Sparse tensor recovery via combined first and second order high-accuracy total variation

The conventional numerical approaches in wide range of restoration problems encode either first or second order total variation (TV) using low accuracy FIR filters, i.e. [-1, 1] and [1, -2, 1]. This leads to inappropriate feature estimation of high-frequency components in an underlying signal for reconstruction. We introduce high-order-of-accuracy (HOA) numerical differentiation to encode such features in combined first and second order TV regularization. In particular we design appropriate gradient and hessian operators embedded with HOA filters to incorporate in combined regularizers. We seek the solution to the combined approach using the alternating direction methods of multipliers minimization algorithm to reconstruct three dimensional sparse tensors. Particular application of this combined regularizer is studied over compressed video sensing problem. Numerical experiments state significantly better recoveries over consecutive frames from their compressed measurements.