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Convolutional Analysis Operator Learning: Acceleration and Convergence
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DOI：10.1109/TIP.2019.2937734.png)
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摘要
En 中文
Convolutional operator learning is gaining attention in many signal processing and computer vision applications. Learning kernels has mostly relied on so-called patch-domain approaches that extract and store many overlapping patches across training signals. Due to memory demands, patch-domain methods have limitations when learning kernels from large datasets - particularly with multi-layered structures, e.g., convolutional neural networks - or when applying the learned kernels to high-dimensional signal recovery problems. The so-called convolution approach does not store many overlapping patches, and thus overcomes the memory problems particularly with careful algorithmic designs; it has been studied within the synthesis signal model, e.g., convolutional dictionary learning. This paper proposes a new convolutional analysis operator learning (CAOL) framework that learns an analysis sparsifying regularizer with the convolution perspective, and develops a new convergent Block Proximal Extrapolated Gradient method using a Majorizer (BPEG-M) to solve the corresponding block multi-nonconvex problems. To learn diverse filters within the CAOL framework, this paper introduces an orthogonality constraint that enforces a tight-frame filter condition, and a regularizer that promotes diversity between filters. Numerical experiments show that, with sharp majorizers, BPEG-M significantly accelerates the CAOL convergence rate compared to the state-of-the-art block proximal gradient (BPG) method. Numerical experiments for sparse-view computational tomography show that a convolutional sparsifying regularizer learned via CAOL significantly improves reconstruction quality compared to a conventional edge-preserving regularizer. Using more and wider kernels in a learned regularizer better preserves edges in reconstructed images.
Keyword:
Convolution
Training
Kernel
Convolutional codes
Computed tomography
Convergence
Image reconstruction
Convolutional regularizer learning
convolutional dictionary learning
convolutional neural networks
unsupervised machine learning algorithms
nonconvex-nonsmooth optimization
block coordinate descent
inverse problems
X-ray computed tomography
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期刊
IF:
13.7
论文数:
1.0W
被引数:
8.4W
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