I have an optical sensor that produces 2D images. The sensor has been characterized in the lab, and the point spread function is known with subpixel resolution. i.e. it has been measured with 1/10 resolution than the image provided. What can I do to deconvolve, since all the algorithms I know of make use of a PSF of the same resolution than the image. My first guess was to interpolate the image, but it would introduce artifacts. Surely there is a smarter way to achieve this.
If you have the variogram of the image at a given resolution you can deconvolve it to get the PUNCTUAL VARIOGRAM..which then will help you to produce the image at any intermediate resolution....if you have the sensor PSF at subpixel then you can evaluate the accuracy of your punctual variogram and the ways to achieve the best punctual variogram....Your data would be very useful...I and Professor Peter Atkinson at the University of Southampton were working on this problem..can you please contact him (you can easily find him in google search)...
Luis,
I have no experience with the PSF so I don't know, whether a resampling of the PSF is doable (anyway, this would reduce resolution). But thinking of the image it is possible to resample it without introducing artifacts other than the +-0.5 LSB rounding error inherent with all mathematical operations.
Deconvolution of noisy signals always involves a trade-off between removal of convolution and noise amplification. In addition, here you need to interpolate anyway, because otherwise the more accurate PSF cannot provide any extra information.
Choose a factor n, preferably in {1,2,5,10}, say n = 5. Decimate the PSF by n:1 and upsample the image by 1:(10/n). Depending on the SNR and degree of non-linearity, it might be sufficient to do this in a simple way. For example take the average of 5x5 PSF samples and repeat each image sample 2x2.
Now the decimated PSF and upsampled image are at the same sample frequency, so we can calculate meaningful (de-)convolutions. A simple method for deconvolution is "van Cittert's algorithm," which is an iterative inversion of the PSF, using 1/(1 - x) = 1 + x + x^2 + ... The number of iterations gives you a single parameter controlling the trade-off. (Have a look at the images in http://de.wikipedia.org/wiki/Van-Cittert-Dekonvolution).
There are better ways to decimate, upsample and deconvolve. (For a start, refer to
http://en.wikipedia.org/wiki/Decimation_(signal_processing) and
http://en.wikipedia.org/wiki/Upsampling.) If this results in a useful improvement in quality or not depends on a number of aspects, in particular the measure of quality in your application, the SNR, the non-linearities and the availability of a quantitative noise model.
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