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Reconstruction Error in Nonuniformly Sampled Approximately Sparse Signals

Abstract : With its aim to reduce the amount of sensed data and to improve the energy efficiency, compressive sensing (CS) is recently witnessing a growing research interest in remote-sensing applications. The Fourier transform domain plays a significant role as a signal-processing tool and the sparsity domain for the CS-reconstruction methods. A generalized expression for the error in the reconstruction of nonuniformly sampled, approximately sparse, or nonsparse, noisy signals in the Fourier domain is presented in this letter. This expression holds for a wide range of practically important nonuniform signal-sampling strategies, covering the uniform and completely random sampling as the special cases. Additive noise and noise-folding effects are included in the analysis. Statistical examples and two real-world examples validate the presented theory.
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Submitted on : Thursday, February 27, 2020 - 10:06:56 AM
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Ljubisa Stankovic, Milos Brajovic, Isidora Stankovic, Cornel Ioana, Milos Dakovic. Reconstruction Error in Nonuniformly Sampled Approximately Sparse Signals. IEEE Geoscience and Remote Sensing Letters, IEEE - Institute of Electrical and Electronics Engineers, 2021, 18 (1), pp.28 - 32. ⟨10.1109/LGRS.2020.2968137⟩. ⟨hal-02492532⟩



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