# Convolutional Sparse Coding Fast Approximation with Application to Seismic Reflectivity Estimation

arXiv: https://arxiv.org/abs/2106.15296 · HTML: https://mlsanity.com/paper/2106.15296/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 39 references that are in the map.
- First posted on arXiv 29 Jun 2021.

## Builds on (most cited first, 4 of 4)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [FISTA-Net: Learning A Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging](https://mlsanity.com/paper/2008.02683/) (2020)
- [Convolutional Neural Networks Analyzed via Convolutional Sparse Coding](https://mlsanity.com/paper/1607.08194/) (2016)
- [Ada-LISTA: Learned Solvers Adaptive to Varying Models](https://mlsanity.com/paper/2001.08456/) (2020)

## Built on by (most cited first, 3 of 3)

- [Less is More: Rethinking Few-Shot Learning and Recurrent Neural Nets](https://mlsanity.com/paper/2209.14267/) (2022)
- [One-Shot Image Restoration](https://mlsanity.com/paper/2404.17426/) (2024)
- [On Inverse Problems, Parameter Estimation, and Domain Generalization](https://mlsanity.com/paper/2506.06024/) (2025)

## Abstract (arXiv)

In sparse coding, we attempt to extract features of input vectors, assuming that the data is inherently structured as a sparse superposition of basic building blocks. Similarly, neural networks perform a given task by learning features of the training data set. Recently both data-driven and model-driven feature extracting methods have become extremely popular and have achieved remarkable results. Nevertheless, practical implementations are often too slow to be employed in real-life scenarios, especially for real-time applications. We propose a speed-up upgraded version of the classic iterative thresholding algorithm, that produces a good approximation of the convolutional sparse code within 2-5 iterations. The speed advantage is gained mostly from the observation that most solvers are slowed down by inefficient global thresholding. The main idea is to normalize each data point by the local receptive field energy, before applying a threshold. This way, the natural inclination towards strong feature expressions is suppressed, so that one can rely on a global threshold that can be easily approximated, or learned during training. The proposed algorithm can be employed with a known predetermined dictionary, or with a trained dictionary. The trained version is implemented as a neural net designed as the unfolding of the proposed solver. The performance of the proposed solution is demonstrated via the seismic inversion problem in both synthetic and real data scenarios. We also provide theoretical guarantees for a stable support recovery. Namely, we prove that under certain conditions the true support is perfectly recovered within the first iteration.