RADAR: Robust Algorithm for Depth Image Super Resolution Based on FRI Theory and Multimodal Dictionary Learning

Depth image super-resolution is a challenging problem, since normally high upscaling factors are required (e.g., 16\times ), and depth images are often noisy. In order to achieve large upscaling factors and resilience to noise, we propose a Robust Algorithm for Depth imAge super Resolution (RADAR) that combines the power of finite rate of innovation (FRI) theory with multimodal dictionary learning. Given a low-resolution (LR) depth image, we first model its rows and columns as piece-wise polynomials and propose an FRI-based depth upscaling (FDU) algorithm to super-resolve the image. Then, the upscaled moderate quality (MQ) depth image is further enhanced with the guidance of a registered high-resolution (HR) intensity image. This is achieved by learning multimodal mappings from the joint MQ depth and HR intensity pairs to the HR depth, through a recently proposed triple dictionary learning (TDL) algorithm. Moreover, to speed up the super-resolution process, we introduce a new projection-based rapid upscaling (PRU) technique that pre-calculates the projections from the joint MQ depth and HR intensity pairs to the HR depth. Compared with the state-of-the-art deep learning-based methods, our approach has two distinct advantages: we need a fraction of training data but can achieve the best performance, and we are resilient to mismatches between training and testing datasets. The extensive numerical results show that the proposed method outperforms other state-of-the-art methods on either noise-free or noisy datasets with large upscaling factors up to 16\times and can handle unknown blurring kernels well.