# NuSPAN: A Proximal Average Network for Nonuniform Sparse Model -- Application to Seismic Reflectivity Inversion

arXiv: https://arxiv.org/abs/2105.00003 · HTML: https://mlsanity.com/paper/2105.00003/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 78 references that are in the map.
- First posted on arXiv 1 May 2021.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [Deep-learning inversion: a next generation seismic velocity-model building method](https://mlsanity.com/paper/1902.06267/) (2019)
- [Stochastic seismic waveform inversion using generative adversarial networks as a geological prior](https://mlsanity.com/paper/1806.03720/) (2018)
- [Data-driven Seismic Waveform Inversion: A Study on the Robustness and Generalization](https://mlsanity.com/paper/1809.10262/) (2018)
- [Learned Convolutional Sparse Coding](https://mlsanity.com/paper/1711.00328/) (2017)
- [Sparse Regularization via Convex Analysis](https://mlsanity.com/paper/1803.06765/) (2018)
- [Semi-supervised Learning for Acoustic Impedance Inversion](https://mlsanity.com/paper/1905.13412/) (2019)
- [Deep Recurrent Architectures for Seismic Tomography](https://mlsanity.com/paper/1908.07824/) (2019)
- [Unfolding Neural Networks for Compressive Multichannel Blind Deconvolution](https://mlsanity.com/paper/2010.11391/) (2020)
- [Deep Sparse Coding Using Optimized Linear Expansion of Thresholds](https://mlsanity.com/paper/1705.07290/) (2017)
- [DuRIN: A Deep-unfolded Sparse Seismic Reflectivity Inversion Network](https://mlsanity.com/paper/2104.04704/) (2021)

## Abstract (arXiv)

We solve the problem of sparse signal deconvolution in the context of seismic reflectivity inversion, which pertains to high-resolution recovery of the subsurface reflection coefficients. Our formulation employs a nonuniform, non-convex synthesis sparse model comprising a combination of convex and non-convex regularizers, which results in accurate approximations of the l0 pseudo-norm. The resulting iterative algorithm requires the proximal average strategy. When unfolded, the iterations give rise to a learnable proximal average network architecture that can be optimized in a data-driven fashion. We demonstrate the efficacy of the proposed approach through numerical experiments on synthetic 1-D seismic traces and 2-D wedge models in comparison with the benchmark techniques. We also present validations considering the simulated Marmousi2 model as well as real 3-D seismic volume data acquired from the Penobscot 3D survey off the coast of Nova Scotia, Canada.