Debarre, Thomas Jean
Fageot, Julien René
Gupta, Harshit
Unser, Michaël
Solving Continuous-Domain Problems Exactly with Multiresolution B-Splines
Proceedings of the Forty-Fourth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'19)
Proceedings of the Forty-Fourth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'19)
Proceedings of the Forty-Fourth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'19)
Proceedings of the Forty-Fourth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'19)
5
2019
2019
We propose a discretization method for continuous-domain linear inverse problems with multiple-order total-variation (TV) regularization. It is based on a recent result that proves that such inverse problems have sparse polynomial-spline solutions. Our method consists in restricting the search space to splines with knots on a uniform grid, which results in a standard convex finite-dimensional problem. As basis functions for this search space, we use the B-splines matched to the regularization order, which are optimally localized. This leads to a well-conditioned, computationally feasible optimization task. Our proposed iterative multiresolution algorithm then refines the grid size until a desired level of accuracy is met and converges to sparse solutions of our inverse problem. Finally, we present experimental results that validate our approach.
Proceedings of the Forty-Fourth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'19)
Conference Papers
10.1109/ICASSP.2019.8683214