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The recently introduced theory of compressive sensing enables the recovery of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquist-rate samples. Interestingly, it has been shown that random projections are a near-optimal measurement scheme. This has inspired the design of hardware...
It is now well understood that l1 minimization algorithm is able to recover sparse signals from incomplete measurements and sharp recoverable sparsity thresholds have also been obtained for the l1 minimization algorithm. In this paper, we investigate a new iterative reweighted l1 minimization algorithm and showed that the new algorithm can increase the sparsity recovery threshold of l1 minimization...
A major drawback of OFDM is its large peak to average power ratio (PAPR). While subcarrier reservation is a common approach to combat this problem, little is known about the performance of algorithms that utilize subcarrier reservation. By combining properties of sparse signals with an abstract form of the uncertainty principle related to multiple subcarrier signals, we design an efficient iterative...
Quantization is an important but often ignored consideration in discussions about compressed sensing. This paper studies the design of quantizers for random measurements of sparse signals that are optimal with respect to mean-squared error of the lasso reconstruction. We utilize recent results in high-resolution functional scalar quantization and homotopy continuation to approximate the optimal quantizer...
The batch least-absolute shrinkage and selection operator (Lasso) has well-documented merits for estimating sparse signals of interest emerging in various applications, where observations adhere to parsimonious linear regression models. To cope with linearly growing complexity and memory requirements that batch Lasso estimators face when processing observations sequentially, the present paper develops...
There are two main algorithmic approaches to sparse signal recovery: geometric and combinatorial. The geometric approach utilizes geometric properties of the measurement matrix Phi. A notable example is the Restricted Isometry Property, which states that the mapping Phi preserves the Euclidean norm of sparse signals; it is known that random dense matrices satisfy this constraint with high probability...
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