Infinite-Dimensional Inverse Problems with Finite Measurements

We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only finite-dimensional approximation of the measurements is available. For large class satisfying Lipschitz we show that same estimate holds even with finite number measurements. also derive globally convergent algorithm based on Landweber iteration. This theory applies nonlinear ill-posed such as electrical impedance tomography (EIT), scattering quantitative photoacoustic (QPAT), under assumption unknown belongs subspace. In particular, estimates EIT matrix Neumann-to-Dirichlet map; problem amplitude at directions $$S^2 \times S^2$$ ; QPAT low-pass filter internal energy.