The final vector ({mathbf {d}}^{(hat {L}_{a})}_{ast }) provides the estimate of channel sparsity, where (hat {L}_{a}) denotes the estimate of the active channel length.
The estimates of noise variance and sparsity rate need not to be known rather SABMP algorithm estimates them in a robust manner.
The current state of estimation can be the current estimated signal energy or the estimated sparsity of the current signal.
In general, sparsity can arise in a sensor network from two main perspectives: (1) Sparsity of node distribution in spatial terms (2) Sparsity of the field to be estimated . Sparsity of node distribution in spatial terms.
The lasso estimate of the regression coefficients can be obtained by solving the following: (3) where λ is a regularization parameter that controls the amount of sparsity in the estimated regression coefficients.
Minimum description length (MDL) criterion is often used, in this scenario, to estimate the sparsity of the signal [18], i.e., the eigenvalues of the sample covariance matrix R of the received signal y, denoted by λ i is used to estimate the signal sparsity as k ̂ = arg min k ∈ { 1, 2, …, n } MDL ( k ), (21).
Since our methods in the GFlasso family include the lasso penalty, the results from GcFlasso, GwFlasso and GwFlasso show the same property of sparsity as lasso in their estimates, as can be seen in Figure 9F H.
This was an improvement over OMP algorithm, which usually requires the level of sparsity as a priori information to estimate the original signal.
Figure 1 Simulation results: waveforms of the MAS, EEG estimated, and sparsity pattern of the estimated BES matrix.
The relations are presented in Figure 2 and the corresponding equations are: Lmin = 0.4044 + D * 0.0870 f o r all Pinus elliottii experiments (10) Lmin = 0.4178 + D * 0.0980 f o r all Pinus patula experiments (11) Figure 2 Estimates of maximum density with Nilson's Sparsity.
