I worked on real time denoising of the input data and data io this week. For the real time denoising, we confirmed the feasibility of denoising using ICA last week, but it is not fast enough so we decided to try performing denoising in real time using some heuristic. The reason why we avoided data driven approaches for this particular problem is that we do not have sufficient time to record and annotate data for training a denoiser. The approach we take utilizes the sparsity of blinking signals.
The idea is that we find two vector spaces (known as the “dictionaries”), where the blinking artifacts and the original signals are sparse (meaning that most of the coefficients are zero). Then we find the projecting coefficients of the mixed signal on both spaces, and reconstruct the clean signal using only the coefficient from the “clean” vector space.
(block diagram by Maitiko et. al)
While the idea seems simple, there are a lot of design choices in implementation. For instance, we find the dictionaries using Short Time Fourier Transform with a long Hann window and a short Hann window. The time-frequency trade off makes the frequency resolution of the found dictionary basis vectors different. To ensure the consistency of the length of our basis vector, we chose to fill zeros to improve frequency resolution. Also, to save storage spaces, we decide to only keep the nonnegative Fourier coefficients during basis matching, because the Fourier transform for real signals is symmetric around zero.
Last example is the choice of optimizer. We chose Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) with the PyLop library because it solves an unconstrained problem with L1 regularization and (as the name suggests) it is faster than ISTA.
(objective function with L1 regularization)
While the code for the denoiser is complete, I am still debugging, eye-examining, and testing with previously recorded data to make sure it works. This week we will test with real-time data frames once it is done.