ABSTRACT
This paper analyzes data-based online nonlinear extremum-seeker (DONE), an online optimization algorithm that iteratively minimizes an unknown function based on costly and noisy measurements. The algorithm maintains a surrogate of the unknown function in the form of a random Fourier expansion. The surrogate is updated whenever a new measurement is available, and then used to determine the next measurement point. The algorithm is comparable with Bayesian optimization algorithms, but its computational complexity per iteration does not depend on the number of measurements. We derive several theoretical results that provide insight on how the hyperparameters of the algorithm should be chosen. The algorithm is compared with a Bayesian optimization algorithm for an analytic benchmark problem and three applications, namely, optical coherence tomography, optical beam-forming network tuning, and robot arm control. It is found that the DONE algorithm is significantly faster than Bayesian optimization in the discussed problems while achieving a similar or better performance.
ABSTRACT
In this report, which is an international collaboration of OCT, adaptive optics, and control research, we demonstrate the Data-based Online Nonlinear Extremum-seeker (DONE) algorithm to guide the image based optimization for wavefront sensorless adaptive optics (WFSL-AO) OCT for in vivo human retinal imaging. The ocular aberrations were corrected using a multi-actuator adaptive lens after linearization of the hysteresis in the piezoelectric actuators. The DONE algorithm succeeded in drastically improving image quality and the OCT signal intensity, up to a factor seven, while achieving a computational time of 1 ms per iteration, making it applicable for many high speed applications. We demonstrate the correction of five aberrations using 70 iterations of the DONE algorithm performed over 2.8 s of continuous volumetric OCT acquisition. Data acquired from an imaging phantom and in vivo from human research volunteers are presented.