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Although these vectors are not exactly sparse, they are well approximated by a K-sparse vector.
Our objective is to efficiently design a robust projection matrix Φ for the Compressive Sensing (CS) systems when applied to the signals that are not exactly sparse.
Or, even if sports content isn't exactly sparse, to give sports fans an easier and less "noisy" reading experience, with realtime functionality, adds weight to the startup's value proposition.
One such framework is known in the SLAM literature as the Exactly Sparse Delayed-state Filter (ESDF) [39].
In practical communication systems, channels cannot be exactly sparse; the inactive taps have very small (but non-zero) values.
In addition, an extension of projection matrix design is derived for the scenarios where the signals cannot be represented exactly sparse in a specified dictionary.
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Let us acknowledge that even if the measurements are corrupted by noise or if α is non-exactly sparse, the theory of compressed sensing also shows that the reconstruction obtained by solving the ℓ1-minimization problem remains accurate and stable: Theorem 2 ([7], Theorem 4.4).
When x is not exactly block sparse, Aldroubi et al. [34] also showed that NSP actually guarantees stability.
Fortunately, optimization algorithms, such as the basic matching pursuit (MP) [19] and orthogonal matching pursuit (OMP) [20], can exactly recover sparse signals with high probability.
The performance of both recovery techniques also degrades gracefully if x is not exactly K-sparse but rather is well approximated by a K-sparse signal.
Moreover, even exactly k-sparse signals may be corrupted by additive noise.
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