  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.
