  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.
