  This paper is concerned with the problem of recovering third-order tensor
data from limited samples. A recently proposed tensor decomposition (BMD)
method has been shown to efficiently compress third-order spatiotemporal data.
Using the BMD, we formulate a slicewise nuclear norm penalized algorithm to
recover a third-order tensor from limited observed samples. We develop an
efficient alternating direction method of multipliers (ADMM) scheme to solve
the resulting minimization problem. Experimental results on real data show our
method to give reconstruction comparable to those of HaLRTC (Liu et al., IEEE
Trans Ptrn Anal Mchn Int, 2012), a well-known tensor completion method, in
about the same number of iterations. However, our method has the advantage of
smaller subproblems and higher parallelizability per iteration.
