Understanding approximate and unrolled dictionary learning for pattern recovery
This work addresses the computational bottleneck in dictionary learning for signal processing applications, offering a faster alternative with specific performance gains, though it is incremental in nature.
The paper tackles the high computational cost of alternating minimization in dictionary learning by proposing an approximate unrolled formulation, showing that unrolling performs better on support recovery and early iterations, and applies it to MEG pattern learning with competitive results.
Dictionary learning consists of finding a sparse representation from noisy data and is a common way to encode data-driven prior knowledge on signals. Alternating minimization (AM) is standard for the underlying optimization, where gradient descent steps alternate with sparse coding procedures. The major drawback of this method is its prohibitive computational cost, making it unpractical on large real-world data sets. This work studies an approximate formulation of dictionary learning based on unrolling and compares it to alternating minimization to find the best trade-off between speed and precision. We analyze the asymptotic behavior and convergence rate of gradients estimates in both methods. We show that unrolling performs better on the support of the inner problem solution and during the first iterations. Finally, we apply unrolling on pattern learning in magnetoencephalography (MEG) with the help of a stochastic algorithm and compare the performance to a state-of-the-art method.