On online learning of
sparse basis dictionaries,
Blind IIR deconvolution with an unusual loss function.
or “shift invariant sparse coding”.
It seems like this would boil down to something like sparse dictionary
learning, with the sparse activations, and a dictionary
sparse in LPC components.
There are two ways to do this - time domain, and frequency domain.
For the latter, sparse time-domain activations are non local in Fourier components, but possibly simple to recover.
For the former, one could solve Durbin-Watson equations in the time domain, although we expect that to be unstable.
We could go for sparse simultaneous kernel inference in the time domain, which might be better, or directly infer the Horner-form.
Then we have a lot of simultaneous filter components and tedious inference for them.
Otherwise, we could do it directly in the FFT domain, although this makes MIMO harder, and excludes the potential for non-linearities.
The fact that I am expecting to identify many distinct systems in Fourier space as atoms complicates this slightly.
Thought: can I use HPSS to do this with the purely harmonic components?
And use the percussive components as priors for the activations?
How do you enforce causality for triggering in the FFT-transformed domain?
We have activations and components, but the activations are a KxT matrix, and
the K components the rows of a KxL matrix.
We wish the convolution of one with the other to approximately recover the
original signal with a certain loss function.
It’s tuned percussion, with a non-trivial tuning system, and no pitch bending.
Infer chained biquads? Even restrict them to be bandpass?
Or sparse, high-order filters of some description?
See original: Learning Gamelan