The existing single depth image super-resolution (SR)
methods suppose that the image to be interpolated is noise
free. However, the supposition is invalid in practice because
noise will be inevitably introduced in the depth image acquisition
process. In this paper, we address the problem of image
denoising and SR jointly based on designing sparse graphs
that are useful for describing the geometric structures of data
domains. In our method, we first cluster similar patches in a
noisy depth image and compute an average patch. Different
from the majority of the graph Fourier transform (GFT) that
assumed an underlying 4-connected graph structure with vertical
and horizontal edges only, we select more general sparse
graph structures and edges weights based on the difference of
the blocks’ structure tensors. For the average patch, a graph
template with edges orthogonal to the principal gradient is designed.
Finally, the graph based transform (GBT) dictionary
is learned from the derived correlation graph for signal representation.
As shown in our experimental results, the proposed
method obtains a lot of improvement in performance.