Deblurring is the process of removing blurring artifacts from images. Deblurring recovers a sharp image ''S'' from a blurred image ''B'', where ''S'' is convolved with ''K'' (the blur
kernel) to generate ''B''. Mathematically, this can be represented as
(where * represents
convolution
In mathematics (in particular, functional analysis), convolution is a operation (mathematics), mathematical operation on two function (mathematics), functions f and g that produces a third function f*g, as the integral of the product of the two ...
).
While this process is sometimes known as ''unblurring'', ''deblurring'' is the correct technical word.
The blur K is typically modeled as
point spread function
The point spread function (PSF) describes the response of a focused optical imaging system to a point source or point object. A more general term for the PSF is the system's impulse response; the PSF is the impulse response or impulse response ...
and is
convolved with a hypothetical sharp image ''S'' to get ''B'', where both the ''S'' (which is to be recovered) and the point spread function ''K'' are unknown. This is an example of an
inverse problem
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, sound source reconstruction, source reconstruction in ac ...
. In almost all cases, there is insufficient information in the blurred image to uniquely determine a plausible original image, making it an
ill-posed problem. In addition the blurred image contains additional noise which complicates the task of determining the original image. This is generally solved by the use of a
regularization term to attempt to eliminate implausible solutions. This problem is analogous to
echo removal in the signal processing domain. Nevertheless, when coherent beam is used for imaging, the
point spread function
The point spread function (PSF) describes the response of a focused optical imaging system to a point source or point object. A more general term for the PSF is the system's impulse response; the PSF is the impulse response or impulse response ...
can be modeled mathematically.
By proper
deconvolution of the
point spread function
The point spread function (PSF) describes the response of a focused optical imaging system to a point source or point object. A more general term for the PSF is the system's impulse response; the PSF is the impulse response or impulse response ...
''K'' and the blurred image ''B'', the blurred image ''B'' can be deblurred (unblur) and the sharp image ''S'' can be recovered.
See also
*
Denoising
*
Super-resolution
*
Blind deconvolution
*
Modulation transfer function
References
Image processing
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