Accelerating cross-validation with total variation and its application
  to super-resolution imaging
  We develop an approximation formula for the cross-validation error (CVE) of a
sparse linear regression penalized by $\ell_1$-norm and total variation terms,
which is based on a perturbative expansion utilizing the largeness of both the
data dimensionality and the model. The developed formula allows us to reduce
the necessary computational cost of the CVE evaluation significantly. The
practicality of the formula is tested through application to simulated
black-hole image reconstruction on the event-horizon scale with super
resolution. The results demonstrate that our approximation reproduces the CVE
values obtained via literally conducted cross-validation with reasonably good
precision.
