Learning Geometry for Inverse Problems in Imaging

点击翻译按钮获取中文摘要

The quantity of digital image data our society relies on for medical, military, and a wide range of engineering and scientific applications continues to increase, yet digital images still typically exhibit some level of degradation during formation, transmission, and storage, often obscuring vital information. Despite significant advances in the fields of image processing and computer vision, this problem still persists due to the difficulty in accurately modeling random degradations such as noise, pixel loss, and blur. The main objectives for this project are to learn critical geometric and higher order image features for accurately solving a variety of inverse problems in imaging, including image denoising, image deblurring, image inpainting (filling in of missing data), and super-resolution. The new algorithms developed in this project are expected to yield improvements over existing algorithms in the form of standard image quality metrics as well as in the preservation of accurate, fine details, a feature missing from many current state of the art image processing algorithms, yet vital for automatically interpreting this image data in practice. In recent work the PI and collaborators have developed several frameworks for image denoising that attempt to recover an image from a denoised geometric feature of the image. These approaches have successfully improved upon existing state of the art denoising algorithms, providing information in the reconstruction that has been elusive using alternate approaches. The challenge in working with this geometric data is that while it is very robust in practice, mathematically sound mechanisms developed for handling natural image data do not necessarily apply to their geometric features. This project involves learning geometric descriptors from image data that have suffered from some combination of the aforementioned random and/or linear degradations for the purpose of aiding in image reconstruction, analysis, and interpretation. Preliminary analyses and experiments indicate that the benefits of this approach could be significant, yet computationally intensive experiments are required to explore how best to exploit these benefits in practice. Theoretical analyses of these models will be an important part of this project as well, in order to better to understand when these models are guaranteed to be reliable in practice.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.