Deblurring on:
[Wikipedia]
[Google]
[Amazon]
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
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
Kernel may refer to:
Computing
* Kernel (operating system), the central component of most operating systems
* Kernel (image processing), a matrix used for image convolution
* Compute kernel, in GPGPU programming
* Kernel method, in machine learn ...
) to generate ''B''. Mathematically, this can be represented as (where * represents convolution
In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions ( and ) that produces a third function (f*g) that expresses how the shape of one is modified by the other. The term ''convolution'' ...
).
While this process is sometimes known as ''unblurring'', ''deblurring'' is the correct technical word.
The blur K is typically modeled as point spread function and is convolved
In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions ( and ) that produces a third function (f*g) that expresses how the shape of one is modified by the other. The term ''convolution'' ...
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, source reconstruction in acoustics, or calculating the ...
. 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
The mathematical term well-posed problem stems from a definition given by 20th-century French mathematician Jacques Hadamard. He believed that mathematical models of physical phenomena should have the properties that:
# a solution exists,
# the sol ...
. 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
Regularization may refer to:
* Regularization (linguistics)
* Regularization (mathematics)
* Regularization (physics)
In physics, especially quantum field theory, regularization is a method of modifying observables which have singularities in ...
term to attempt to eliminate implausible solutions. This problem is analogous to echo removal Echo removal is the process of removing echo and reverberation artifacts from audio signals. The reverberation is typically modeled as the convolution of a (sometimes time-varying) impulse response with a hypothetical clean input signal, where both ...
in the signal processing domain. Nevertheless, when coherent beam is used for imaging, the point spread function can be modeled mathematically. By proper deconvolution
In mathematics, deconvolution is the operation inverse to convolution. Both operations are used in signal processing and image processing. For example, it may be possible to recover the original signal after a filter (convolution) by using a deco ...
of the point spread function ''K'' and the blurred image ''B'', the blurred image ''B'' can be deblurred (unblur) and the sharp image ''S'' can be recovered.
See also
*Blind deconvolution In electrical engineering and applied mathematics, blind deconvolution is deconvolution without explicit knowledge of the impulse response function used in the convolution. This is usually achieved by making appropriate assumptions of the input to ...
* Modulation transfer function
* Denoising
* Super-resolution
Super-resolution imaging (SR) is a class of techniques that enhance (increase) the resolution of an imaging system. In optical SR the diffraction limit of systems is transcended, while in geometrical SR the resolution of digital imaging sensors ...
External links Deblur software
References
Image processing {{Signal-processing-stub