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In this paper we study the compressed sensing problem of recovering a sparse signal from a system of underdetermined linear equations when we have prior information about the probability of each entry of the unknown signal being nonzero. In particular, we focus on a model where the entries of the unknown vector fall into two sets, each with a different… (More)

In this paper we study the compressed sensing problem of recovering a sparse signal from a system of underdetermined linear equations when we have prior information about the probability of each entry of the unknown signal being nonzero. In particular, we focus on a model where the entries of the unknown vector fall into two sets, each with a different… (More)

- M. Amin Khajehnejad, Weiyu Xu, Amir Salman Avestimehr, Babak Hassibi
- IEEE Trans. Signal Processing
- 2011

In this paper we introduce a nonuniform sparsity model and analyze the performance of an optimized weighted `1 minimization over that sparsity model. In particular, we focus on a model where the entries of the unknown vector fall into two sets, with entries of each set having a specific probability of being nonzero. We propose a weighted `1 minimization… (More)

- Aydin Sezgin, Amir Salman Avestimehr, M. Amin Khajehnejad, Babak Hassibi
- IEEE Transactions on Information Theory
- 2012

The capacity region of multi-pair bidirectional relay networks, in which a relay node facilitates the communication between multiple pairs of users, is studied. This problem is first examined in the context of the linear shift deterministic channel model. The capacity region of this network when the relay is operating at either full-duplex mode or… (More)

- M. Amin Khajehnejad, Alexandros G. Dimakis, Weiyu Xu, Babak Hassibi
- IEEE Transactions on Signal Processing
- 2011

We investigate the problem of reconstructing a high-dimensional nonnegative sparse vector from lower-dimensional linear measurements. While much work has focused on dense measurement matrices, sparse measurement schemes can be more efficient both with respect to signal sensing as well as reconstruction complexity. Known constructions use the adjacency… (More)

- Amir Salman Avestimehr, M. Amin Khajehnejad, Aydin Sezgin, Babak Hassibi
- 2009 IEEE Information Theory Workshop on…
- 2009

In this paper we study the capacity region of the multi-pair bidirectional (or two-way) wireless relay network, in which a relay node facilitates the communication between multiple pairs of users. This network is a generalization of the well known bidirectional relay channel, where we have only one pair of users. We examine this problem in the context of… (More)

We investigate the sparse recovery problem of reconstructing a high-dimensional non-negative sparse vector from lower dimensional linear measurements. While much work has focused on dense measurement matrices, sparse measurement schemes are crucial in applications, such as DNA microarrays and sensor networks, where dense measurements are not practically… (More)

- Samet Oymak, M. Amin Khajehnejad, Babak Hassibi
- 2012 IEEE International Symposium on Information…
- 2012

We consider the problem of recovering a sparse signal from underdetermined measurements when we have prior information about the sparsity structure of the signal. In particular, we assume that the entries of the signal can be partitioned into two known sets S<sub>1</sub>, S2 where the relative sparsities over the two sets are different. In this situation it… (More)

- M. Amin Khajehnejad, Alexandros G. Dimakis, Babak Hassibi, Benjamin Vigoda, William Bradley
- IEEE Transactions on Information Theory
- 2010

We introduce a novel algorithm for decoding binary linear codes by linear programming (LP). We build on the LP decoding algorithm of Feldman and introduce a postprocessing step that solves a second linear program that reweights the objective function based on the outcome of the original LP decoder output. Our analysis shows that for some LDPC ensembles we… (More)

It is well known that l1 minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity, as a function of the ratio between the system dimensions, so that with high probability almost all sparse signals can be recovered from iid Gaussian measurements, have been computed… (More)