  A common approach for performing sparse tensor recovery is to use an N-mode
FISTA method. However, this approach may fail in some cases by missing some
values in the true support of the tensor and compensating by erroneously
assigning nearby values to the support. This work proposes a four-stage method
for performing sparse tensor reconstruction that addresses a case where N-mode
FISTA may fail by augmenting the support set. Moreover, the proposed method
preserves a Tucker-like structure throughout computations for computational
efficiency. Numerical results on synthetic data demonstrate that the proposed
method produces results with similar or higher accuracy than N-mode FISTA, and
is often faster.
