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The algorithm tries to minimize the -averaged mutual coherence between and, where is fixed.
We showed that optimized transmit waveform and sensing matrices lead to smaller mutual coherence between different target responses.
In this section we concisely recall some basics of compressed sensing, emphasizing on the role of mutual coherence between the sparsity and sensing bases.
Unlike orthogonal spreading signatures whose mutual coherence is equal to zero, the mutual coherence between the LCS signatures is non-zero, but is very low, such as far less than 1.
Instead of targeting on -averaged mutual coherence between and, this method addressed the problem by making any subset of columns in as orthogonal as possible, or equivalently, making the Gram matrix as close as possible to an identity matrix.
This RIP of H is connected to the mutual coherence between the atoms of the dictionary which is defined as μ ( H ) = max i ≠ j | < a i, a j > | ∥ a i ∥ ∥ a j ∥ (20).
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However, the recovery conditions depend on the mutual coherence μ between ϕ and ψ.
Mutual coherence measures the maximal correlation between both matrix elements and plays an important role in the success of reconstruction algorithm.
The mutual coherence of measurement matrix is the orthogonality between the columns of it and can be defined as mu{boldsymbol{Phi} } = max_{i neq j} frac{phi_{i}^{H} phi_{j}}{|phi_{i} ||phi_{j} |} (6).
The maximal correlation between different normalized frame vectors, also known as mutual coherence, is defined as μ(F)= max1≤k,ℓ≤Nk≠ℓ|〈f k,f ℓ 〉|.
The -averaged mutual coherence of is defined as the average of all absolute and normalized inner products between different columns in (denoted as ) that are above.
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