Figure 2.

Model data: Exact solution using the SVD method: P(r) versus number of singular value contributions (SVCs). Unimodal distance distribution: (A1) Noise-free dipolar signal. Comparison of model distribution with P(r) generated from (B1) fewer SVCs k = 3, σ_k = 8.04, (C1) exact solution obtained for k = 83, σ_k = 4.8 × 10⁻⁶, (D1) more SVCs k = 85, σ_k = 10⁻⁹, and (E1) Picard plot of ${\log }_{10}\left({\sum }_i{\mid {\sum }_{l=1}^M{\left({\Sigma }^{-1}\right)}_{\mathit{ii}}{U_{\mathit{il}}}^T{S}_l\mid }^2\right)$ versus the number of singular values from k = 1 to 200 starting from largest value. It shows the contributions of singular values that lead to stable and unstable distributions. Bimodal distance distribution: (A2) Noise-free dipolar signal. Comparison of model distribution with P(r) generated from (B2) fewer SVCs k = 3, σ_k = 8.04, (C2) exact solution obtained for k = 82, σ_k = 5.1 × 10, (D2) more SVCs k = 84, σ_k = 10⁻⁷, and (E2) Picard plot of ${\log }_{10}\left({\sum }_i{\mid {\sum }_{l=1}^M{\left({\Sigma }^{-1}\right)}_{\mathit{ii}}{U_{\mathit{il}}}^T{S}_l\mid }^2\right)$ versus the number of singular values from k = 1 to 200 starting from largest value. It shows the contributions of singular values that lead to stable and unstable distributions.⁷ Reprinted with permission from ref 7.