Sparsity and low-rank models have been popular for reconstructing images and videos from limited or corrupted measurements. Dictionary or transform learning methods are useful in applications such as denoising, inpainting, and medical image reconstruction. In this paper, we propose a framework for online (or time-sequential) adaptive reconstruction of dynamic image sequences from linear (typically undersampled) measurements. We model the spatiotemporal patches of the underlying dynamic image sequence as sparse in a dictionary, and we simultaneously estimate the dictionary and the images sequentially from streaming measurements. Multiple constraints on the adapted dictionary are also considered such as a unitary matrix, or low-rank dictionary atoms that provide additional efficiency or robustness. The proposed online algorithms are memory efficient and involve simple updates of the dictionary atoms, sparse coefficients, and images. Numerical experiments demonstrate the usefulness of the proposed methods in inverse problems such as video reconstruction or inpainting from noisy, subsampled pixels, and dynamic magnetic resonance image reconstruction from very limited measurements.

中文翻译：

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使用字典模型的在线自适应图像重建 (OnAIR)

稀疏和低秩模型在从有限或损坏的测量中重建图像和视频方面很受欢迎。字典或变换学习方法在去噪、修复和医学图像重建等应用中很有用。在本文中，我们提出了一个框架，用于根据线性（通常是欠采样）测量对动态图像序列进行在线（或时序）自适应重建。我们在字典中将底层动态图像序列的时空块建模为稀疏的，并且我们同时从流测量中依次估计字典和图像。还考虑了对适应字典的多个约束，例如酉矩阵或提供额外效率或鲁棒性的低秩字典原子。所提出的在线算法具有内存效率，并且涉及字典原子、稀疏系数和图像的简单更新。数值实验证明了所提出的方法在逆问题中的有用性，例如视频重建或从噪声、二次采样像素进行修复，以及从非常有限的测量中重建动态磁共振图像。