The inverse problem of positive autoconvolution
We pose the problem of approximating optimally a given nonnegative signal with the scalar autoconvolution of a nonnegative signal. The I-divergence is chosen as the optimality criterion being well suited to incorporate nonnegativity constraints. After proving the existence of an optimal approximatio...
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| Veröffentlicht in: | IEEE transactions on information theory 2023-06, Vol.69 (6), p.1-1 |
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| creator | Finesso, Lorenzo Spreij, Peter |
| description | We pose the problem of approximating optimally a given nonnegative signal with the scalar autoconvolution of a nonnegative signal. The I-divergence is chosen as the optimality criterion being well suited to incorporate nonnegativity constraints. After proving the existence of an optimal approximation, we derive an iterative descent algorithm of the alternating minimization type to find a minimizer. The algorithm is based on the lifting technique developed by Csiszár and Tusnádi and exploits the optimality properties of the related minimization problems in the larger space. We study the asymptotic behavior of the iterative algorithm and prove, among other results, that its limit points are Kuhn-Tucker points of the original minimization problem. Numerical experiments confirm the asymptotic results and exhibit the fast convergence of the proposed algorithm. |
| doi_str_mv | 10.1109/TIT.2023.3244407 |
| format | Article |
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Numerical experiments confirm the asymptotic results and exhibit the fast convergence of the proposed algorithm.</description><subject>alternating minimization</subject><subject>Approximation</subject><subject>Approximation algorithms</subject><subject>Asymptotic properties</subject><subject>autoconvolution</subject><subject>Behavioral sciences</subject><subject>Convergence</subject><subject>Convolution</subject><subject>Divergence</subject><subject>I-divergence</subject><subject>inverse problem</subject><subject>Inverse problems</subject><subject>Iterative algorithms</subject><subject>Iterative methods</subject><subject>Minimization</subject><subject>Optimality criteria</subject><subject>Optimization</subject><subject>positive system</subject><subject>Signal processing algorithms</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpNkM1LxDAQxYMoWFfvHjwUPLeb7yZHWXRdWPBSzyGNU-zSbWrSFvzvzbJ78DS84b2Zxw-hR4JLQrBe17u6pJiyklHOOa6uUEaEqAotBb9GGcZEFZpzdYvuYjwkyQWhGVrX35B3wwIhQj4G3_RwzH2bjz52U7dAbufJOz8svp-nzg_36Ka1fYSHy1yhz7fXevNe7D-2u83LvnBU06lQsuG0lcAZJVymIq4ClVZc4UprxShQYZ0G0TAsLdO0tU41Qkvb6K9KObZCz-e7qdPPDHEyBz-HIb00VBEhNVZKJxc-u1zwMQZozRi6ow2_hmBzwmISFnPCYi5YUuTpHOkA4J8dp3JSsj-VNFzj</recordid><startdate>20230601</startdate><enddate>20230601</enddate><creator>Finesso, Lorenzo</creator><creator>Spreij, Peter</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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| subjects | alternating minimization Approximation Approximation algorithms Asymptotic properties autoconvolution Behavioral sciences Convergence Convolution Divergence I-divergence inverse problem Inverse problems Iterative algorithms Iterative methods Minimization Optimality criteria Optimization positive system Signal processing algorithms |
| title | The inverse problem of positive autoconvolution |
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