  Recovery algorithms play a key role in compressive sampling (CS). Most of
current CS recovery algorithms are originally designed for one-dimensional (1D)
signal, while many practical signals are two-dimensional (2D). By utilizing 2D
separable sampling, 2D signal recovery problem can be converted into 1D signal
recovery problem so that ordinary 1D recovery algorithms, e.g. orthogonal
matching pursuit (OMP), can be applied directly. However, even with 2D
separable sampling, the memory usage and complexity at the decoder is still
high. This paper develops a novel recovery algorithm called 2D-OMP, which is an
extension of 1D-OMP. In the 2D-OMP, each atom in the dictionary is a matrix. At
each iteration, the decoder projects the sample matrix onto 2D atoms to select
the best matched atom, and then renews the weights for all the already selected
atoms via the least squares. We show that 2D-OMP is in fact equivalent to
1D-OMP, but it reduces recovery complexity and memory usage significantly.
What's more important, by utilizing the same methodology used in this paper,
one can even obtain higher dimensional OMP (say 3D-OMP, etc.) with ease.
