MR image reconstruction using deep density priors

Algorithms for Magnetic Resonance (MR) image reconstruction from undersampled measurements exploit prior information to compensate for missing k-space data. Deep learning (DL) provides a powerful framework for extracting such information from existing image datasets, through learning, and then using it for reconstruction. Leveraging this, recent methods employed DL to learn mappings from undersampled to fully sampled images using paired datasets, including undersampled and corresponding fully sampled images, integrating prior knowledge implicitly. In this article, we propose an alternative approach that learns the probability distribution of fully sampled MR images using unsupervised DL, specifically Variational Autoencoders (VAE), and use this as an explicit prior term in reconstruction, completely decoupling the encoding operation from the prior. The resulting reconstruction algorithm enjoys a powerful image prior to compensate for missing k-space data without requiring paired datasets for training nor being prone to associated sensitivities, such as deviations in undersampling patterns used in training and test time or coil settings. We evaluated the proposed method with T1 weighted images from a publicly available dataset, multi-coil complex images acquired from healthy volunteers (N=8) and images with white matter lesions. The proposed algorithm, using the VAE prior, produced visually high quality reconstructions and achieved low RMSE values, outperforming most of the alternative methods on the same dataset. On multi-coil complex data, the algorithm yielded accurate magnitude and phase reconstruction results. In the experiments on images with white matter lesions, the method faithfully reconstructed the lesions. Keywords: Reconstruction, MRI, prior probability, machine learning, deep learning, unsupervised learning, density estimationComment: Published in IEEE TMI. Main text and supplementary material, 19 pages tota

Determination of the intrinsic behavior of polymers using digital image correlation combined with video-monitored testing

AbstractThree methods for the determination of the large-strain behavior of ductile polymers are compared in both tension and compression. Each method relies on some (non-contact) measurement of the strain and some approximations in the calculation of stress. The strain measurement techniques include digital image correlation (DIC) and two techniques of video-based extensometry: marker tracking and area variation monitoring. Since the specimens are inevitably subject to structural plastic instabilities (necking in tension, barreling in compression) the strain and stress states are no longer uniform in the gauge section after the peak load. Under such circumstances, it is demonstrated that the three experimental methods can lead to significant differences. It is inferred from the comparative analysis that the method based on vertical marker tracking is not reliable. Validated by DIC, video-based area variation is shown to be a simple alternative way to obtain an excellent estimate of the intrinsic true stress–strain behavior of the polymer

Custom Integrated Circuits

Contains reports on six research projects.U.S. Air Force - Office of Scientific Research (Contract F49620-84-C-0004)Analog Devices, Inc.Defense Advanced Research Projects Agency (Contract N00014-80-C-0622)National Science Foundation (Grant ECS83-10941

Directional couplers with integrated carbon nanotube incandescent light emitters

We combine on-chip single-walled carbon nanotubes (SWNTs) emitters with directional coupling devices as fundamental building blocks for carbon photonic systems. These devices are essential for studying the emission properties of SWNTs in the few photon regime for future applications in on-chip quantum photonics. The combination of SWNTs with on-chip beam splitters herein provides the basis for correlation measurements as necessary for nanoscale source characterization. The employed fabrication methods are fully scalable and thus allow for implementing a multitude of functional and active circuits in a single fabrication run. Our metallic SWNT emitters are broadband and cover both visible and near-infrared wavelengths, thus holding promise for emerging hybrid optoelectronic devices with fast reconfiguration times

Computational 3-D inversion for seismic exploration

This is the final report of a four-month, Laboratory Directed Research and Development (LDRD) project carried out at the Los Alamos National Laboratory (LANL). There is a great need for a new and effective technology with a wide scope of industrial applications to investigate media internal properties of which can be explored only from the backscattered data. The project was dedicated to the development of a three-dimensional computational inversion tool for seismic exploration. The new computational concept of the inversion algorithm was suggested. The goal of the project was to prove the concept and the practical validity of the algorithm for petroleum exploration

A Survey of Signal Processing Problems and Tools in Holographic Three-Dimensional Television

Cataloged from PDF version of article.Diffraction and holography are fertile areas for application of signal theory and processing. Recent work on 3DTV displays has posed particularly challenging signal processing problems. Various procedures to compute Rayleigh-Sommerfeld, Fresnel and Fraunhofer diffraction exist in the literature. Diffraction between parallel planes and tilted planes can be efficiently computed. Discretization and quantization of diffraction fields yield interesting theoretical and practical results, and allow efficient schemes compared to commonly used Nyquist sampling. The literature on computer-generated holography provides a good resource for holographic 3DTV related issues. Fast algorithms to compute Fourier, Walsh-Hadamard, fractional Fourier, linear canonical, Fresnel, and wavelet transforms, as well as optimization-based techniques such as best orthogonal basis, matching pursuit, basis pursuit etc., are especially relevant signal processing techniques for wave propagation, diffraction, holography, and related problems. Atomic decompositions, multiresolution techniques, Gabor functions, and Wigner distributions are among the signal processing techniques which have or may be applied to problems in optics. Research aimed at solving such problems at the intersection of wave optics and signal processing promises not only to facilitate the development of 3DTV systems, but also to contribute to fundamental advances in optics and signal processing theory. © 2007 IEEE

Nonlocal Graph-PDEs and Riemannian Gradient Flows for Image Labeling

In this thesis, we focus on the image labeling problem which is the task of performing unique pixel-wise label decisions to simplify the image while reducing its redundant information. We build upon a recently introduced geometric approach for data labeling by assignment flows [ APSS17 ] that comprises a smooth dynamical system for data processing on weighted graphs. Hereby we pursue two lines of research that give new application and theoretically-oriented insights on the underlying segmentation task. We demonstrate using the example of Optical Coherence Tomography (OCT), which is the mostly used non-invasive acquisition method of large volumetric scans of human retinal tis- sues, how incorporation of constraints on the geometry of statistical manifold results in a novel purely data driven geometric approach for order-constrained segmentation of volumetric data in any metric space. In particular, making diagnostic analysis for human eye diseases requires decisive information in form of exact measurement of retinal layer thicknesses that has be done for each patient separately resulting in an demanding and time consuming task. To ease the clinical diagnosis we will introduce a fully automated segmentation algorithm that comes up with a high segmentation accuracy and a high level of built-in-parallelism. As opposed to many established retinal layer segmentation methods, we use only local information as input without incorporation of additional global shape priors. Instead, we achieve physiological order of reti- nal cell layers and membranes including a new formulation of ordered pair of distributions in an smoothed energy term. This systematically avoids bias pertaining to global shape and is hence suited for the detection of anatomical changes of retinal tissue structure. To access the perfor- mance of our approach we compare two different choices of features on a data set of manually annotated 3 D OCT volumes of healthy human retina and evaluate our method against state of the art in automatic retinal layer segmentation as well as to manually annotated ground truth data using different metrics. We generalize the recent work [ SS21 ] on a variational perspective on assignment flows and introduce a novel nonlocal partial difference equation (G-PDE) for labeling metric data on graphs. The G-PDE is derived as nonlocal reparametrization of the assignment flow approach that was introduced in J. Math. Imaging & Vision 58(2), 2017. Due to this parameterization, solving the G-PDE numerically is shown to be equivalent to computing the Riemannian gradient flow with re- spect to a nonconvex potential. We devise an entropy-regularized difference-of-convex-functions (DC) decomposition of this potential and show that the basic geometric Euler scheme for inte- grating the assignment flow is equivalent to solving the G-PDE by an established DC program- ming scheme. Moreover, the viewpoint of geometric integration reveals a basic way to exploit higher-order information of the vector field that drives the assignment flow, in order to devise a novel accelerated DC programming scheme. A detailed convergence analysis of both numerical schemes is provided and illustrated by numerical experiments