Moreover, although many progresses of sparse representation theory have been made in feature extraction of fault information, the theory also confronts inevitable performance degradation due to the fact that relatively weak fault information has not sufficiently prominent and sparse representations.
Recently a novel shape prior modeling method has been proposed based on sparse learning theory.
Before sparse reconstruction theory can be applied, the time-sequence sampling model should first be established.
EXAMINE takes advantage of sparse graph theory to overcome the excessive-parameter problem with an adaptive-connectivity model and fitting algorithm.
The signal X should be written in a sparser form to ensure a better performance before applying sparse reconstruction theory to recover it.
This article is expected to serve as a tutorial and source of reference for researchers preparing to enter the field or who desire to employ the sparse representation theory in other fields.
In sparse information theory, a central goal is to get the sparsest solutions of underdetermined linear systems including visual coding [1], matrix completion [2], source localization [3], and face recognition [4].
For applying the sparse representation theory successfully, exploiting the special banded symmetric Toeplitz structure of mutual coupling matrices (MCM) in both transmit array and receive array, the unknown MCM in received data can be turned into a diagonal one to eliminate the mutual coupling.
Let us acknowledge that even if the measurements are corrupted by noise or if α is non-exactly sparse, the theory of compressed sensing also shows that the reconstruction obtained by solving the ℓ1-minimization problem remains accurate and stable: Theorem 2 ([7], Theorem 4.4).
