High-Accuracy Total Variation With Application to Compressed Video Sensing

Numerous total variation (TV) regularizers, engaged in image restoration problem, encode the gradients by means of simple [-1, 1] finite-impulse-response (FIR) filter. Despite its low computational processing, this filter severely distorts 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 undersampled 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.