Neural Proximal Gradient Descent for Compressive Imaging

By Morteza Mardani, Qingyun Sun, Shreyas S. Vasawanala, Vardan Papyan, Hatef Monajemi, John M. Pauly, David L. Donoho. 2018

174 citations recorded by the source corpus.

Recovering high-resolution images from limited sensory data typically leads to a serious ill-posed inverse problem, demanding inversion algorithms that effectively capture the prior information. Learning a good inverse mapping from training data faces severe challenges, including: (i) scarcity of training data; (ii) need for plausible reconstructions that are physically feasible; (iii) need for fast reconstruction, especially in real-time applications. We develop a successful system solving all these challenges, using as basic architecture the repetitive application of alternating proximal and data fidelity constraints. We learn a proximal map that works well with real images based on residual networks with recurrent blocks. Extensive experiments are carried out under different settings: (a) reconstructing abdominal MRI of pediatric patients from highly undersampled k-space data and (b) super-resolving natural face images. Our key findings include: 1. a recurrent ResNet with a single residual block (10-fold repetition) yields an effective proximal which accurately reveals MR image details. 2. Our architecture significantly outperforms conventional non-recurrent deep ResNets by 2dB SNR; it is also trained much more rapidly. 3. It outperforms state-of-the-art compressed-sensing Wavelet-based methods by 4dB SNR, with 100x speedups in reconstruction time.

Subfields: Biomedical Engineering, Computational Mechanics, Radiology, Nuclear Medicine and Imaging

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Citations in the corpus

Understanding and mitigating gradient pathologies in physics-informed neural networks (2020, methodology): “From an optimization standpoint, this setting has motivated the development of proximal gradient algorithms [36] that have been successfully applied to ill-posed inverse problems involving stiff regularization terms [37], as well as effective algorithms for finding Nash equilibria in multi-player ga”
On instabilities of deep learning in image reconstruction and the potential costs of AI (2019, background): “Artiﬁcial intelligence (AI) techniques such as deep learning and neural networks [5] have provided a new paradigm with new techniques in inverse problems [6]–[14] that may change the ﬁeld.”
Differentiable Convex Optimization Layers (2019, methodology): “In contrast, methods that differentiate through every step of an optimization procedure must be customized for each algorithm ( e.g. , [33, 30, 56]).”
Self‐supervised learning of physics‐guided reconstruction neural networks without fully sampled reference data (2019, methodology): “that characterizes similarity with a reference image obtained from fully-sampled data (20). The parameters of the network can be different across the unrolled iterations (27,31) or shared across them (28,33). The aforementioned physics-guided methods have been trained in a supervised manner, where f”
Learning to Optimize: A Primer and A Benchmark (2021, unknown): “Popular application examples include denoising [63; 172; 256; 51; 192; 126; 234; 134; 142], deblurring [63; 256; 146; 127; 58; 142; 162; 257; 121], super-resolution [175; 72; 172; 256; 51; 127; 257], inpainting [175; 172; 192; 3], and compressive sensing [175; 153; 43; 63; 171; 141; 255; 98; 142], J”
Inverting Deep Generative models, One layer at a time (2019, background): “Consequently, there is substantial work on improving compressed sensing with generative adversarial network (GANs) [9, 17, 13, 18, 20].”