Tensor-Networked Square-Root Kalman Filter for Online Video Completion
P. van Klaveren (TU Delft - Mechanical Engineering)
Kim Batselier – Mentor (TU Delft - Team Kim Batselier)
R. Ferrari – Graduation committee member (TU Delft - Team Riccardo Ferrari)
C.M. Menzen – Graduation committee member (TU Delft - Team Manon Kok)
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Abstract
Online video completion aims to complete corrupted frames of a video in an online fashion. Consider a surveillance camera that suddenly outputs corrupted data, where up to 95% of the pixels per frame are corrupted. Real time video completion and correction is often desirable in such scenarios. Therefore, this thesis improves the Tensor-Networked Kalman Filter (TNKF) as presented in [12] by developing the Tensor-Networked Square-Root Kalman Filter (TNSRKF). The TNSRKF is a Square-Root Kalman Filter (SRKF) realized in a Tensor Networks (TN) structure. The square-root Kalman filter is an inherently stable algorithm, and indirectly allows for more information retention throughout the algorithm. Thereby, the filter aims to improve the performance of the TNKF. Furthermore, implementing the filter in TN results in an intuitive implementation of the filter while allowing for larger video dimensions than the widely used matrix format. This thesis concludes that the TNSRKF is too computationally burdensome to complete a video in an online fashion due to the implementation of the Modified Gram-Schmidt (MGS) algorithm in Tensor-Train (TT)-format. In addition, results demonstrate that a low-rank orthogonality matrix is not realizable, making it impractical to update the state covariance matrix via any method that uses an orthonormal matrix.