Convolutional Analysis Operator Learning: Acceleration and Convergence
Convolutional Analysis Operator Learning: Acceleration and Convergence
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DOI：
10.1109/tip.2019.2937734
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发表时间：
2020-01-01
影响因子：
10.6
通讯作者：
Fessler, Jeffrey A.
中科院分区：
文献类型：
--
作者：
Chun, Il Yong;Fessler, Jeffrey A.
卷积算子学习在许多信号处理和计算机视觉应用中受到关注。学习内核主要依赖于所谓的补丁域方法，该方法在训练信号中提取和存储许多重叠的补丁。由于内存需求，补丁域方法在从大型数据集学习内核时具有限制-特别是具有多层结构，例如，卷积神经网络-或者将学习的内核应用于高维信号恢复问题时。所谓的卷积方法不存储许多重叠的补丁，因此克服了记忆问题，特别是通过仔细的算法设计;它已经在“合成”信号模型中进行了研究，例如，卷积字典学习本文提出了一种新的卷积分析算子学习（CAOL）框架，该框架从卷积的角度学习分析稀疏化正则化器，并开发了一种新的收敛的使用Majorizer的块邻近外推梯度方法（BPEG-M）来解决相应的块多非凸问题。为了在CAOL框架内学习不同的过滤器，本文引入了一个正交约束，强制执行紧框架过滤器条件，以及一个正则化器，促进过滤器之间的多样性。数值实验表明，尖锐的优化器，BPEG-M显着加快CAOL的收敛速度相比，最先进的块邻近梯度（BPG）方法。稀疏视图计算断层扫描的数值实验表明，通过CAOL学习的卷积稀疏化正则化器与传统的边缘保持正则化器相比，显着提高了重建质量。在学习的正则化器中使用更多和更宽的内核可以更好地保留重建图像中的边缘。
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.