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 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 e i = cos + i sin 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) 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 Test with various types of blue kernels Second step: reverse process and deconvolute Noise Reduction as a follow up step Blur kernel estimation