Spike detection from inaccurate samplings

作者: Jean-Marc Azais , Fabrice Gamboa , Yohann De Castro

DOI:

关键词:

摘要: This article investigates the support detection problem using LASSO estimator in space of measures. More precisely, we study recovery a discrete measure (spike train) from few noisy observations (Fourier samples, moments...) an $\ell_{1}$-regularization procedure. In particular, provide explicit quantitative localization spikes.

参考文章(19)
Carlos Fernandez-Granda, Support detection in super-resolution arXiv: Information Theory. pp. 145- 148 ,(2013)
Peter B. Borwein, Tamás Erdélyi, Polynomials and Polynomial Inequalities ,(1995)
Otmar Scherzer, Birgit Walch, Sparsity Regularization for Radon Measures international conference on scale space and variational methods in computer vision. pp. 452- 463 ,(2009) , 10.1007/978-3-642-02256-2_38
B Hofmann, B Kaltenbacher, C Pöschl, O Scherzer, A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators Inverse Problems. ,vol. 23, pp. 987- 1010 ,(2007) , 10.1088/0266-5611/23/3/009
David L. Donoho, Superresolution via Sparsity Constraints SIAM Journal on Mathematical Analysis. ,vol. 23, pp. 1309- 1331 ,(1992) , 10.1137/0523074
Martin Burger, Stanley Osher, Convergence rates of convex variational regularization Inverse Problems. ,vol. 20, pp. 1411- 1421 ,(2004) , 10.1088/0266-5611/20/5/005
Elena Resmerita, Otmar Scherzer, Error estimates for non-quadratic regularization and the relation to enhancement Inverse Problems. ,vol. 22, pp. 801- 814 ,(2006) , 10.1088/0266-5611/22/3/004
F. Gamboa, E. Gassiat, Sets of Superresolution and the Maximum Entropy Method on the Mean SIAM Journal on Mathematical Analysis. ,vol. 27, pp. 1129- 1152 ,(1996) , 10.1137/S0036141092233202
Sung Cheol Park, Min Kyu Park, Moon Gi Kang, Super-resolution image reconstruction: a technical overview IEEE Signal Processing Magazine. ,vol. 20, pp. 21- 36 ,(2003) , 10.1109/MSP.2003.1203207
V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, M. Dahan, Compressive fluorescence microscopy for biological and hyperspectral imaging Proceedings of the National Academy of Sciences of the United States of America. ,vol. 109, pp. 10136- 10137 ,(2012) , 10.1073/PNAS.1119511109