GSCAD (version 0.1.0)

gscad.DL: Learn dictionary under GSCAD regularization

Description

This function learns the dictionary D under the framework of matrix factorization \(Y=DA\). Y is a given m by n matrix of n samples. D is an m by p matrix, where p is unkonw as well, and A ia a p by n matrix. Both D and A are unkonwn. GSCAD regularization is applied to D and lasso regularization is applied to A.

Usage

gscad.DL(Y, D0 = NULL, p0, sigma = 0, c = 3.7, lambda = 0.05,
  maxrun = 20, maxrun_ADMM = 20, err_bnd = 1e-06, err_bnd2 = 1e-04,
  rho = 16, cor_bnd = 1, L = 30, LassoMode = 1, LassoLambda = NULL)
gscad.DLmask(Y, Mask, D0 = NULL, p0, sigma = 0, c = 3.7, lambda = 0.05,
  maxrun = 20, maxrun_ADMM = 20, err_bnd = 1e-06, err_bnd2 = 1e-06,
  rho = 16, LassoMode = 1, LassoLambda = NULL)

Arguments

Y

An m by n matrix in Y=DA. Each column of Y is a sample of size m (usually a vectorized sqrt(m) by sqrt(m) patches).

D0

Initial dictionary. If D0 specified, p0 is not needed, otherwise D0 is evaluated as overcompleted DCT basis using function ODCT(m,p0). Either D0 or p0 needs to be specified.

p0

Initial size of the dictionary.

sigma

Noise level.

c, lambda

Parameters for GSCAD.

maxrun

(optional) Maximun number of outer iterations to run. Default is 20.

maxrun_ADMM

(optional) Maximun number of iterations to run for updating dictionary using ADMM. Default is 20.

err_bnd

(optional) Stopping criterion for iterations. Default is 1e-6.

err_bnd2

(optional) Stopping criterion for updating dictionary UpDic. Default is 1e-4.

rho

(optional) Parameter for ADMM. Default is 16.

cor_bnd

(optional) When normalize dictionary, checking if the correlation of any two atoms are above the cor_bnd, one of the atom is removed. Default is 1.

L

(optional) This parameter controls the maximum number of non-zero elements in each column of sparsecolding A.

LassoMode

(optional) At the sparse coding stage, the optimization can be done in three modes L1COEFFS (0), L2ERROR (1), PENALTY(2). Default is 1.

LassoLambda

(optional) Tuning parameter for Lasso

Mask

0,1 matrix of the same size as Y to indicate the location of corrupted pixels.

Value

The learned dictionary dictionary

Functions

• gscad.DLmask: Adding Mask 0,1 matrix of the same size as Y to indicate the location of corrupted pixel

Details

See https://arxiv.org/abs/1605.07870

Examples

# NOT RUN {
I = lena_crop #use a smaller image as an example
## add noise
sigma=20;m=64
I_noise=AddNoise(I,sigma)
## spliting image into patches
Y_nc = ImageSplit(I_noise,sqrt(m),sqrt(m));
mu=colMeans(Y_nc)
Y=Y_nc-rep(mu,each=nrow(Y_nc))
## learning dictionary
# }
# NOT RUN {
dictionary=gscad.DL(Y,p0=256,sigma=sigma)
# }
# NOT RUN {
I=lena_crop
## corrupt 30% of the image
out_corrupt=AddHoles(I,0.3)
I_corrupt=out_corrupt$corruptedImage
I_mask=out_corrupt$maskImage
## split image
m=64
Y_nc = ImageSplit(I_corrupt,sqrt(m),sqrt(m));
M = ImageSplit(I_mask,sqrt(m),sqrt(m));
mu=colSums(Y_nc*M)/colSums(M)
Y=Y_nc-M*rep(mu,each=nrow(Y_nc))
mask = matrix(as.logical(M),ncol=ncol(M))
## learn dictionary for inpainting, this function is slow
# }
# NOT RUN {
dic=gscad.DLmask(Y, mask,  p0=100, sigma=1)
# }