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Column 4 represents the information domain, where the order of sparsity, locations, and amplitudes can be determined by proper sampling (column 5) in this domain.
If the sparsity locations of a signal are known in a transform domain, then the number of samples needed in the time (space) domain should be at least equal to the number of sparse coefficients, i.e., the so-called Nyquist rate.
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We know the samples in the information domain (both position and amplitude) and we know the location of sparsity in the transform domain.
When the location of sparsity is not known, by the law of algebra, the number of samples needed to specify the sparsity is at least twice the number of sparse coefficients.
In this article, we suggest a deterministic structure for the pilot locations in sparsity-based channel estimation methods which minimizes the inter-atom interference in discrete fourier transform (DFT) submatrices.
Although further refinement of the triangulation increases the number of possible optode locations, the sparsity-promoting property of the minimized functional discourages placing additional optodes.
Second, a grid-based approach can avoid the data sparsity problem when predicting future location.
In this section, we will study the sub-optimum pilot locations when greedy sparsity-based methods such as OMP and the introduced IMAT are employed.
The lack of preceding outlooks was attributed to the storm's unusual location and the sparsity of data for storms in the region.
For discrete signals, if the nonzero coefficients ("frequency" sparsity) are consecutive, depending on the location of the zeros, they are called lowpass, bandpass, or multiband discrete signals; if the locations of the nonzero coefficients do not follow any of these patterns, the "frequency" sparsity is random.
Figure 9 The IMAT for detecting the number, location, and values of sparsity.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com