Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography

By 'atmospheric tomography' we mean the estimation of a layered atmospheric turbulence profile from measurements of the pupil-plane phase (or phase gradients) corresponding to several different guide star directions. We introduce what we believe to be a new Fourier domain preconditioned conjugate gradient (FD-PCG) algorithm for atmospheric tomography, and we compare its performance against an existing multigrid preconditioned conjugate gradient (MG-PCG) approach. Numerical results indicate that on conventional serial computers, FD-PCG is as accurate and robust as MG-PCG, but it is from one to two orders of magnitude faster for atmospheric tomography on 30 m class telescopes. Simulations are carried out for both natural guide stars and for a combination of finite-altitude laser guide stars and natural guide stars to resolve tip-tilt uncertainty

\u3cem\u3eIn vivo\u3c/em\u3e Imaging of Human Cone Photoreceptor Inner Segments

Purpose. An often overlooked prerequisite to cone photoreceptor gene therapy development is residual photoreceptor structure that can be rescued. While advances in adaptive optics (AO) retinal imaging have recently enabled direct visualization of individual cone and rod photoreceptors in the living human retina, these techniques largely detect strongly directionally-backscattered (waveguided) light from normal intact photoreceptors. This represents a major limitation in using existing AO imaging to quantify structure of remnant cones in degenerating retina. Methods. Photoreceptor inner segment structure was assessed with a novel AO scanning light ophthalmoscopy (AOSLO) differential phase technique, that we termed nonconfocal split-detector, in two healthy subjects and four subjects with achromatopsia. Ex vivo preparations of five healthy donor eyes were analyzed for comparison of inner segment diameter to that measured in vivo with split-detector AOSLO. Results. Nonconfocal split-detector AOSLO reveals the photoreceptor inner segment with or without the presence of a waveguiding outer segment. The diameter of inner segments measured in vivo is in good agreement with histology. A substantial number of foveal and parafoveal cone photoreceptors with apparently intact inner segments were identified in patients with the inherited disease achromatopsia. Conclusions. The application of nonconfocal split-detector to emerging human gene therapy trials will improve the potential of therapeutic success, by identifying patients with sufficient retained photoreceptor structure to benefit the most from intervention. Additionally, split-detector imaging may be useful for studies of other retinal degenerations such as AMD, retinitis pigmentosa, and choroideremia where the outer segment is lost before the remainder of the photoreceptor cell

Effects of Intraframe Distortion on Measures of Cone Mosaic Geometry from Adaptive Optics Scanning Light Ophthalmoscopy

Purpose: To characterize the effects of intraframe distortion due to involuntary eye motion on measures of cone mosaic geometry derived from adaptive optics scanning light ophthalmoscope (AOSLO) images. Methods: We acquired AOSLO image sequences from 20 subjects at 1.0, 2.0, and 5.08 temporal from fixation. An expert grader manually selected 10 minimally distorted reference frames from each 150-frame sequence for subsequent registration. Cone mosaic geometry was measured in all registered images (n ¼ 600) using multiple metrics, and the repeatability of these metrics was used to assess the impact of the distortions from each reference frame. In nine additional subjects, we compared AOSLO-derived measurements to those from adaptive optics (AO)-fundus images, which do not contain system-imposed intraframe distortions. Results: We observed substantial variation across subjects in the repeatability of density (1.2%–8.7%), inter-cell distance (0.8%–4.6%), percentage of six-sided Voronoi cells (0.8%–10.6%), and Voronoi cell area regularity (VCAR) (1.2%–13.2%). The average of all metrics extracted from AOSLO images (with the exception of VCAR) was not significantly different than those derived from AO-fundus images, though there was variability between individual images. Conclusions: Our data demonstrate that the intraframe distortion found in AOSLO images can affect the accuracy and repeatability of cone mosaic metrics. It may be possible to use multiple images from the same retinal area to approximate a ‘‘distortionless’’ image, though more work is needed to evaluate the feasibility of this approach. Translational Relevance: Even in subjects with good fixation, images from AOSLOs contain intraframe distortions due to eye motion during scanning. The existence of these artifacts emphasizes the need for caution when interpreting results derived from scanning instruments

Adaptive estimation of the density matrix in quantum homodyne tomography with noisy data

In the framework of noisy quantum homodyne tomography with efficiency parameter $1/2 < \eta \leq 1$, we propose a novel estimator of a quantum state whose density matrix elements $\rho_{m,n}$ decrease like $Ce^{-B(m+n)^{r/ 2}}$, for fixed $C\geq 1$, $B>0$ and $0<r\leq 2$. On the contrary to previous works, we focus on the case where $r$, $C$ and $B$ are unknown. The procedure estimates the matrix coefficients by a projection method on the pattern functions, and then by soft-thresholding the estimated coefficients. We prove that under the $\mathbb{L}_2$ -loss our procedure is adaptive rate-optimal, in the sense that it achieves the same rate of conversgence as the best possible procedure relying on the knowledge of $(r,B,C)$. Finite sample behaviour of our adaptive procedure are explored through numerical experiments

WARP: Wavelets with adaptive recursive partitioning for multi-dimensional data

Effective identification of asymmetric and local features in images and other data observed on multi-dimensional grids plays a critical role in a wide range of applications including biomedical and natural image processing. Moreover, the ever increasing amount of image data, in terms of both the resolution per image and the number of images processed per application, requires algorithms and methods for such applications to be computationally efficient. We develop a new probabilistic framework for multi-dimensional data to overcome these challenges through incorporating data adaptivity into discrete wavelet transforms, thereby allowing them to adapt to the geometric structure of the data while maintaining the linear computational scalability. By exploiting a connection between the local directionality of wavelet transforms and recursive dyadic partitioning on the grid points of the observation, we obtain the desired adaptivity through adding to the traditional Bayesian wavelet regression framework an additional layer of Bayesian modeling on the space of recursive partitions over the grid points. We derive the corresponding inference recipe in the form of a recursive representation of the exact posterior, and develop a class of efficient recursive message passing algorithms for achieving exact Bayesian inference with a computational complexity linear in the resolution and sample size of the images. While our framework is applicable to a range of problems including multi-dimensional signal processing, compression, and structural learning, we illustrate its work and evaluate its performance in the context of 2D and 3D image reconstruction using real images from the ImageNet database. We also apply the framework to analyze a data set from retinal optical coherence tomography

Multi-Conjugate Adaptive Optics Simulator for the Thirty Meter Telescope: Design, Implementation, and Results

We present a multi-conjugate adaptive optics (MCAO) system simulator bench, HeNOS (Herzberg NFIRAOS Optical Simulator). HeNOS is developed to validate the performance of the MCAO system for the Thirty Meter Telescope, as well as to demonstrate techniques critical for future AO developments. In this paper, we focus on describing the derivations of parameters that scale the 30-m telescope AO system down to a bench experiment and explain how these parameters are practically implemented on an optical bench. While referring other papers for details of AO technique developments using HeNOS, we introduce the functionality of HeNOS, in particular, three different single-conjugate AO modes that HeNOS currently offers: a laser guide star AO with a Shack-Hartmann wavefront sensor, a natural guide star AO with a pyramid wavefront sensor, and a laser guide star AO with a sodium spot elongation on the Shack-Hartmann corrected by a truth wavefront sensing on a natural guide star. Laser tomography AO and ultimate MCAO are being prepared to be implemented in the near future