ImageRestore

ImageRestore [/Z /ITER=iterations /DEST=destWave] srcWave=wSrc , psfWave=wPSF [, relaxationGamma=h , startingImage=wRecon ]

The ImageRestore operation performs the Richardson-Lucy iterative image restoration.

Parameters

psfWave=wPSF	Specifies a known point spread function. wPSF must be a 2D (square NxN) wave of the same numeric type as wSRC . N must be an odd number greater than 1.
relaxationGamma=h
	Specifies positive power gamma of in the relaxation mapping (see Details).
startingImage=wRecon
	Use this keyword to specify a starting image that could be for example the output from a previous call to this operation. wRecon must have the same dimensions as wSRC and the same numeric type.
	You must make sure that wRecon is not the user-specified or the default destination wave of the operation.
srcWave=wSrc
	Specifies the degraded image which must be a 2D single-precision or double-precision real wave.

Flags

/DEST=destWave	Specifies the desired output wave.
	If /DEST is omitted, the output from the operation is stored in the wave M_Reconstructed in the current data folder.
/FREE	Creates destWave as a free wave.
	/FREE is allowed only in functions and only if the destination wave names are simple names or wave reference structure fields.
	See Free Waves for more discussion.
	The /FREE flag was added in Igor Pro 10.00.
/ITER=iterations	Specifies the number of iterations. The default number of iterations is 100.
/Z	Do not report errors.

Details

ImageRestore performs the Richardson-Lucy iteration solution to the deconvolution of an image. The input consists of the degraded image and point spread function as well as the desired number of iterations.

The operation allows you to apply additional iterations by setting the starting image to the restored output wave from a previous call to ImageRestore using the startingImage keyword. If startingImage is omitted, the starting image is created by ImageRestore with each pixel set to the value 1.

In the case of stellar images it may be useful to apply a relaxation step that involves scaling the correction evaluated at each iteration by

$$\displaystyle \operatorname{factor}(v)=\sin \left(\frac{\pi}{2} \frac{v-v_{\min }}{v_{\max }-v_{\min }}\right)^{\gamma},$$

where v is pixel value, vmax and vmin are the maximum and minimum level pixels in the image, and gamma is the user-specified relaxationGamma.

References

W.H. Richardson, "Bayesian-Based Iterative Method of Image Restoration". JOSA 62 (1) : 55–59, 1972.

L.B. Lucy, "An iterative technique for the rectification of observed distributions", Astronomical Journal 79, 6 : 745–754, 1974.