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.
While, in principle, this just means that we should take the basis that returns the smallest metrics, we have in practice to cope with reconstruction noise, which in fact prevents the recovered tampering to be exactly sparse.
Exactly sparse state representations, such as that of Pose SLAM, alleviate the cost of state recovery either in time or in memory, but not in both.
Although these vectors are not exactly sparse, they are well approximated by a K-sparse vector.
Because of the weakly sparseness of the sources in noise, we hereafter prefer following[37] dedicated to stable recovery of not exactly sparse signals.
In this paper, we extend our previous work from [31, 32] in two specific ways: (i) we extend the network source model used from exactly sparse to near-sparse signals, and (ii) we provide a detailed mathematical and numerical justification of the usage of sparse recovery algorithms (including a bound on the reconstruction error) for this source model.
In our earlier work [31], we combined the idea of using real field network coding with the concepts of compressed sensing and proposed a non-adaptive distributed compression scheme, called Quantized Network Coding (QNC), for exactly sparse sources.
However, the signal is only sparse in the DFT atoms if all of the sinusoids are exactly at the pre-defined grid points [13].
We know that signals and natural images must be sparse in a certain transform domain or dictionary, in order for them to be reconstructed exactly within the CS framework.
