Denoise an Image via the 2D Discrete Wavelet Transform

Perform simple de-noising of an image using the two-dimensional discrete wavelet transform.

denoise.dwt.2d(x, wf = "la8", J = 4, method = "universal", H = 0.5, 
               noise.dir = 3, rule = "hard")
denoise.modwt.2d(x, wf = "la8", J = 4, method = "universal", H = 0.5, 
                 rule = "hard")

Arguments

x	input matrix (image)
wf	name of the wavelet filter to use in the decomposition
J	depth of the decomposition, must be a number less than or equal to \(\log_2(\min\{M,N\})\)
method	character string describing the threshold applied, only "universal" and "long-memory" are currently implemented
H	self-similarity or Hurst parameter to indicate spectral scaling, white noise is 0.5
noise.dir	number of directions to estimate background noise standard deviation, the default is 3 which produces a unique estimate of the background noise for each spatial direction
rule	either a "hard" or "soft" thresholding rule may be used

Value

Image of the same dimension as the original but with high-freqency fluctuations removed.

Details

See Thresholding.

References

See Thresholding for references concerning de-noising in one dimension.

See also

Thresholding

Author

B. Whitcher

Examples

## Xbox image
data(xbox)
n <- NROW(xbox)
xbox.noise <- xbox + matrix(rnorm(n*n, sd=.15), n, n)
par(mfrow=c(2,2), cex=.8, pty="s")
image(xbox.noise, col=rainbow(128), main="Original Image")
image(denoise.dwt.2d(xbox.noise, wf="haar"), col=rainbow(128),
      zlim=range(xbox.noise), main="Denoised image")
image(xbox.noise - denoise.dwt.2d(xbox.noise, wf="haar"), col=rainbow(128),
      zlim=range(xbox.noise), main="Residual image")

## Daubechies image
data(dau)
n <- NROW(dau)
dau.noise <- dau + matrix(rnorm(n*n, sd=10), n, n)
par(mfrow=c(2,2), cex=.8, pty="s")

image(dau.noise, col=rainbow(128), main="Original Image")
dau.denoise <- denoise.modwt.2d(dau.noise, wf="d4", rule="soft")
image(dau.denoise, col=rainbow(128), zlim=range(dau.noise),
      main="Denoised image")
image(dau.noise - dau.denoise, col=rainbow(128), main="Residual image")