Some questions about "Learning filter widths of spectral decompositions using wavelets"

[imliangh]

Hello!

Thank you very much for the "WaveletDeconv" open source project published on Github and the publication of "Learning filter widths of spectral decompositions with wavelets" Academic papers, which have been of great help to my academic research. When I was debugging the neural network model constructed in your "WaveletDeconv" open source project and reading the description of the model(Figure 1) in the paper, I had some doubts. I hope you could answer them! Here are some of my doubts.

Q1: As shown in Figure 1, the following is my understanding of the model diagram constructed in the article. Is it appropriate? The first layer is the input layer (A), which is mainly used for receiving signals. The second layer is the deconvolution layer (B), which mainly deconvolution processing the output data of the input layer. The third layer is the convolutional layer (C), which mainly carries out convolution processing on the output data of the deconvolutional layer. The fourth part is the output layer (D), which is mainly responsible for receiving the data of the convolutional layer and output the final result value.

But with you in the description of the paper, can infer deconvolution layer as a preprocessing step, input signal, the output is after transformation of the signal, in order to optimize parameters, reduce the gradient, so I guess the first layer should be deconvolution, it served as the input signal processing, deconvolution processing again. At the same time, the deconvolution layer is also the first layer in your project code. I wonder if My understanding is appropriate?

Q2: I didn't find the description of the first layer in the paper and the code, so I didn't understand what the input and output values of A1 and A2 in the first layer were. We look forward to your reply:

1. What is the first layer mainly responsible for?
2. Why is there a small layer(X) between A1 and A2, and what data is stored there?
3. Is the deconvolution layer in the second layer of the diagram, but why is it in the code as the first layer in the model? And it says in the description of the paper that what is received directly is the signal, so should the deconvolution layer be the first layer in the diagram and not the second?

Thank you for reading my letter. I sincerely wish you and your family good health and smooth work. Looking forward to reply. I am looking forward to further communication with you, both academically and in daily life. Please give me more advice. Thank you.

(Figure 1)

[haidark]

Hi! Thanks for your question.

Q1: The figure you shared is almost right, but not quite. Basically, you can shift each of A and B down to correct it - like I show in the attached figure.

Q2. This question is partially answered by the attached figure as well. basically, the boxes above the raw signal (black signal) represent the weights of the waveled deconvolution layer that produce the green/blue signal when applied to the raw signal.

1,2, &3 - the first layer in the figure and the code is supposed to be the wavelet deconvolution layer, the weights of the wavelet deconv layer are represented by the blocks you marked as "X".