Blind free deconvolution over one-parameter sparse families via eigenmatrix
Abstract
This note considers the blind free deconvolution problems of sparse spectral measures from one-parameter families. These problems pose significant challenges since they involve nonlinear sparse recovery. The main technical tool is the eigenmatrix method for solving unstructured sparse recovery problems. The key idea is to turn the nonlinear inverse problem into a linear inverse problem by leveraging the R-transform for free addition and the S-transform for free product. The resulting linear problem is solved with the eigenmatrix method tailored to the domain of the parametric family. Numerical results are provided for both the additive and multiplicative free deconvolutions.
Fields of Study & Subjects
Sparse and Compressive Sensing Techniques
Blind Source Separation Techniques
Image and Signal Denoising Methods
Publication details
- Journal / source
- Communications in Mathematical Sciences
- Volume
- 24
- Issue
- 5
- Pages
- 1459–1469
- Publication date
- 1 January 2026
- Language
- EN