2014/02/23 by Yohann de Castro, De Castro, Yohann, Guillaume Mijoule +1 · 1 citation
Engineering · Medicine · #Advanced MRI Techniques and Applications #FOS: Mathematics #Numerical Analysis (math.NA) #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.1402.5662
openalex publication_date 2014/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 amplitudes 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.