Image Fusion using Wavelets
	Matt Boardman, Faculty of Computer Science

Reducing unwanted noise in digital photography is not an easy task. One way to reduce noise is to take many identical photographs, then "fuse" them into a single image by taking the average value of each pixel. However, this requires that your images be perfectly aligned, and even then, some dynamics of the image may be lost.

Here, we will use a technique called wavelet image fusion instead. For an excellent introduction to wavelets, please see an article by Amara Graps. For a much more detailed description of how wavelet image fusion works, see several examples. (More to come, but for now I'll just show the results.)

Reducing Noise

First, we will simulate the process by creating artificially-noisy versions of an existing image.

On the left is the original image. In the centre, an example of one of sixteen noisy images is shown. Here, we add Gaussian noise with a mean of zero and a variance of 0.1 to each image, resulting in a noisy image with a great loss of detail. On the right is the restored image, resulting from wavelet image fusion of the sixteen noisy images. Although the reconstruction is not perfect, a great deal more detail can be seen than in the noisy images. For this fusion, a Symlet wavelet of degree four was used, with a level five mean.

Enhancing Dark Images

For the next trick, we will take several images of a dark scene with a low exposure setting and no flash.

On the left is one of the eight original images: the exposure is far too low, so very little detail can be seen. In the centre, we boost the brightness of the image, resulting in a grainy image. On the right, the image reconstructed from these eight images using wavelet image fusion is shown. Much of the graininess is gone, but the image is not perfect as the images are not perfectly aligned: some artifacts of camera movement can be seen.

Finally, we will fuse a series of images taken with a low exposure setting and no flash, but this time using a tripod to align the pixels in each image. Our goal is to brighten the photograph, while preserving image quality.

On the left is one of the sixteen original images: the exposure is far too low, so very little detail can be seen. In the centre, we take the mean of each pixel for all images and normalize, to obtain a reasonable result with less noise. On the right, the image reconstructed from these eight images using wavelet image fusion is shown.

Both the mean and the wavelet reconstructions have enhanced the brightness of the image while keeping the noise levels low. However, close examination of the details of the image, in comparison to the mean image in the centre, shows that much more detail is visible: the shiny areas are more shiny, the black areas are consistently black, and the reflection in the guitar body is more visible.