Properties and Iterative Methods for the Q-Lasso
We introduce the Q-lasso which generalizes the well-known lasso of Tibshirani (1996) with Q a closed convex subset of a Euclidean m-space for some integer m≥1. This set Q can be interpreted as the set of errors within given tolerance level when linear measurements are taken to recover a signal/image...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/250943 |
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| Summary: | We introduce the Q-lasso which generalizes the well-known lasso of Tibshirani (1996)
with Q a closed convex subset of a Euclidean m-space for some integer m≥1. This set Q can be interpreted as the set of errors within given tolerance level when linear measurements
are taken to recover a signal/image via the lasso. Solutions of the Q-lasso depend on a tuning parameter γ. In this paper, we obtain basic properties of the solutions as a function of γ. Because of ill posedness, we also apply l1-l2 regularization to the Q-lasso. In addition, we discuss iterative methods for solving the Q-lasso which include the proximal-gradient algorithm and the projection-gradient algorithm. |
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| ISSN: | 1085-3375 1687-0409 |