A module for reconstructing images as a linear sum of reference images based on weighted least squares, optionally using a truncated basis of principal components of the reference images rather than the reference images themselves. Arrays of any dimension can be reconstructed, not only 2D images.
The use of weighted least squares allows uncertainties in the target image to be taken into account as well as a region to be masked such that it can be reconstructed based on the best fit in the unmasked region. This allows you to mask a feature of an image and reconstruct what the reference images predict the image would look like there in the absence of that feature.
The primary use of this for me is absorption imaging of cold atoms. Two images are taken, one with atoms absorbing some of the imaging light, and one just with the imaging light (the 'probe' or 'flat' image). The ratio between the two is the quantity of interest, but because laser powers may change a bit or things might be vibrating a bit, the two images do not perfectly correspond to the same imaging light profile - it might be a bit different between the two, even if they are taken within milliseconds of each other. So we can reconstruct from the image with the atoms in it what imaging light profile, as a linear sum of a number of previously acquired probe images, fits it best in the region where the atoms are not present, and then assume the same linear sum holds in the region where the atoms are present (which is masked out to have zero weight in the reconstruction). So we can reconstruct the 'best' probe image from the atoms image (plus a mask to zero the weights of the fit where atoms are present) and a set of probe images.
Moreover, the probe image reconstructed this way has much lower photon shot noise, since it is a linear sum of other probe images and their noise cancels somewhat. This can improve the signal-to-noise of the resulting images even if the imaging has good laser and vibrational stability.
When the number of reference images becomes comparable to the number of pixels in the image, there is a risk of overfitting - a reconstructed image is a sum of so many reference images that there are enough degrees of freedom for the weighted least squares fit to reproduce all the noise in the unmasked region - likely to the detriment of the reconstruction in the masked region. When this is a risk the basis can be truncated using principle component analysis, and images reconstructed using a number of principal components much smaller than the number of pixels, avoiding overfitting whilst using the basis that describes most of the variation within the set of reference images.
To install, clone this repository somewhere in your PYTHONPATH or into the working directory of your project.
See test/test.py for examples.
There are two classes for image reconstruction - CPUReconstructor and CUDAReconstructor. The latter does its calculations on a GPU using CUDA, if available. This is much faster, and necessary for large numbers of images since the bottleneck of the reconstruction algorithm runs in quadratic time with respect to the number of images, but parallelises nicely.
The principal component analysis functionality is only implemented in the CPU reconstructor, but there is no barrier to it being implemented using CUDA as well.