High Dimensional Data Completion using Transform induced t-SVD

Abstract

High-Dimensional Data completion algorithms provide the solution to most of the machine learning and color image processing applications. It is a process of recovering of corrupted data from uncorrupted data set. The recovery issues are addressed by minimizing the rank of tensor-based algorithms, which is an extension to matrix completion. It acquired the attention of researchers, to work towards the low rank tensor completion. The low rank tensor completion algorithms are introduced by the researchers to retrieve the incomplete visual data present in highly corrupted high- dimensional data. A transform based low rank tensor completion can produce more accurate results. Here an approach, Lifting Wavelet Transform (LWT) induced tensor singular value decomposition (t-SVD) based regularizer is introduced to recover the more than 80% corrupted tensors from un-corrupted tensors. The LWT features like in-place implementation and custom design filters, are leading to use. The optimization method, Accelerated Proximal Gradient Line (APGL) is used. The recovered results are assessed with various measures like Peak Signal to Noise Ratio (PSNR), Structural Similarity (SSIM), and Natural Image Quality Evaluator (NIQE) and Perceptual Image Quality Evaluator (PIQE). The proposed approach has better results than state-of-the-art methods.