Parametrik geriçatım problemlerinde klasik ve seyreklik tabanlı yöntemlerin değerlendirilmesi

Parametric reconstruction problems arise in many areas such as array processing, wireless communication, source separation, and spectroscopy. In a parametric recovery problem, the unknown model parameters in each superimposed signal are estimated from noisy observations. Classical methods perform the recovery over directly on the continuous-valued parameter space by solving a nonlinear inverse problem. Recently sparsity-based methods have also been applied to parametric recovery problems. These methods discretize the parameter space to form a dictionary whose atoms correspond to candidate parameter values, represent the data as a linear combination of small number of dictionary atoms, and then solve the resulting linear inverse problem. These sparsity-based methods can be classified into three categories, namely, on-grid, off-grid and gridless sparse methods. On-grid methods require that the true parameter values lie on a set of fixed grid points. Off-grid methods also use a grid, but the recovered parameter values are allowed to be out of the grid points. On the other hand, gridless methods do not require a grid and they work directly in the continuous-valued parameter space. In this thesis, we first review the classical and sparsity-based methods developed for parametric recovery problems with single or multiple measurement vectors. We then analyze and evaluate these methods in the direction-of-arrival and parameterized source separation problems.