The Self-Deconvolving Data Restoration Algorithm, or SeDDaRA, was developed to quickly and effectively remove degradations such as focus and motion from digital images. The algorithm does so in the presence of noise, without knowledge of the form of degradation or imaging system (which makes it a Blind Deconvolution technique), and with limited user input. The entire operation can be performed in less than a couple of seconds on a typical computer.

Thus far, the technique has been applied to personal photography, space-based imagery, medical x-rays, ultrasonic waveforms, and recorded sound. The algorithm works on any signal that has been subject to some form of low-pass degradation. 

Recently,  we launched our initiative to investigate in more detail the use of SeDDaRA on audio-frequency sound.  Potential applications include enhancing hearing aids, sound systems, and telephones.  You can view our progress at SeDDaRA Sound .

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An image of  a southwestern mountain with synthetic blur added.   The blur was removed from the image using the SeDDaRA process (as shown when you pass your mouse over the image).

How does it work? In a nutshell, the degradation is extracted from the degraded image through a series of mathematical operations. The degradation is then used to 'clean up' the data. This algorithm does not create information that is not buried in the image. Thus, a blurry image with a low signal-to-noise level dose not reconstruct well. This also applies to highly compressed jpeg images. However, if there is information there to retrieve, this process will retrieve it, without artifacts. More examples can be viewed in the Gallery .

SeDDaRA is a non-iterative method.  It takes only one application to produce the result.  This is the main advantage over the more common iterative methods.  There is a prevailing notion that the more processing you apply to an image, the more you can restore.  Hollywood reflected this idea on the TV show "Numb3rs".   In the show, a physicist/mathematician helps his detective brother solve murders in similar fashion to CSI.  In one episode,  the main characters were using some iterative technique to restore a security video.  The detective was skeptical that it would work, but the Physicist assured him that "There is almost no limit to how much you can enhance an image."  I bursted out laughing!  I think a more accurate statement is "There is almost no limit to how much you can process an image."  How well you enhance the image is different question.  SeDDaRA can identify and remove very complicated blur functions as well, if not better than iterative methods, and do so on a much shorter time frame.

An image of the Eye of Jupiter	A restoration of the image using the SeDDaRA process.

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For further information, you can read the news article in the November 2001 issue of LaserFocus World, or see the articles in Optics Letters and Applied Optics. References can be found in Research. Research performed since then has found that the algorithm described in these articles is actually an approximation of the full theory. The approximation theory has since been designated the 'Caron' filter. Full application of the theory produces superior results with some additional processing. This paper was published in Applied Optics in November 2002.

You can also read more about blind deconvolutions here.  A discussion on the differences between image restoration and image enhancement is here.