arXiv subjects

Laura Waller

Publications and source records attributed to Laura Waller.

64 records · Page 4Linked to original sources

arXiv2018

A Practical Reconstruction Method for Three-Dimensional Phase Contrast Atomic Electron Tomography

Electron tomography is a technique used in both materials science and structural biology to image features well below optical resolution limit. In this work, we present a new algorithm for reconstructing the three-dimensional(3D) electrostatic potential of a sample at atomic resolution from phase contrast imaging using high-resolution transmission electron microscopy. Our method accounts for dynamical and strong phase scattering, providing more accurate results with much lower electron doses than those current atomic electron tomography experiments. We test our algorithm using simulated images of a synthetic needle geometry dataset composed of an amorphous silicon dioxide shell around a silicon core. Our results show that, for a wide range of experimental parameters, we can accurately determine both atomic positions and species, and also identify vacancies even for light elements such as silicon and disordered materials such as amorphous silicon dioxide and also identify vacancies.

eess.SP↗

arXiv2018

Efficient illumination angle self-calibration in Fourier ptychography

Fourier ptychography captures intensity images with varying source patterns (illumination angles) in order to computationally reconstruct large space-bandwidth-product images. Accurate knowledge of the illumination angles is necessary for good image quality; hence, calibration methods are crucial, despite often being impractical or slow. Here, we propose a fast, robust, and accurate self-calibration algorithm that uses only experimentally-collected data and general knowledge of the illumination setup. First, our algorithm makes a direct estimate of the brightfield illumination angles based on image processing. Then, a more computationally-intensive spectral correlation method is used inside the iterative solver to further refine the angle estimates of both brightfield and darkfield images. We demonstrate our method for correcting large and small misalignment artifacts in both 2D and 3D Fourier ptychography with different source types: an LED array, a galvo-steered laser, and a high-NA quasi-dome LED illuminator.

eess.SP↗

arXiv2018

Accelerated Wirtinger Flow for Multiplexed Fourier Ptychographic Microscopy

Fourier ptychographic microscopy enables gigapixel-scale imaging, with both large field-of-view and high resolution. Using a set of low-resolution images that are recorded under varying illumination angles, the goal is to computationally reconstruct high-resolution phase and amplitude images. To increase temporal resolution, one may use multiplexed measurements where the sample is illuminated simultaneously from a subset of the angles. In this paper, we develop an algorithm for Fourier ptychographic microscopy with such multiplexed illumination. Specifically, we consider gradient descent type updates and propose an analytical step size that ensures the convergence of the iterates to a stationary point. Furthermore, we propose an accelerated version of our algorithm (with the same step size) which significantly improves the convergence speed. We demonstrate that the practical performance of our algorithm is identical to the case where the step size is manually tuned. Finally, we apply our parameter-free approach to real data and validate its applicability.

eess.SP↗

arXiv2018

Learning-based Image Reconstruction via Parallel Proximal Algorithm

In the past decade, sparsity-driven regularization has led to advancement of image reconstruction algorithms. Traditionally, such regularizers rely on analytical models of sparsity (e.g. total variation (TV)). However, more recent methods are increasingly centered around data-driven arguments inspired by deep learning. In this letter, we propose to generalize TV regularization by replacing the l1-penalty with an alternative prior that is trainable. Specifically, our method learns the prior via extending the recently proposed fast parallel proximal algorithm (FPPA) to incorporate data-adaptive proximal operators. The proposed framework does not require additional inner iterations for evaluating the proximal mappings of the corresponding learned prior. Moreover, our formalism ensures that the training and reconstruction processes share the same algorithmic structure, making the end-to-end implementation intuitive. As an example, we demonstrate our algorithm on the problem of deconvolution in a fluorescence microscope.

cs.CV↗

arXiv2017

DiffuserCam: Lensless Single-exposure 3D Imaging

We demonstrate a compact and easy-to-build computational camera for single-shot 3D imaging. Our lensless system consists solely of a diffuser placed in front of a standard image sensor. Every point within the volumetric field-of-view projects a unique pseudorandom pattern of caustics on the sensor. By using a physical approximation and simple calibration scheme, we solve the large-scale inverse problem in a computationally efficient way. The caustic patterns enable compressed sensing, which exploits sparsity in the sample to solve for more 3D voxels than pixels on the 2D sensor. Our 3D voxel grid is chosen to match the experimentally measured two-point optical resolution across the field-of-view, resulting in 100 million voxels being reconstructed from a single 1.3 megapixel image. However, the effective resolution varies significantly with scene content. Because this effect is common to a wide range of computational cameras, we provide new theory for analyzing resolution in such systems.

cs.CV↗

arXiv2017

Multiplexed phase-space imaging for 3D fluorescence microscopy

Optical phase-space functions describe spatial and angular information simultaneously; examples include light fields in ray optics and Wigner functions in wave optics. Measurement of phase-space enables digital refocusing, aberration removal and 3D reconstruction. High-resolution capture of 4D phase-space datasets is, however, challenging. Previous scanning approaches are slow, light inefficient and do not achieve diffraction-limited resolution. Here, we propose a multiplexed method that solves these problems. We use a spatial light modulator (SLM) in the pupil plane of a microscope in order to sequentially pattern multiplexed coded apertures while capturing images in real space. Then, we reconstruct the 3D fluorescence distribution of our sample by solving an inverse problem via regularized least squares with a proximal accelerated gradient descent solver. We experimentally reconstruct a 101-Megavoxel 3D volume ($1010\times510\times500μ$m with NA 0.4), demonstrating improved acquisition time, light throughput and resolution compared to scanning aperture methods. Our flexible patterning scheme further allows sparsity in the sample to be exploited for reduced data capture.

physics.optics↗

arXiv2017

SEAGLE: Sparsity-Driven Image Reconstruction under Multiple Scattering

Multiple scattering of an electromagnetic wave as it passes through an object is a fundamental problem that limits the performance of current imaging systems. In this paper, we describe a new technique-called Series Expansion with Accelerated Gradient Descent on Lippmann-Schwinger Equation (SEAGLE)-for robust imaging under multiple scattering based on a combination of a new nonlinear forward model and a total variation (TV) regularizer. The proposed forward model can account for multiple scattering, which makes it advantageous in applications where linear models are inaccurate. Specifically, it corresponds to a series expansion of the scattered wave with an accelerated-gradient method. This expansion guarantees the convergence even for strongly scattering objects. One of our key insights is that it is possible to obtain an explicit formula for computing the gradient of our nonlinear forward model with respect to the unknown object, thus enabling fast image reconstruction with the state-of-the-art fast iterative shrinkage/thresholding algorithm (FISTA). The proposed method is validated on both simulated and experimentally measured data.

cs.CV↗

arXiv2017

Structured illumination microscopy with unknown patterns and a statistical prior

Structured illumination microscopy (SIM) improves resolution by down-modulating high-frequency information of an object to fit within the passband of the optical system. Generally, the reconstruction process requires prior knowledge of the illumination patterns, which implies a well-calibrated and aberration-free system. Here, we propose a new \textit{algorithmic self-calibration} strategy for SIM that does not need to know the exact patterns {\it a priori}, but only their covariance. The algorithm, termed PE-SIMS, includes a Pattern-Estimation (PE) step requiring the uniformity of the sum of the illumination patterns and a SIM reconstruction procedure using a Statistical prior (SIMS). Additionally, we perform a pixel reassignment process (SIMS-PR) to enhance the reconstruction quality. We achieve 2$\times$ better resolution than a conventional widefield microscope, while remaining insensitive to aberration-induced pattern distortion and robust against parameter tuning.

cs.CV↗

arXiv2015

Experimental robustness of Fourier Ptychography phase retrieval algorithms

Fourier ptychography is a new computational microscopy technique that provides gigapixel-scale intensity and phase images with both wide field-of-view and high resolution. By capturing a stack of low-resolution images under different illumination angles, a nonlinear inverse algorithm can be used to computationally reconstruct the high-resolution complex field. Here, we compare and classify multiple proposed inverse algorithms in terms of experimental robustness. We find that the main sources of error are noise, aberrations and mis-calibration (i.e. model mis-match). Using simulations and experiments, we demonstrate that the choice of cost function plays a critical role, with amplitude-based cost functions performing better than intensity-based ones. The reason for this is that Fourier ptychography datasets consist of images from both brightfield and darkfield illumination, representing a large range of measured intensities. Both noise (e.g. Poisson noise) and model mis-match errors are shown to scale with intensity. Hence, algorithms that use an appropriate cost function will be more tolerant to both noise and model mis-match. Given these insights, we propose a global Newton's method algorithm which is robust and computationally efficient. Finally, we discuss the impact of procedures for algorithmic correction of aberrations and mis-calibration.

physics.optics↗

arXiv2015

Computational illumination for high-speed in vitro Fourier ptychographic microscopy

We demonstrate a new computational illumination technique that achieves large space-bandwidth-time product, for quantitative phase imaging of unstained live samples in vitro. Microscope lenses can have either large field of view (FOV) or high resolution, not both. Fourier ptychographic microscopy (FPM) is a new computational imaging technique that circumvents this limit by fusing information from multiple images taken with different illumination angles. The result is a gigapixel-scale image having both wide FOV and high resolution, i.e. large space-bandwidth product (SBP). FPM has enormous potential for revolutionizing microscopy and has already found application in digital pathology. However, it suffers from long acquisition times (on the order of minutes), limiting throughput. Faster capture times would not only improve imaging speed, but also allow studies of live samples, where motion artifacts degrade results. In contrast to fixed (e.g. pathology) slides, live samples are continuously evolving at various spatial and temporal scales. Here, we present a new source coding scheme, along with real-time hardware control, to achieve 0.8 NA resolution across a 4x FOV with sub-second capture times. We propose an improved algorithm and new initialization scheme, which allow robust phase reconstruction over long time-lapse experiments. We present the first FPM results for both growing and confluent in vitro cell cultures, capturing videos of subcellular dynamical phenomena in popular cell lines undergoing division and migration. Our method opens up FPM to applications with live samples, for observing rare events in both space and time.

physics.optics↗