tvR (version 0.3.3)

denoise2: Total Variation Denoising for Image

Description

Given an image f, it solves an optimization of the form, $$u^* = argmin_u E(u,f)+\lambda V(u)$$ where \(E(u,f)\) is fidelity term and \(V(u)\) is total variation regularization term. The naming convention of a parameter method is <problem type> + <name of algorithm>. For more details, see the section below.

Usage

denoise2(
  data,
  lambda = 1,
  niter = 100,
  method = c("TVL1.PrimalDual", "TVL2.PrimalDual", "TVL2.FiniteDifference"),
  normalize = FALSE
)

Value

denoised array as same size of data.

Arguments

data

standard 2d or 3d array.

lambda

regularization parameter (positive real number).

niter

total number of iterations.

method

indicating problem and algorithm combination.

normalize

a logical; TRUE to make the range in \([0,1]\), or FALSE otherwise.

Data format

An input data can be either (1) 2-dimensional matrix representaing grayscale image, or (2) 3-dimensional array for color image.

Algorithms for TV-L1 problem

The cost function for TV-L2 problem is $$min_u |u-f|_1 + \lambda |\nabla u|$$ where for a given 2-dimensional array, \(|\nabla u| = \sum sqrt(u_x^2 + u_y^2)\) Algorithms (in conjunction with model type) for this problems are

"TVL1.PrimalDual"

Primal-Dual algorithm.

Algorithms for TV-L2 problem

The cost function for TV-L2 problem is $$min_u |u-f|_2^2 + \lambda |\nabla u|$$ and algorithms (in conjunction with model type) for this problems are

"TVL2.PrimalDual"

Primal-Dual algorithm.

"TVL2.FiniteDifference"

Finite Difference scheme with fixed point iteration.

References

rudin_nonlinear_1992tvR

chambolle_first-order_2011tvR

Examples

if (FALSE) {
## Load grey-scale 'lena' data
data(lena128)

## Add white noise
sinfo   <- dim(lena128)   # get the size information
xnoised <- lena128 + array(rnorm(128*128, sd=10), sinfo)

## apply denoising models
xproc1 <- denoise2(xnoised, lambda=10, method="TVL2.FiniteDifference")
xproc2 <- denoise2(xnoised, lambda=10, method="TVL1.PrimalDual")

## compare
gcol = gray(0:256/256)
opar <- par(no.readonly=TRUE)
par(mfrow=c(2,2), pty="s")
image(lena128, main="original", col=gcol)
image(xnoised, main="noised", col=gcol)
image(xproc1, main="TVL2.FiniteDifference", col=gcol)
image(xproc2, main="TVL1.PrimalDual", col=gcol)
par(opar)
}