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AcceleratedCVon2DTVLR

Approximate cross-validation for linear regression penalized by terms of L1 and two-dimensional total variation.

This is free software, you can redistribute it and/or modify it under the terms of the GNU General Public License, version 3 or above. See LICENSE.txt for details.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

DESCRIPTION

Using the estimated explanatory variables x given the measument matrix A and the measurement result y, this program computes and returns an approximate leave-one-out error (LOOE) and its standard error for linear regression penalized by L1 norm and two-dimensional total variation (TV).

USAGE

   [LOOE,ERR] = LOOEapprox_2DTV(x,y,A,Nx,Ny,lambda_T,delta,theta)

Inputs:

  • x: Estimated explanatory variables (N=Nx*Ny dimensional vector). A two-dimensional (2D) image is expected in common cases.
  • y: Measurement result (M dimensional vector)
  • A: Measurement matrix (M*N dimensional matrix)
  • Nx: One side length of x in 2D.
  • Ny: Another side length of x in 2D.
  • lambda_T: Regularization weight of TV
  • delta: Softening constant of TV. Default value is 10^(-4).
  • theta: Threshold to determine clusters induced by TV. Default value is 10^(-12).

Outputs:

  • LOOE: Approximate value of the leave-one-out error
  • ERR: Approximate standard error of the leave-one-out error

For more details, type help LOOEapprox_2DTV.

REFERENCE

Tomoyuki Obuchi, Shiro Ikeda, Kazunori Akiyama, and Yoshiyuki Kabashima: "Accelerating cross-validation with total variation and its application to super-resolution imaging", arXiv: 1611.07197