Compressive Sensing - Incoherence Property
I am trying to answer your question about incoherence here rather than update my previous answer on another question of yours.

Compressive sensing requires low coherent pairs. So the lower $\mu(\Phi,\Psi)$, the better. Actually is $\Phi$ is spike basis (identity matrix) with $\phi_k(t) = \delta(t-k)$, and $\Psi$ is Fourier basis with $\psi_j(t) = 1/\sqrt n e^{-i \cdot 2\pi \cdot jt/n}$, which is just the example I showed you in another question, $\mu(\Phi,\Psi) = 1$, and the maximal incoherence is achieved. It is similar that if you apply the spike basis and the orthogonal basis obtained from SVD. 

Other coherence includes but not limited to: coherence between noiselets and Haar wavelets is $\sqrt2$; coherence between noiselets and Baubechies D4 and D8 are $2.2$ and $2.9$, respectively; random matrices are largely incoherent with any fixed basis $\Psi$.

You may refer to Candes-Romberg theorem for more details on incoherent sampling.