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Sparse decomposition [13] assumes that a source is a weighted sum of bases from an overcomplete set, considering that most of these bases are inactive most of the time [14], that is, their relative weights are presumed to be mostly zero.
c Sparse decomposition.
d Image reconstructed by the low-rank sparse decomposition approach.
The sparse decomposition based on matching pursuit is an adaptive sparse expression of the signals.
The second extension is based on low-rank sparse decomposition of the phase error matrix.
Mallat and Zhang [38] have developed a general iterative method for approximating sparse decomposition.
To achieve this goal, we employ TV3D to guarantee the exact low-rank and sparse decomposition.
However, it still uses the wavelet transform as [13] does to achieve sparse decomposition.
This paper addresses the structurally constrained sparse decomposition of multi-dimensional signals onto overcomplete families of vectors, called dictionaries.
For comparison, the traditional sparse decomposition and the PCA-based subspace decomposition are shown in Fig. 4c, d.
In the sparse decomposition, basis vectors ({mathbf {d}_{k} }_{k=1}^{K}) are prototypes of signal segments.
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