컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0256 |
|---|---|
| 분류(Section) | Special Session |
| 분과(Session) | Algebraic geometry and computer vision (SS-09) |
| 영문제목 (Title(Eng.)) |
Deep convolutional framelets: A general deep learning framework for inverse problems |
| 저자(Author(s)) |
Jong Chul Ye1, Yoseob Han1, Eunju Cha1 KAIST1 |
| 초록본문(Abstract) | Recently, deep learning approaches with various network architectures have achieved significant performance improvement over existing iterative reconstruction methods in various imaging problems. However, it is still unclear {\em why} these deep learning architectures work for specific inverse problems. Moreover, in contrast to the usual evolution of signal processing theory around the classical theories, the link between deep learning and the classical signal processing approaches such as wavelets, non-local processing, compressed sensing, etc, are not yet well understood. To address these issues, here we show that the long-searched-for missing link is the convolution framelets for representing a signal by convolving local and non-local bases. The convolution framelets was originally developed to generalize the theory of low-rank Hankel matrix approaches for inverse problems, and this paper further extends the idea so that we can obtain a deep neural network using multilayer convolution framelets with perfect reconstruction (PR) under rectilinear linear unit nonlinearity (ReLU). Our analysis also shows that the popular deep network components such as residual block, redundant filter channels, and concatenated ReLU (CReLU) do indeed help to achieve the PR, while the pooling and unpooling layers should be augmented with high-pass branches to meet the PR condition. Moreover, by changing the number of filter channels and bias, we can control the shrinkage behaviors of the neural network. This discovery reveals the limitations of many existing deep learning architectures for inverse problems, and leads us to propose a novel theory for {\em deep convolutional framelets} neural network. Using numerical experiments with various inverse problems, we demonstrated that our deep convolution framelets network shows consistent improvement over existing deep architectures. This discovery suggests that the success of deep learning is not from a magical power of a black-box, but rather comes from the power of a novel signal representation using non-local basis combined with data-driven local basis, which is indeed a natural extension of classical signal processing theory. |
| 분류기호 (MSC number(s)) |
94A08, 97R40, 94A12, 92C55, 65T60, 42C40, Secondary; 44A12 |
| 키워드(Keyword(s)) | convolutional neural network, framelets, deep learning, inverse problems, ReLU, perfect reconstruction condition |
| 강연 형태 (Language of Session (Talk)) |
English |