Vincent DeVitoComputer 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

From Fergus, et al.

Machine Vision Requires input images to be of good clarity Blur could ruin techniques such as edge

detection Intermediate step

Extremely useful for convolution and deconvolution

Convert image to frequency domain

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)

Inverse Fourier Transform converts back to spatial domain

Also possible to separate Need full complex number from DFT or FFT

Original Picture Magnitude Only Phase Only

Successful FFT and IFFT program Successful convolution program

Takes any image (square image of size 128x128 or smaller for best runtime) and blurs it using any given blur kernel

Start to image deconvolution using a given kernel Inconsistent and somewhat noisy

Fix deconvolution algorithm Inconsistent and produces large, clustered

values Need a new transform or more research into

kernel types Noise reduction

Research into deconvolution based on kernel type