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2-D adaptive noise-removal filtering

**The syntax wiener2(I,[m n],[mblock nblock],noise) has
been removed. Use the wiener2(I,[m n],noise) syntax
instead.**

`J = wiener2(I,[m n],noise)`

[J,noise] = wiener2(I,[m n])

`wiener2`

lowpass-filters a grayscale image
that has been degraded by constant power additive noise. `wiener2`

uses
a pixelwise adaptive Wiener method based on statistics estimated from
a local neighborhood of each pixel.

`J = wiener2(I,[m n],noise)`

filters
the image `I`

using pixelwise adaptive Wiener filtering,
using neighborhoods of size `m`

-by-`n`

to
estimate the local image mean and standard deviation. If you omit
the `[m n]`

argument, `m`

and `n`

default
to 3. The additive noise (Gaussian white noise) power is assumed to
be `noise`

.

`[J,noise] = wiener2(I,[m n])`

also
estimates the additive noise power before doing the filtering. `wiener2`

returns
this estimate in `noise`

.

The input image `I`

is a two-dimensional image
of class `uint8`

, `uint16`

, `int16`

, `single`

,
or `double`

. The output image `J`

is
of the same size and class as `I`

.

`wiener2`

estimates the local mean and variance
around each pixel.

$$\mu =\frac{1}{NM}{\displaystyle \sum _{{n}_{1},{n}_{2}\in \eta}a({n}_{1},{n}_{2})}$$

and

$${\sigma}^{2}=\frac{1}{NM}{\displaystyle \sum _{{n}_{1},{n}_{2}\in \eta}{a}^{2}({n}_{1},{n}_{2})-{\mu}^{2}},$$

where $$\eta $$ is the *N*-by-*M* local
neighborhood of each pixel in the image `A`

. `wiener2`

then
creates a pixelwise Wiener filter using these estimates,

$$b({n}_{1},{n}_{2})=\mu +\frac{{\sigma}^{2}-{\nu}^{2}}{{\sigma}^{2}}(a({n}_{1},{n}_{2})-\mu ),$$

where ν^{2} is the noise variance.
If the noise variance is not given, `wiener2`

uses
the average of all the local estimated variances.

[1] Lim, Jae S., *Two-Dimensional Signal and Image
Processing*, Englewood Cliffs, NJ, Prentice Hall, 1990,
p. 548, equations 9.26, 9.27, and 9.29.

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