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Journal Articles IEEE Transactions on Information Theory Year : 2015

## Sparsity-based Recovery of Finite Alphabet Solutions to Underdetermined Linear Systems

Abdeldjalil Aissa El Bey
Dominique Pastor
Si Mohamed Aziz Sbai
• Function : Author

#### Abstract

We consider the problem of estimating a deterministic finite alphabet vector f from underdetermined measurements y = A f, where A is a given (random) n x M matrix. Two new convex optimization methods are introduced for the recovery of finite alphabet signals via l1-norm minimization. The first method is based on regularization. In the second approach, the problem is formulated as the recovery of sparse signals after a suitable sparse transform. The regularization-based method is less complex than the transform-based one. When the alphabet size $p$ equals 2 and (n,N) grows proportionally, the conditions under which the signal will be recovered with high probability are the same for the two methods. When p > 2, the behavior of the transform-based method is established. Experimental results support this theoretical result and show that the transform method outperforms the regularization-based one.

### Dates and versions

hal-01194517 , version 1 (07-09-2015)

### Identifiers

• HAL Id : hal-01194517 , version 1
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### Cite

Abdeldjalil Aissa El Bey, Dominique Pastor, Si Mohamed Aziz Sbai, Yasser Fadlallah. Sparsity-based Recovery of Finite Alphabet Solutions to Underdetermined Linear Systems. IEEE Transactions on Information Theory, 2015, 61 (4), pp.2008 - 2018. ⟨10.1109/TIT.2015.2399914⟩. ⟨hal-01194517⟩

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