1.4 Blurred image generation

Blurred Image Generation

We use linear convolution to simulate our test image. For coded blurring, we convolve our test picture with a 52-length coded pulsetrain $[10100001110....]$ , which generates an image resembling one that is taken by a camera with a fluttered shutter. Foruncoded blurring, we convolve our test picture with a 52-length boxcar signal, which results in the effect of linear, one-dimensional blur ofthe entire image. Gaussian white noise is added to the blurred image to mimic the readout noise produced by camera sensors in the real world.

The convolution is done by superpositioning the frames according to the code sequence. This hardcoding approach exactly models the generation ofone-dimensional motion blurred images by a real camera. For each value $a_j$ in the code sequence, regardless of 0 or 1, we shift the corresponding frame down by $j$ elements. If $a_j=1$ , we add the corresponding frame to the final blurred image. If $a_j=0$ , then we ignore the corresponding frame.

1. Begin with the original image as the base frame.
2. Look at the code sequence. If the $j$ -th value in the sequence is a `1', then produce another frame that is the base frame shifteddownwards by j elements.
3. If k is the number of `1's in the sequence, then we should have k total shifted frames, including the base frame, after the codesequence is entirely processed.
4. We superposition all the shifted frames together to generate the blurred image.
5. We scale the image by k to set pixel values back to the valid interval [0, 1]to avoid over-exposure.
6. We add independent and identically distributed zero-mean Gaussian white noise to each element of the blurred image. The variance of thisnoise will be our independent/manipulated variable, which characterizes the noise power.
7. We repeat the generation of noisy blurred image for different variances of Gaussian noise.

Boxcar-blur image

Coded-blur image