An implementation of the following paper

Furuya, Hiroko et al. “Image Restoration via Wiener Filtering in the Frequency Domain.” (2009).

Using A variant of a Wiener filter as an Image restoration technique for Gaussian and Defocus Blur.

Wiener filter is a signal filter which tries to minimze the mean square error between the input image and the output image. Thus given an image with blur and noise added, we can create a filter which restores the image. In order to achieve this, the impulse response of the filter must be equal to

W = H`/(|H|^2 + |N|^2/|F|^2)

where

• H is the impulse response in the fourier domain
• N is the Power Spectral Density of the input signal
• F is the Power Spectral Density of the Noise function
• |N|^2/|F|^2 = k

However given we don't we have the input image and the noise function. We thus estimate the value of k and apply that to our weiner filter.

Our model works on two optimization methods for k.

WE thus compare our metric scores of our optimization techniques, over a set of images. The blue graph is Opt-1 and the green graph is Opt-2. More details about the optimization techniques in the report

In order to run the following program

# Clone this repository
git clone https://github.com/sahitpj/Wiener-Filter/

# Go into the repository
cd Wiener-Filet

# Install dependencies
pip install -r requirements.txt

# Run the app
python main.py <path to image>

dataset credits - http://www.vision.caltech.edu/Image_Datasets/Caltech101/Caltech101.html