1. Image Deblurring and noise reduction in python
Vincent DeVito
Computer Systems Lab

2. Abstract
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.

3. Background 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

4. Related Projects
The group of Lu Yuan, et al. designed a 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 a project to estimate blur kernel from naturally blurred image
A few inputs + kernel estimation algorithm + deconvolution = deblurred output image with few artifacts

5. Application Photography Improve image quality Restore image
From Fergus, et al.

6. Application (Cont.) Machine Vision
Requires input images to be of good clarity
Blur could ruin techniques such as edge detection
Intermediate step

7. Fourier Transform Extremely useful for convolution and deconvolution
Convert image to frequency domain
Utilizes the formula eθi = cosθ + isinθ
Usually display the magnitude, since DFT produces complex number (a + bi). Magnitude = (a2 + b2)1/2
Scale to range
O(n2)

8. Fourier Transform (Cont.)
Separate sums
1D DFT in one direction (vertical/horizontal), then in the other
O(nlog2n)

9. Fourier Transform (Cont.)
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

10. Completed Work Successful convolution program
Takes any image (square image of size 128x128 or smaller for best runtime) and blurs it using any given blur kernel

11. Completed Work (Cont.) Image deconvolution using a given kernel
Inconsistent, depending on what type of kernel
Noisy

12. Current Work Noise Reduction for deblurred output image My algorithm
Tried a few simple methods
One edge-sensitive Gaussian smoothing algorithm
Created my own selective Gaussian smoothing noise reduction algorithm
My algorithm
Average of 3x3 neighborhood
Average of all pixels in neighborhood within range of average
Use unsharp sharpening filter to resharpen edges

13. Picture after My Noise Reduction Algorithm
Current Work (Cont.)
Picture after Deblurring Picture after Edge Sensitive Noise Reduction
Picture after My Noise Reduction Algorithm

14. Full Process Original Picture Blur Kernel Blurred Picture
Deblurred Picture Edge Sensitive Noise My Noise Reduction Reduction Algorithm

15. Future Work
Expand deconvolution algorithm to include other forms of blur
Research into deconvolution based on kernel type
Kernel estimation
Color restoration