High-Accuracy Total Variation for Compressed Video Sensing

TL;DR

This paper introduces a high-order accuracy differential FIR filter-based total variation model for compressed video sensing, significantly improving edge preservation and reducing texture loss compared to traditional methods.

Contribution

It proposes a novel high-order differential FIR filter approach for TV regularization, extending it to multidimensional tensorial representation for better video frame recovery.

Findings

Outperforms state-of-the-art methods in accuracy and visual quality

Achieves high-quality recovery at lower sampling rates

Handles various boundary conditions effectively

Abstract

Numerous total variation (TV) regularizers, engaged in image restoration problem, encode the gradients by means of simple $[-1,1]$ FIR filter. Despite its low computational processing, this filter severely deviates signal's high frequency components pertinent to edge/discontinuous information and cause several deficiency issues known as texture and geometric loss. This paper addresses this problem by proposing an alternative model to the TV regularization problem via high order accuracy differential FIR filters to preserve rapid transitions in signal recovery. A numerical encoding scheme is designed to extend the TV model into multidimensional representation (tensorial decomposition). We adopt this design to regulate the spatial and temporal redundancy in compressed video sensing problem to jointly recover frames from under-sampled measurements. We then seek the solution via alternating direction methods of multipliers and find a unique solution to quadratic minimization step with capability of handling different boundary conditions. The resulting algorithm uses much lower sampling rate and highly outperforms alternative state-of-the-art methods. This is evaluated both in terms of restoration accuracy and visual quality of the recovered frames.