# Deep Learning: Classification vs. Convolution for Signal Restoration

Assume we have vector $$X = [x_1, x_2, x_3, x_4 ,..... x_N], ∈ -1,1$$. Therefore the value of $$x$$ is either 1 or -1. The vector $$X$$ is convoluted with random generated vector $$Y$$ whose length is the same of $$X$$, so $$r = X*Y$$ where $$*$$ denote to the convolution operation.

Is there classification deep learning model which can extract the vector $$X$$ based on $$r$$ ?? I mean the input should be the vector $$r$$ and output the vector $$X$$.

By deep learning, I'll assume you mean neural network. To develop a neural network, you'll need labeled data. This means you need a bunch of example inputs ($$r$$) and outputs ($$X$$). Once you have that, you need to build a network. As far as I can tell, currently the guidelines for building these things are very loose and ad-hoc. There is general consensus on good or bad activation functions and general suggestions, but there is no formal theory about how many neurons to choose, how many layers, etc. (at least since the last time I took a dive into this).