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