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This learned dictionary adapted to sparse signal descriptions has proved to be more effective in signal reconstruction and classification tasks than the PCA method, which is demonstrated in the next section.
X = [ x 1, x 2, …, x M ] is the set of sparse codes representing the input samples Y in terms of columns of the learned dictionary D. The given sparsity level T0 restricts that each sample has fewer than T0 terms in its decomposition.
It relies on the sparse model of compressed sensing, involving the sparse dictionary learning and redundant representations over the learned dictionary.
Due to the fact that the discriminative signal lie in a low dimensional subspace and can be well represented only via a few atoms of the learned dictionary, this paper addresses the feature extraction via learning a dictionary, whose sub dictionaries preserve correspondence to the class labels, and an optimal linear classifier jointly based on the structure of energy contribution.
To enable a fair comparison, the data samples are sparse-coded using OMP under the learned dictionary for both algorithms after the learning procedure, these implementations lead to approximate patches with reduced noise { b ̃ 1, b ̃ 2, ⋯, b ̃ 6 2 0 0 1 }.
We study seismic deblending by advanced sparse inversion with a learned dictionary in this paper.
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These learned dictionaries along with their inherent mapping functions are used for the reconstruction of the desired images.
Thus, we have finished learning dictionary D j for the patches in the group with the index j.
Chen et al. [10] generalized the idea of the learning dictionary to explore identity information in multiple frames of videos.
The proposed method learns dictionary directly from the estimated high-resolution image patches (extracted features), and the dictionary learning and the super-resolution can be fused together naturally into one coherent and iterated process.
In this section, we will learn dictionaries on image data, more precisely on image patches, and compare the learned dictionaries to those learned by wKSVD and BPFA as well as to analytic dictionaries.
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