  Computational reconstruction plays a vital role in computer vision and
computational photography. Most of the conventional optimization and deep
learning techniques explore local information for reconstruction. Recently,
nonlocal low-rank (NLR) reconstruction has achieved remarkable success in
improving accuracy and generalization. However, the computational cost has
inhibited NLR from seeking global structural similarity, which consequentially
keeps it trapped in the tradeoff between accuracy and efficiency and prevents
it from high-dimensional large-scale tasks. To address this challenge, we
report here the global low-rank (GLR) optimization technique, realizing
highly-efficient large-scale reconstruction with global self-similarity.
Inspired by the self-attention mechanism in deep learning, GLR extracts
exemplar image patches by feature detection instead of conventional uniform
selection. This directly produces key patches using structural features to
avoid burdensome computational redundancy. Further, it performs patch matching
across the entire image via neural-based convolution, which produces the global
similarity heat map in parallel, rather than conventional sequential block-wise
matching. As such, GLR improves patch grouping efficiency by more than one
order of magnitude. We experimentally demonstrate GLR's effectiveness on
temporal, frequency, and spectral dimensions, including different computational
imaging modalities of compressive temporal imaging, magnetic resonance imaging,
and multispectral filter array demosaicing. This work presents the superiority
of inherent fusion of deep learning strategies and iterative optimization, and
breaks the persistent dilemma of the tradeoff between accuracy and efficiency
for various large-scale reconstruction tasks.
