image deblurring

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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 learnin ...
) to generate ''B''. Mathematically, this can be represented as $B=S*K$ (where * represents
convolution In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities a ...
). 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 an imaging system to a point source A point source is a single identifiable ''localised'' source of something. A point source has negligible extent, distinguishing it from other source ...
and is
convolved In mathematics (in particular, functional analysis), convolution is a operation (mathematics), mathematical operation on two function (mathematics), functions ( and ) that produces a third function (f*g) that expresses how the shape of one is ...
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. 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 (physics), 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 an imaging system to a point source A point source is a single identifiable ''localised'' source of something. A point source has negligible extent, distinguishing it from other source ...
can be modeled mathematically. By proper deconvolution of the
point spread function The point spread function (PSF) describes the response of an imaging system to a point source A point source is a single identifiable ''localised'' source of something. A point source has negligible extent, distinguishing it from other source ...
''K'' and the blurred image ''B'', the blurred image ''B'' can be deblurred (unblur) and the sharp image ''S'' can be recovered.