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Vincent DeVito
Computer Systems Lab
2009-2010
The goal of my project is to take an image
input, artificially blur it using a known blur
kernel, then using deconvolution to deblur and
restore the image, then run a last step to reduce
the noise of the image. The goal is to have the
input and output images be identical with a
blurry intermediate image. The final step is
then to estimate the blur kernel of an image
with an unknown blur kernel.
Running goal for image processors and photo
editors
Many methods of deconvolution exist
Many utilize the Fourier Transform
Current progress focused on blur kernel
estimation
Better kernel more accurate, clear output image
The group of Lu Yuan, et al. designed project
with blurry/noisy image pairs
Blurry image intensity + noisy image sharpness +
deconvolution = sharp, deblurred output image
The group of Rob Fergus, et al. designed
project to estimate blur kernel from naturally
blurred image
A few inputs + kernel estimation algorithm +
deconvolution = deblurred output image with few
artifacts
Photography
Improve image quality
Restore image
Machine Vision
Requires input images to be of good clarity
Blur could ruin techniques such as edge detection
Intermediate step
Convert image to frequency domain using the
2D Discrete Fourier Transform and the FFT.
Utilize the formula eθi = cosθ + isinθ
Usually display the magnitude, since DFT produces
complex number (a + bi). Magnitude = (a2 + b2)1/2
Scale to 0-255 range
O(n2)
Separate sums
1D DFT in one direction (vertical/horizontal), then
in the other
O(nlog2n)
Converting image back to spatial domain with
Inverse Fourier Transform
Also possible to separate
Need full complex number from DFT or FFT
Original Picture
Magnitude Only
Phase Only
First step: get FFT and IFFT to work in
conjunction convolution
Second step: reverse process and deconvolute
Test with various types of blue kernels
Noise Reduction as a follow up step
Blur kernel estimation