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By the recent advances in computer technology leading to the invention ofmore powerful processors, the importance of creating models using data trainingis even greater than ever. Given the significance of this issue, this worktries to establish a connection among Machine Learning, Inverse Problems, andApplied Harmonic Analysis. Inspired by methods introduced in [12, 17, 22, 30],which are connections between Wavelet and Inverse Problems, we offer a modelwith the capability of learning in terms of an application in signalprocessing. In order to reach this model, a bi-level optimization problem willhave to be faced. For solving this, a sequence of step functions is presentedthat its convergence to the solution will be proved. Each of these stepfunctions derives from several constrained optimization problems on$\mathbb{R^n}$ that will be introduced here.

Using Supervised Learning to Construct the Best Regularization Term and the Best Multiresolution Analysis