## View abstract

### Session S08 - Inverse Problems and Applications

Friday, July 23, 17:50 ~ 18:20 UTC-3

## An $\ell_p$ Variable Projection Method for Large-Scale Separable Nonlinear Inverse Problems

### Malena Espanol

#### Arizona State University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak44643871d15ccdd84fd65302fb6a17a0').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy44643871d15ccdd84fd65302fb6a17a0 = 'm&#97;l&#101;n&#97;.&#101;sp&#97;n&#111;l' + '&#64;'; addy44643871d15ccdd84fd65302fb6a17a0 = addy44643871d15ccdd84fd65302fb6a17a0 + '&#97;s&#117;' + '&#46;' + '&#101;d&#117;'; var addy_text44643871d15ccdd84fd65302fb6a17a0 = 'm&#97;l&#101;n&#97;.&#101;sp&#97;n&#111;l' + '&#64;' + '&#97;s&#117;' + '&#46;' + '&#101;d&#117;';document.getElementById('cloak44643871d15ccdd84fd65302fb6a17a0').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy44643871d15ccdd84fd65302fb6a17a0 + '\'>'+addy_text44643871d15ccdd84fd65302fb6a17a0+'<\/a>';

Variable projection methods are among the classical and efficient methods to solve separable nonlinear least squares problems such as blind deconvolution, system identification, and machine learning. In this talk, we present a modified variable projection method for large-scale separable nonlinear inverse problems, that promotes edge-preserving and sparsity properties on the desired solution, and enhances the convergence of the parameters that define the forward problem. Specifically, we adopt a majorization minimization method that relies on constructing quadratic tangent majorants to approximate an $\ell_p$ regularization term, by a sequence of $\ell_2$ problems that can be solved by the aid of generalized Krylov subspace methods at a relatively low cost compared to the original unprojected problem. In addition, more potential generalized regularizers including total variation (TV), framelet, and wavelet operators can be used, and the regularization parameter can be defined automatically at each iteration with the aid of generalized cross validation. Numerical examples on large-scale two-dimensional imaging problems arising from blind deconvolution are used to highlight the performance of the proposed method in both quality of the reconstructed image as well as the reconstructed forward operator.

Joint work with Mirjeta Pasha (Arizona State University, USA).