[SciPy-User] deconvolution of 1-D signals

Charles R Harris charlesr.harris@gmail....
Mon Aug 1 09:14:13 CDT 2011


On Sun, Jul 31, 2011 at 11:20 PM, Anne Archibald <aarchiba@physics.mcgill.ca
> wrote:

> I realize this discussion has gone rather far afield from efficient 1D
> deconvolution, but we do a funny thing in radio interferometry, and
> I'm curious whether this is normal for other kinds of deconvolution as
> well.
>
> In radio interferometry we obtain our images convolved with the
> so-called "dirty beam", a convolution kernel that has a nice narrow
> peak but usually a chaos of monstrous sidelobes often only marginally
> smaller than the main lobe. We use a different regularization
> condition to do our deconvolution: we treat the underlying image as a
> modest collection of point sources. (One can see why this appeals to
> astronomers.) Through an iterative process (the "CLEAN" algorithm and
> its many descendants) we obtain an estimate of this underlying image.
> But we very rarely actually work with this image directly. We normally
> convolve it with a sort of idealized version of our kernel without all
> the sidelobes. This then gives an image one might have obtained from a
> normal telescope the size of the interferometer array. (Apart from all
> the CLEAN artifacts.)
>
> What I'm wondering is, is this final step of convolving with an
> idealized version of the kernel standard practice elsewhere?
>
>
That's interesting. It sounds like fitting a parametric model, which yields
points, followed by a smoothing that in some sense represents the error. Are
there frequency aliasing problems associated with the deconvolution?

<snip>

Chuck
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