Vincent DeVito Computer Systems Lab

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 e θ i = cos θ + i sin θ  Usually display the magnitude, since DFT produces complex number (a + b i ). Magnitude = (a 2 + b 2 ) 1/2  Scale to range  O(n 2 )

 Separate sums   1D DFT in one direction (vertical/horizontal), then in the other  O(nlog 2 n)

 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