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## Radial Deblurring with FFTs

##### Date

2007-08-15##### Author

Webster, Christopher

##### Type of Degree

Thesis##### Department

Electrical and Computer Engineering##### Metadata

Show full item record##### Abstract

Radial blurring (sometimes called zoom blurring) of an image occurs when a camera acquires an image while traveling at a high rate of speed towards an object. Removing this blur is a challenging problem because it is a shift-variant blur. As one travels outward from the center of an image, the blur length
increases linearly. This
shift-variant characteristic precludes the use of traditional
FFT-based deblurring techniques. We propose a way around this
problem by transforming the coordinate system of the blurred image
into a coordinate system in which the blur is linear shift-invariant (LSI). Equivalently, the blurred image
is sampled in a particular nonuniform fashion so that the blur
becomes LSI in the new discrete-space coordinates. As a result, the
blur can be modeled by convolution so that FFT-based deblurring can
be used. In a similar fashion, rotational blur about the center point of an image can also be modeled in this way. We define the overall method as exponentially-sampled radial-space deblurring (ESRSD).
Specific focus is given to identifying the blur percentage of a given image because this value is required to perform the proposed ESRSD method. The blur identification is conducted on the image after the coordinate system has been transformed and nonuniform sampling has occurred. Using the characteristics of a motion blur in the frequency domain, a minimization problem is then set up to acquire the blur percentage based on the given data. Results demonstrate that the method yields high-quality restored images in a computationally efficient manner.

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