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The problem of synthetic aperture radar image recovery in the presence of wideband interference (WBI) is investigated. Delayed versions of a transmitted signal are utilized to construct a dictionary in which a signal of interest (SOI) has a sparse representation. In this letter, WBI is sparsely represented by the time-frequency domain. By utilizing the transform domains, a joint estimation approach...
We consider demixing a pair of sparse signals in orthonormal basis via convex optimization. Theoretically, we characterize the condition under which the solution of the convex optimization problem correctly demixes the true signal components. In specific, we introduce the local subspace coherence to characterize how a basis vector is coherent with a signal subspace, and show that the convex optimization...
The frequency recovery problem from impulsive noise corrupted signal with missing data is considered. The main motive of this work is to explore the signal sparse property that is proven to be advantageous if it is properly utilized. To that end, first, a transformation domain, namely frequency domain, is constructed in which multiple sinusoids have a sparse representation. Second, the data missing...
In this work, a sparse Kalman filter (SKF) exploring the signal sparse property is developed to track unknown time-varying signals. To derive SKF, the measurement update in KF is reformulated into a convex optimization problem first, and then a regularization term ℓ1-norm on parameters of interest is introduced to yield sparse estimates. Coupled the reformulated measurement update with prediction...
The frequency estimation problem is studied in this work in the presence of missing measurements. The approach developed in this work is mainly inspired by sparse signal theory. To find a sparse representation of frequency estimation problem, a DFT-like matrix is created in which the frequency sparsity is discovered. The missing measurements are modeled by a sparse representation as well where missing...
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