Search for: All records

In this article, we initiate the study of the weighted paging problem with predictions. This continues the recent line of work in online algorithms with predictions, particularly that of Lykouris and Vassilvitski (ICML 2018) and Rohatgi (SODA 2020) on unweighted paging with predictions. We show that unlike unweighted paging, neither a fixed lookahead nor a knowledge of the next request for every page is sufficient information for an algorithm to overcome the existing lower bounds in weighted paging. However, a combination of the two, which we call strong per request prediction (SPRP), suffices to give a 2-competitive algorithm. We also explore the question of gracefully degrading algorithms with increasing prediction error, and give both upper and lower bounds for a set of natural measures of prediction error. 

Abstract Fourier ptychography (FP) is an enabling imaging technique that produces high‐resolution complex‐valued images with extended field coverages. However, when FP images a phase object with any specific spatial frequency, the captured images contain only constant values, rendering the recovery of the corresponding linear phase ramp impossible. This challenge is not unique to FP but also affects other common microscopy techniques — a rather counterintuitive outcome given their widespread use in phase imaging. The underlying issue originates from the non‐uniform phase transfer characteristic inherent in microscope systems, which impedes the conversion of object wavefields into discernible intensity variations. To address this challenge, spatially‐coded Fourier ptychography (scFP) is presented for true quantitative phase imaging. In scFP, a flexible and detachable coded thin film is attached atop the image sensor in a regular FP setup. The spatial modulation of this thin film ensures a uniform phase response across the entire synthetic bandwidth. It improves reconstruction quality, corrects refractive index underestimation issues prevalent in conventional FP, and adds a new dimension of measurement diversity in spatial domain. The development of scFP is expected to catalyze new research directions and applications for phase imaging, emphasizing the need for true quantitative accuracy with uniform frequency response.