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Deblur image using Lucy-Richardson method

`J = deconvlucy(I, PSF)`

J = deconvlucy(I, PSF, NUMIT)

J = deconvlucy(I, PSF, NUMIT, DAMPAR)

J = deconvlucy(I, PSF, NUMIT, DAMPAR,
WEIGHT)

J = deconvlucy(I, PSF, NUMIT, DAMPAR,
WEIGHT, READOUT)

J = deconvlucy(I, PSF, NUMIT, DAMPAR,
WEIGHT, READOUT, SUBSMPL)

`J = deconvlucy(I, PSF)`

restores
image `I`

that was degraded by convolution with a
point-spread function `PSF`

and possibly by additive
noise. The algorithm is based on maximizing the likelihood of the
resulting image `J`

'`s`

being an
instance of the original image `I`

under Poisson
statistics.

`I`

can be a N-dimensional array.

To improve the restoration, `deconvlucy`

supports
several optional parameters. Use `[]`

as a placeholder
if you do not specify an intermediate parameter.

`J = deconvlucy(I, PSF, NUMIT)`

specifies
the number of iterations the `deconvlucy`

function
performs. If this value is not specified, the default is 10.

`J = deconvlucy(I, PSF, NUMIT, DAMPAR)`

specifies
the threshold deviation of the resulting image from the image `I`

(in
terms of the standard deviation of Poisson noise) below which damping
occurs. Iterations are suppressed for pixels that deviate beyond the `DAMPAR`

value
from their original value. This suppresses the noise generation in
such pixels, preserving necessary image details elsewhere. The default
value is 0 (no damping).

```
J = deconvlucy(I, PSF, NUMIT, DAMPAR,
WEIGHT)
```

specifies the weight to be assigned to each pixel
to reflect its recording quality in the camera. A bad pixel is excluded
from the solution by assigning it zero weight value. Instead of giving
a weight of unity for good pixels, you can adjust their weight according
to the amount of flat-field correction. The default is a unit array
of the same size as input image `I`

.

```
J = deconvlucy(I, PSF, NUMIT, DAMPAR,
WEIGHT, READOUT)
```

specifies a value corresponding to the
additive noise (e.g., background, foreground noise) and the variance
of the readout camera noise. `READOUT`

has to be
in the units of the image. The default value is 0.

```
J = deconvlucy(I, PSF, NUMIT, DAMPAR,
WEIGHT, READOUT, SUBSMPL)
```

, where `SUBSMPL`

denotes
subsampling and is used when the `PSF`

is given on
a grid that is `SUBSMPL`

times finer than the image.
The default value is 1.

The output image `J`

could exhibit ringing
introduced by the discrete Fourier transform used in the algorithm.
To reduce the ringing, use `I = edgetaper(I,PSF)`

before
calling `deconvlucy`

.

If `I`

is a cell array, it can contain a single
numerical array (the blurred image) or it can be the output from
a previous run of `deconvlucy`

.

When you pass a cell array to `deconvlucy`

as
input, it returns a 1-by-4 cell array `J`

, where

`J{1}`

contains `I`

, the original
image.

`J{2}`

contains the result of the last iteration.

`J{3}`

contains the result of the next-to-last
iteration.

`J{4}`

is an array generated by the iterative
algorithm.

`I`

can be `uint8`

, `uint16`

, `int16`

, `double`

,
or `single`

. `PSF`

can be `uint8`

, `uint16`

, `int16`

, `double`

,
or `single`

. Note, however, that `deconvlucy`

converts
the PSF to `double`

without normalization. `DAMPAR`

and `READOUT`

must
have the same class as the input image. Other inputs have to be `double`

.
The output image `J`

(or the first array of the output
cell) has the same class as the input image `I`

.

[1] Biggs, D.S.C. “Acceleration of
Iterative Image Restoration Algorithms.” *Applied
Optics*. Vol. 36. Number 8, 1997, pp. 1766–1775.

[2] Hanisch, R.J., R.L. White, and R.L. Gilliland.
“Deconvolution of Hubble Space Telescope Images and Spectra.” *Deconvolution
of Images and Spectra* (P.A. Jansson, ed.). Boston, MA:
Academic Press, 1997, pp. 310–356.

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