To test whether the order of the inputs mattered in the asymmetry of the quality of reconstruction of x1 and x2, noted above, we tried feeding a new CNN of the same structure with inputs in reversed order. Explicitly, instead of using the input data {(y1j,y2j)}j=1N, we used {(y2j,y1j)}j=1N. Since the cost function of Eq. 2 is symmetric, our expectation was that the results should be roughly the same. However, as can be seen in Figs. 3 and 4, the quality of the reconstructions of this run were in reverse order as well: The reconstruction of x2 was now far better than that of x1, and the MSE was now 0.0145 and 0.0126 when applied on details 1 and 2, respectively, which was roughly the same as in the first approach. The corresponding reconstruction mean absolute errors achieved by this approach were 0.0561 and 0.0495.

Seeing the two outcomes, we decided to mash them together into a single reconstruction and enjoy the benefits of both of them. That is, we wished to have a reconstruction comprising x1 of the first approach and x2 of the second attempt as our final result. More explicitly, adding another label to the outputs to indicate the order of inputs, so that xi[21] indicates the output i when the inputs are ordered (y2, y1, and x), we posit our output, the pair (x1[12],x2[21]). To our amazement, we found that the MSE of this combination yields 0.0016 and 0.0020 when applied on details 1 and 2, respectively (the mean absolute errors here were 0.0175 and 0.0171).

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