Accelerating cross-validation with total variation and its application to super-resolution imaging

Abstract

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.

14 pages, 4 figures. A Matlab package implementing the approximation formula is available from https://github.com/T-Obuchi/AcceleratedCVon2DTVLR

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• High Resolution Linear Polarimetric Imaging for the Event Horizon Telescope
• Imaging the Schwarzschild-radius-scale Structure of M87 with the Event Horizon Telescope using Sparse Modeling
• 230 GHz VLBI observations of M87: event-horizon-scale structure at the enhanced very-high-energy $\gamma$-ray state in 2012
• Super-resolution Full Polarimetric Imaging for Radio Interferometry with Sparse Modeling
• Herschel/HIFI Spectral Mapping of C${}^{+}$, CH${}^{+}$, and CH in Orion BN/KL: The Prevailing Role of Ultraviolet Irradiation in CH${}^{+}$ Formation
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Cited by in corpus (6)

• Imaging the Schwarzschild-radius-scale Structure of M87 with the Event Horizon Telescope using Sparse Modeling
• Super-resolution Full Polarimetric Imaging for Radio Interferometry with Sparse Modeling
• Superresolution Interferometric Imaging with Sparse Modeling Using Total Squared Variation --- Application to Imaging the Black Hole Shadow
• The Evolving Radio Photospheres of Long-Period Variable Stars
• Super-resolution Imaging of the Protoplanetary Disk HD 142527 Using Sparse Modeling
• Accelerating Cross-Validation in Multinomial Logistic Regression with ${\ell }_1$-Regularization