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Math to Crack Deep Impact Blurry Vision Problem
starexplorer writes "NASA announced that they believe they have a solution for the Deep Impact mission's blurry vision problem: math. Although the craft will still snap blurry pictures of the Tempel-1 comet, mathmetical manipulation will help scientists clear up the images once they make their way back to Earth. A special report and viewing guide are also available at SPACE.com."
it's a process called deconvolution, right? I did this as a project for sophomore year astronomy... which i believe involved asking on slashdot about it.
The early Hubble pictures suffered from optical distortion due to a miscalculation on what the shape of the mirror would be in obit, and NASA also fixed that problem using digital image filtering techniques to reconstruct a clear image. The key was that they had a precise model of the distortion and that it was invertible.
No, the parent is correct. Before the COSTAR correctional optics package was launched to fix Hubble's spherical aberation problem, NASA engineers were able to digitally de-convolve the aberations out of the image. The digitally-manipulated results weren't as good as the ones COSTAR optics eventually offered, but they did help some initial observing runs.
make world, not war
http://www.cs.brown.edu/exploratories/freeSoftware /repository/edu/brown/cs/exploratories/applets/con volution/convolution_guide.html
"The key operation we perform, both in the theoretical development and in the implementation of filtering, is convolution. This applet allows students to understand the process of convolution. First they create a signal and a filter function to convolve. Then, they place the filter function when they see the product function of the two original signals. In a final graph below, they build up the convolution, seeing the area under the product curve correspond to the value of the convolution at that point.
This applet is useful in understanding both how convolution works and what the effects are of specific signals being convolved together."
Deconvolution.
FTFA: The team will use a process, called deconvolution, to remedy the situation. Deconvolution is widely used in image processing and involves the reversal of the distortion created by the faulty lens of a camera or other optical devices, like a telescope or microscope.
yeah. but they never got a very good set of kernels. because of the nature of the flaw(s), the psfs varied across the image and didn't do so continuously. they got part of the way there, but it was never even close. if only there had been a decent test pattern set lying around in space.
actually it wasn't just NASA engineers. they had an open call for help, and alot of people worked on the problem. which was very cool.
All right, I know I shouldn't be replying to flamebait but here goes.
e w/motiondeblur.html/
It is in fact possible to at least partially reconstruct blurry images as long as you have some idea about what kind of distortion or motion is causing your problems. In some cases you can get useable information without even knowing exactly what your problem was! Don't take my word for it, look up "blind deconvolution" in your favorite image processing textbook or just use google.
If you're an IEEE member there is an interesting tutorial entitled "Image Deblurring: I Can See Clearly Now" by James Nagy and Dianne O'Leary. In addition to this a real world applications in motion deblurring can be seen here http://www1.cs.columbia.edu/CAVE/research/demos/n
The problem may not be identical to NASA's problem but the mathematical deconvolution techniques are the same.
I realize you just want some attention but a small sense of disbelief is in order since many new developments in the sciences are pretty indistinguishable from magic at first glance.
"The table-sized, 820-pound (372-kilogram) impactor is scheduled to smash into the comet's nucleus at 23,000 mph (37,000 kilometers) per hour"
Actually, that comes out to be about 2.8 m/s^2, or less than one third of a gee.
PS: As others pointed out, deconvolution (which is the process used here) is not a new concept. Far from it, in fact.
Imagine an out-of-focus picture of a point of light. The image will be a fuzzy circle or ring (the latter if the lens is catadioptric).
Now take a picture of an entire scene, this time in focus. If you convolve (mathematical process related to multiplication) the first fuzzy image with this sharp image, you would get an image that looks like you had taken the picture through the original fuzzy lens. It's as if every single pixel in the good image were smudged into an pattern like the first image. The fuzzy circle from the first image is called the convolution kernel.
The corollary of this is, if you use the inverse of the convolution process (deconvolution) on an image taken with the out-of-focus lens, and using the fuzzy circle image as the kernel for the deconvolution, you would get a sharp image.
The trick is that you need to know the correct deconvolution kernel. But for that you only need to photograph a point source (such as a star).
But, I wanted socialized health insurance!
I'm not sure if it was a photoshop plugin or a standalone filter, but the filter was able to derive sharp pictures from the bokeh of photographs. ...and it's really not all that breakthrough-ish. Nearly anyone who's taken a signal processing class will have done this. The simplest version is an unsharp mask.
:)
Here's the basic idea: you assume some "spreading" of the data happened, and you assume its shape. Then you try to undo what happened - perform the inverse.
There are two problems with this. First, the original convolution you assumed (that "spreading") is destructive to information. There exists no unique inverse mapping. You have to pick one, and hope that what it yields looks right.
Second, without making some major assumptions (that signal processing people aren't usually keen to make) there is no way to differentiate between true signal and noise. The noise, along with the blurry edges, also get sharpened. You can mitigate this somewhat with your choice of inverse mapping. Again, you pick something that looks right.
They do have some prior information going into this - they know the equipment that took the pictures - but pretty much nothing they do will exactly restore the information that was lost. Math isn't magical enough to do that.
For the hardcore:
http://mathworld.wolfram.com/Deconvolution.html
and follow the links from there.
I got my Linux laptop at System76.
If you can esitmate the blur, or let's say, the point spread function (PSF) of the blur, deconvolution is the application of the inverse of the said blur.
This is not always a simple operation. Most real world blur PSFs will not be invertible, or easily so, and the inverse operation will be unstable (lead to "blowing up" of teh function). Conditioning may solve some suc problems.
Iterative techniques are useful in many cases and there are many varied different techniques to do this.
Wiener filters are commonly used. A bunch of adaptive techniques based on Wiener filtering concepts are very effective too.
-mp-
You can try this at home with the Gimp: Refocus.
-- Ed Avis ed@membled.com
You know in films when they get a really burry satellite image, and some hero guy goes "can we enhaance thaaat?". So some geek clicks a button and it goes a lot sharper, and you're thinking, "if only that worked in real life". Well it does and you can try it yourself. Here is some free software that allows you to have a play and "enhance" all those blurry pics you have lying around.
I've tried this myself and it works quite well. I tried it on a picture I took of the moon with a 400mm lens and it made quite an impressive difference.