  The inverse renormalization group is studied based on the image
super-resolution using the deep convolutional neural networks. We consider the
improved correlation configuration instead of spin configuration for the spin
models, such as the two-dimensional Ising and three-state Potts models. We
propose a block-cluster transformation as an alternative to the block-spin
transformation in dealing with the improved estimators. In the framework of the
dual Monte Carlo algorithm, the block-cluster transformation is regarded as a
transformation in the graph degrees of freedom, whereas the block-spin
transformation is that in the spin degrees of freedom. We demonstrate that the
renormalized improved correlation configuration successfully reproduces the
original configuration at all the temperatures by the super-resolution scheme.
Using the rule of enlargement, we repeatedly make inverse renormalization
procedure to generate larger correlation configurations. To connect
thermodynamics, an approximate temperature rescaling is discussed. The enlarged
systems generated using the super-resolution satisfy the finite-size scaling.
