  In this work, we analyze the regularizing property of the stochastic gradient
descent for the efficient numerical solution of a class of nonlinear ill-posed
inverse problems in Hilbert spaces. At each step of the iteration, the method
randomly chooses one equation from the nonlinear system to obtain an unbiased
stochastic estimate of the gradient, and then performs a descent step with the
estimated gradient. It is a randomized version of the classical Landweber
method for nonlinear inverse problems, and it is highly scalable to the problem
size and holds significant potentials for solving large-scale inverse problems.
Under the canonical tangential cone condition, we prove the regularizing
property for a priori stopping rules, and then establish the convergence rates
under suitable sourcewise condition and range invariance condition.
