Separable Nonlinear Least Squares Sample Clauses

Separable Nonlinear Least Squares. Large-scale inverse problems may also come in nonlinear form: b = A(y true)x true + ε , (1.3) where A(y true) ∈ Rm×n is a matrix defined by parameter vector y true, and ε ∈ Rm is unknown additive noise. If matrix A(y true) is known exactly, the problem follows the linear model, and the goal is to compute an approxi- mation of x true. However, in realistic applications, we may only know the parametric form of A(y), and y true must be approximated through additional measurements or device calibration. Thus, the goal of the nonlinear problem is to compute an approximation of x true, while simultaneously correcting the parameters in y. Similar to the linear model, we assume a Gaussian noise distribution, thus resulting in the following nonlinear least squares system: x,y 2