Solution of Inverse Problem using Learning

Qiqin Dai

doi:https://doi.org/10.21985/N2BQ8W

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Solution of Inverse Problem using Learning

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In this dissertation, we start with the dictionary learning (DL) based single-frame super-resolution (SR) problem, where low resolution (LR) input frames are super-resolved to high resolution (HR) output frames. We propose to extend the previous single-frame SR methods to multiple-frames, i.e., estimating single HR output frame by multiple LR input frames, utilizing DL and motion estimation. Specifically, we adopt the use of bilevel dictionary learning which has been used for single-frame SR. It is extended to multiple frames by using motion estimation with sub-pixel accuracy. By simultaneously solving for a batch of patches from multiple frames, the proposed multiple-frame SR algorithms improve over single-frame SR. We then propose to unfold the iteration process in the LASSO solver to a feed-forward neural network and utilize KKT condition to refine the solution. The X-Ray fluorescence (XRF) image SR method is then investigated to address the trade-off between the spatial resolution of an XRF scan and the Signal-to-Noise Ratio (SNR) of each pixel's spectra. We propose to fuse an LR XRF image and a conventional HR RGB image into a product of HR XRF image. By learning the mapping from RGB signal to XRF signal, the LR XRF image is super-resolved to have the same spatial resolution as the HR RGB image. Finally, the XRF image inpainting problem with adaptive sampling mask is investigated. A Convolutional Neural Network (CNN) is trained to generate adaptive binary sampling mask according to the RGB image. Then the XRF scanner scans a subset of the whole pixels according to the binary sampling mask, to speedup the scanning process. The sub-sampled XRF image is fused with the RGB image to reconstruct the full-sampled XRF image.

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