Robust tensor completion improves image recovery near boundaries
Robust Tensor Completion via Reflective Convolution Nuclear Norm Minimization
Computer Vision and Pattern Recognition
Summary
Recovering incomplete multidimensional data can be difficult when errors and missing parts exist, especially near the edges of images. The authors propose a new method called reflective convolution nuclear norm minimization that fixes problems caused by older methods wrapping data around artificially. Their approach better preserves boundary details by reflecting data at endpoints instead of looping around. Tests on synthetic and real images show clearer improvements near edges and competitive overall image quality.
What this means in practice
- •For image processing teams: Restore damaged or incomplete images with fewer boundary artifacts by using reflective padding in tensor completion algorithms.
- •For multispectral image analysts: Enhance reconstruction quality of multispectral images by employing robust completion methods that handle sparse errors and respect image boundaries.
Authors
Weiguo Zhou, Feng Zhang, Wenjin Qin, Jianwen Huang
Abstract
Robust tensor completion recovers multidimensional data from partial observations corrupted by sparse gross errors. Existing convolutional low-rank models typically construct translated copies using circular continuation, which introduces artificial wrap-around neighborhoods for finite nonperiodic data. We propose reflective convolution nuclear norm minimization (RCNNM), which replaces circular shifts with endpoint-nonrepeating reflection. The resulting lifting has nonuniform entry multiplicities and satisfies a weighted Gram identity that supports both the recovery analysis and the optimization method. Under random sampling and sparse corruption, we establish high-probability exact recovery of the underlying tensor and sparse errors, together with stability under bounded dense perturbations. We further develop a two-block ADMM with a closed-form entrywise tensor update, while singular-value thresholding is implemented through the smaller right Gram matrix. Experiments on synthetic tensors, BSDS color images, and CAVE multispectral images show that RCNNM consistently improves over its circular-lifting counterpart, with the clearest gains near image boundaries. In particular, average boundary-PSNR improvements reach 3.26 dB while global reconstruction quality remains competitive.