33e8075e9970de0cfea955afd4644bb2-Reviews.html

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper proposes an approach for constructing a linear wavelet transform on weighted graphs based on the lifting scheme, which has a number of favourable properties: 1) linear in memory and time with the size of the graph, 2) adaptive to a class of signals, 3) exact analysis and synthesis, i.e. allows for perfect signal reconstruction, 4) efficient training through resemblance with deep auto-encoder networks. The paper is presented well: it is clearly structured and well written. After a nice overview and introduction, the authors give a detailed derivation of their construction and show in a number of experiments the validity and versatility of their approach. The proposed approach and wavelet construction builds on previous work but makes a non-trivial contribution to the field of graph-based signal processing by deriving a general-purpose wavelet transform with a number of favourable properties.