Super sampling is a method that attempts to produce an image that has better resolution than can bephysically obtained by the camera system.  There are two limits.  The first is the physical size of a pixel on the sensor. We call producing resolution beyond the digital sampling limit super-sampling.  The second limit is created by diffration from the front aperture of the camera, called the diffraction limit.  Producing image resolution beyond this limit is called super-resolution.

While many researchers have achieved super-sampling, super-resolution imaging has been limited to microscopy.  Usually it takes some special optics, lasers, or illumination.  But we have shown with our recent paper, that super-sampling can produce super-resolution.  There is much much more research to be done on this, but in a controlled laboratory experiment, our image resolution subceeded the diffraction limit by 68%.  SeDDaRA was used as the final deconvolution step.  I have added some of the images above.  Below is a description on how to super-sample using Tria.

As shown in our Optics Letters paper, SeDDaRA can be used to obtain a super-sampled in a few short steps:  Assume you have a sequence of images that show the scene, but not perfectly aligned.  Using Tria's Sizing function, the images are rescaled to twice (or any number larger than one) their size.  The up-sampled images are aligned using Tria's Registration function, and averaged into a single image.  The averaged image contains motion blur at sub-pixel resolution.  Applying either CARon or SeDDaRA, that motion blur is removed, producing an image, if successful, has better resolution then can be obtained with camera.

As an example, I took a series of images of the moon, during a full eclipse, back in November 2010.  My camera, held by hand, was a Nikon CoolPix camera. It is important to note that since the moon being eclipsed by the Earth, the light was very dim.

One original image in the sequence of 16 is shown here.   Since I was holding the camera by hand, the position of the moon in the image jumped around alot.  If you combine the images without any aligning, you get a Moon Flower.

The next step is to up-sample and align the images.  This can be accomplished using Tria's resizing function in batch mode. This task can also be performed using other programs such as ImageJ.

Tria uses Phase Correlation to measure alignment differences between images to 1/20 pixel accuracy.  The function can also determined rotational and scale differences, but that was not necessary here.  The process takes a couple of seconds per image. After the images are aligned, they are averaged together.  Tria has a batch function that can be applied to all the images in a folder.

The average image is displayed below.  Actually, the average image was a 96-bit RGB image that had to be converted for display here.  It is important to preserve as much bit bepth as possible when you are about to perform a deconvolution.  We also cropped the image to remove much of the empty space.

At first glance, the combined image does not look much different than the original.  However, there are two important differences.  First, the bit depth of the image has been increased by averaging the images together.  Second, the number of pixels has doubled.  Each pixel in the average image contains information from multiple pixels in the original image.

In a sense, we just created an image with motion blur.  This can be de-blurred using SeDDaRA, which only asks for three parameters.  After some trial-and-error, I shows the area of influence (AofI), essentially the upper limit on the size of the blur, to be 32.  The C2 parameter was set to 0.001.

With SeDDaRA, a reference image is used that has characterisitcs of the image, but without blur.  Fractals work very well for this.  I used the 1k version of my Midnight fractal, shown below.  I can't exactly why this fractal worked better the others that I tried, but after doing enough deconvolutions, you develop an instinct for which fractals will work.

The processed, and super-sampled, result is below.  The improvement in resolution is apparent.  The crater Tycho, the white circular feature at the 5 o'clock position, can clearly be resolved.  The Grimaldi crater, a dark feature at the 8 o'clock position, could barely be identified in the original, but is very apparent in the processed image.  The craters Keplar, Copernicus, and Aristarchus can also be identified.

The above image was produced by upsampling, aligning, and averaging 16 images.  Blind deconvolution was applied to the average image to produce this result.  As a result, this image has better resolution that what could be achieved using the optics alone.