Lavanya Nemani       12:16 PM
@Samuel, do you think there might be a benefit in using the different wavelets decomposition as feature maps for a CNN?

Samuel Farrens       12:35 PM
Hi @Lavanya, I believe there has been some work on this already. I don’t remember which group off the top of my head but it is certainly an interesting topic. There are also some people in our group looking at the opposite idea, namely using CNNS (or similar) to generate leaned decompositions called “learnlets”.

James Nightingale       12:17 PM
In Astronomy, the modeling of strong gravitational lenses and reconstruction of their source galaxies is typically posed as a linear inverse problem. For many different models of the galaxy's mass distribution, you effectively produce many different source reconstructions, and rank them based on:

1) How well they reconstruct the image data.
2) How 'complex' the source reconstruction was, in a Bayesian sense.

For techniques that reconstruct the source in 'real space' it is a well defined problem to perform step 2), and this is important for comparing different galaxy mass models objectively.

For a starlet / wavelet basis, is it possible to compare different reconstructions of the data and 'rank' them in a similar fashion? I can imagine you can compare the goodness-of-reconstruction of the image data, but is there a well formalized way to say whether one solution is more or less complex than another? Is this a relevent problem in a medical setting?

Samuel Farrens       12:40 PM
Hi @James, this is a good question and I think also very application dependent. At CosmoStat we use a lot of these tools in a weak lensing setting, so we can effectively measure not only the pixel score (some measure of the quality of the image reconstruction) but also how much this impacts object ellipticities. In the MRI community this can be more challening because you can have a reconstruction that shows things like microbleeding but is less good at showing some cortical structure (or vice versa). They often look at things like PSNR and SSIM scores, but at the end of the day the best reconstruction is the one that better enables diagnosis etc. 

So in summary, I think it is possible to rank the quality of different reconstructions but only based on an application specific metric.

Anonymous Attendee       12:30 PM
How does the denoiser know the correct k value to use to denoise?

Samuel Farrens       12:42 PM
Good question, there have been several papers by e.g. Jean-Luc Starck looking into this and it turns out that using ~3-4 times the standard deviation of the noise (sigma) in the image is a very effective threshold. We can calculate a reliable estimate of sigma using the median absolute deviation (MAD).