Graph Blind Deconvolution with Sparseness Constraint
This work addresses graph signal processing for applications requiring sparse source estimation, but it is incremental as it applies a known constraint to a specific domain.
The paper tackles the problem of blind deconvolution for signals on graphs by imposing an exact sparseness constraint using an ℓ₀ norm, and solves it with an ADMM iterative solver, demonstrating effectiveness in numerical experiments with synthetic signals.
We propose a blind deconvolution method for signals on graphs, with the exact sparseness constraint for the original signal. Graph blind deconvolution is an algorithm for estimating the original signal on a graph from a set of blurred and noisy measurements. Imposing a constraint on the number of nonzero elements is desirable for many different applications. This paper deals with the problem with constraints placed on the exact number of original sources, which is given by an optimization problem with an $\ell_0$ norm constraint. We solve this non-convex optimization problem using the ADMM iterative solver. Numerical experiments using synthetic signals demonstrate the effectiveness of the proposed method.