Figure 2

Reducing coherence for a linear system. (Example 2) (A) the sensing matrix $\mathit{\Omega }\in {\mathbb{R}}^{20\times 25}$, without (top left) and with transformation Ψ (top right) and the corresponding coherence distribution (bottom) (B) reconstruction result (left) L1 (middle) L2 with Ω (right) l ₁ optimization with Ω _Ψ (CS) where x-axis represents indices of $\mathbf{q}\in {\mathbb{R}}^{25}$ and y-axis represents coefficient of q (a.u). By reducing coherence of the sensing matrix with transformation, we can recover the exact structure in (B) (right). However, both L1 and L2 fail to recover the exact structure.