to solve the two-dimensional imaging problem when the Born and the Rytov approximations break down. Numerical simulations were calculated for several cases where the conditions for the first order Born approximation were not satisfied. The results show that in both high and low frequency cases, good reconstructed profiles and smoothed versions of the original profiles can be obtained for smoothly varying permittivity profiles (lossless) and discontinuous profiles (lossless), respectively. A limited number of measurements around the object at a single frequency with four to eight plane incident waves from different directions are used. The method proposed in this article could easily be applied to the three-dimensional inverse scattering problem, if computational resources are available. Statistical inference and information processing of high-dimensional data often require an efficient and accurate estimation of their second-order statistics. With rapidly changing data, limited processing power and storage at the acquisition devices, it is desirable to extract the covariance structure from a single pass over the data and a small number of stored measurements. In this paper, we explore a quadratic (or rank-one) measurement model which imposes minimal memory requirements and low computational complexity during the sampling process, and is shown to be optimal in preserving various low-dimensional covariance structures. Specifically, four popular structural assumptions of covariance matrices, namely, low rank, Toeplitz low rank, sparsity, jointly rank-one and sparse structure, are investigated, while recovery is achieved via convex relaxation paradigms for the respective structure. The proposed quadratic sampling framework has a variety of potential applications, including streaming data processing, high-frequency wireless communication, phase space tomography and phase retrieval in optics, and noncoherent subspace detection. Our method admits universally accurate covariance estimation in the absence of noise, as soon as the number of measurements exceeds the information theoretic limits. We also demonstrate the robustness of this approach against noise and imperfect structural assumptions. Our analysis is established upon a novel notion called the mixed-norm restricted isometry property (RIP- @math ), as well as the conventional RIP- @math for near-isotropic and bounded measurements. In addition, our results improve upon the best-known phase retrieval (including both dense and sparse signals) guarantees using PhaseLift with a significantly simpler approach.