This talk focuses on the convergence analysis of a nonmonotone forward-backward splitting method for tackling a class of nonsmooth composite problems in Hilbert spaces. The objective function is the sum of a Fréchet differentiable (not necessarily convex) function and a lower semicontinuous convex function. These problems are commonly encountered in optimization problems involving nonlinear partial differential equations with sparsity-promoting cost functionals. We discuss the convergence and complexity of the algorithm. In particular, linear convergence will be derived under quadratic growth-type conditions. Additionally, we provide insights from numerical experiments that validate our theoretical findings.