Bayesian Image Aberration Removal Using Transfer Functions
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Solution Overview
Problem
Conventional image recovery methods are limited in effectively addressing image degradation caused by noise, blur, and aberrations in imperfect imaging optics, often requiring complex and costly multi-element lens systems or multiple image acquisitions.
Innovation Solution
A computer-implemented process and apparatus that utilize a Bayesian inverse method to remove aberrations from acquired images by determining a pixel-by-pixel uncertainty and total transfer function, leveraging prior information about the object and imaging system to produce high-fidelity, near-diffraction limited images using low-cost, off-the-shelf optical elements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional image recovery methods are used, then image degradation from noise and blur can be addressed, but the methods require complex multi-element lens systems or multiple image acquisitions
Solution Approach 1:
The patent replaces complex mechanical optical systems with a computational approach. Instead of using multi-element lens systems to correct aberrations physically, the invention uses a processor to execute algorithms that mathematically reverse aberration effects. The system determines a total transfer function from the acquired image and prior information, then applies inverse operations to reconstruct the original image, substituting mechanical optical correction with computational inversion.
Solution Approach 2:
The patent creates a computational model (copy) of the imaging system's aberrations through the transfer function H(k). This mathematical model captures the degradation effects without requiring physical replication of the optical system. By working with this computational copy, the system can apply correction algorithms that would otherwise require complex physical optical components.
2Measurement precision
If conventional image recovery methods are used, then some image degradation can be addressed, but they require multiple image acquisitions
Solution Approach 1:
The patent performs preliminary characterization of the imaging system's aberrations by determining the total transfer function H(k) from the acquired image and prior information about the object and imaging system. This preliminary step captures all necessary correction information in a single acquisition, eliminating the need for multiple images. The transfer function is computed using the relationship between the acquired image, prior expectations, and the imaging model before any correction is applied.
Solution Approach 2:
The system uses feedback from the acquired image itself to determine the transfer function. By analyzing the relationship between the acquired image and the prior model, the system automatically characterizes the aberrations and computes the correction parameters. This feedback mechanism allows single-shot correction without requiring multiple acquisitions for calibration.
3Measurement precision
If sophisticated optics are used to achieve high-fidelity images, then image quality improves, but device complexity and cost increase
Solution Approach 1:
The patent replaces expensive, complex multi-element lens systems with inexpensive, single-element optics. The invention accepts that simple optics will introduce aberrations but uses computational methods to correct these effects. This approach trades the high cost of sophisticated optical components for the lower cost of simple optics combined with software correction, making high-fidelity imaging accessible with affordable hardware.
Data Source
AI summary
A process for removing aberrations in an acquired image from imperfect imaging optics includes: acquiring an acquired image of an object with an imperfect imaging system that includes an imperfect imaging optic, the acquired image including a plurality of pixels; producing a prior that includes an expectation of data for the object; determining a pixel-by-pixel uncertainty of the acquired image; determining a total transfer function of the acquired image from the prior and the acquired image; and determining a data vector from the total transfer function and the acquired image to remove aberrations from the acquired image.