Non-uniform spline recovery from small degree polynomial approximation

作者：De Castro Yohann^*; Mijoule Guillaume

来源：Journal of Mathematical Analysis and Applications, 2015, 430(2): 971-992.

DOI：10.1016/j.j.maa.2015.05.034

• LASSO
• Super-resolution
• Non-uniform splines
• Algebraic polynomials
• l(1)-minimization

We investigate the sparse spikes deconvolution problem onto spaces of algebraic polynomials. Our framework encompasses the measure reconstruction problem from a combination of noiseless and noisy moment measurements. We study a TV-norm regularization procedure to localize the support and estimate the weights of a target discrete measure in this frame. Furthermore, we derive quantitative bounds on the support recovery and the amplitude errors under a Chebyshev-type minimal separation condition on its support. Incidentally, we study the localization of the knots of non-uniform splines when a Gaussian perturbation of their inner-products with a known polynomial basis is observed (i.e. a small degree polynomial approximation is known) and the boundary conditions are known. We prove that the knots can be recovered in a grid-free manner using semidefinite programming.

• 出版日期2015-10-15