Question about the multi-resolution coefficients of the learned wavelet

[alwaysuu]

Thanks for the inspiring work. I would like to know how to set up an alternative wavelet version with multi-resolution coefficients. I naively set stride = 2 for each splitting module (e.g., DCTSplit with stride = 2 and appropriate paddings), which leads to the right shape but the wrong value of coefficients, e.g., the first-level low-frequency approximation drops the image content.

[KBowei]

Thank you very much for your work for inspiring me, and I would like to ask why using an orthogonal matrix such as a DCT matrix as a convolution kernel guarantees that merge and split are invertible.

[jjhuangcs]

Hi,

Thanks for being interested to our work!

In the paper, we use a stride=1 as the default setting. This helps us to have a redundant representation of the image, so that we can obtain an improved performance on denoising. The wrong values of coefficients could be due the normalization value.

We use DCT for convolutional kernel since it is easy to have different sizes of DCT matrices so that we can adapt to settings with different redundancy.