Online Optimization With Costly and Noisy Measurements Using Random Fourier Expansions

Kernel Correntropy Conjugate Gradient Algorithms Based on Half-Quadratic Optimization

As a nonlinear similarity measure defined in the kernel space, the correntropic loss (C-Loss) can address the stability issues of second-order similarity measures thanks to its ability to extract high-order statistics of data. However, the kernel adaptive filter (KAF) based on the C-Loss uses the stochastic gradient descent (SGD) method to update its weights and, thus, suffers from poor performance and a slow convergence rate. To address these issues, the conjugate gradient (CG)-based correntropy algorithm is developed by solving the combination of half-quadratic (HQ) optimization and weighted least-squares (LS) problems, generating a novel robust kernel correntropy CG (KCCG) algorithm. The proposed KCCG with less computational complexity achieves comparable performance to the kernel recursive maximum correntropy (KRMC) algorithm. To further curb the growth of the network in KCCG, the random Fourier features KCCG (RFFKCCG) algorithm is proposed by transforming the original input data into a fixed-dimensional random Fourier features space (RFFS). Since only one current error information is used in the loss function of RFFKCCG, it can provide a more efficient filter structure than the other KAFs with sparsification. The Monte Carlo simulations conducted in the prediction of synthetic and real-world chaotic time series and the regression for large-scale datasets validate the superiorities of the proposed algorithms in terms of robustness, filtering accuracy, and complexity.

Adaptive-glasses time-domain FFOCT for wide-field high-resolution retinal imaging with increased SNR

The highest three-dimensional (3D) resolution possible in in vivo retinal imaging is achieved by combining optical coherence tomography (OCT) and adaptive optics. However, this combination brings important limitations, such as small field-of-view and complex, cumbersome systems, preventing so far the translation of this technology from the research lab to clinics. In this Letter, we mitigate these limitations by combining our compact time-domain full-field OCT (FFOCT) with a multi-actuator adaptive lens positioned just in front of the eye, in a technique we call the adaptive-glasses wavefront sensorless approach. Through this approach, we demonstrate that ocular aberrations can be corrected, increasing the FFOCT signal-to-noise ratio (SNR) and enabling imaging of different retinal layers with a 3D cellular resolution over a 5^∘×5^∘ field-of-view, without apparent anisoplanatism.

Extended-image-based correction of aberrations using a deformable mirror with hysteresis

With a view to the next generation of large space telescopes, we investigate guide-star-free, image-based aberration correction using a unimorph deformable mirror in a plane conjugate to the primary mirror. We designed and built a high-resolution imaging testbed to evaluate control algorithms. In this paper we use an algorithm based on the heuristic hill climbing technique and compare the correction in three different domains, namely the voltage domain, the domain of the Zernike modes, and the domain of the singular modes of the deformable mirror. Through our systematic experimental study, we found that successive control in two domains effectively counteracts uncompensated hysteresis of the deformable mirror.

Lens-based wavefront sensorless adaptive optics swept source OCT

Optical coherence tomography (OCT) has revolutionized modern ophthalmology, providing depth resolved images of the retinal layers in a system that is suited to a clinical environment. Although the axial resolution of OCT system, which is a function of the light source bandwidth, is sufficient to resolve retinal features at a micrometer scale, the lateral resolution is dependent on the delivery optics and is limited by ocular aberrations. Through the combination of wavefront sensorless adaptive optics and the use of dual deformable transmissive optical elements, we present a compact lens-based OCT system at an imaging wavelength of 1060 nm for high resolution retinal imaging. We utilized a commercially available variable focal length lens to correct for a wide range of defocus commonly found in patient’s eyes, and a novel multi-actuator adaptive lens for aberration correction to achieve near diffraction limited imaging performance at the retina. With a parallel processing computational platform, high resolution cross-sectional and en face retinal image acquisition and display was performed in real time. In order to demonstrate the system functionality and clinical utility, we present images of the photoreceptor cone mosaic and other retinal layers acquired in vivo from research subjects.