# Multivariate Convolutional Sparse Coding for Electromagnetic Brain Signals

arXiv: https://arxiv.org/abs/1805.09654 · HTML: https://mlsanity.com/paper/1805.09654/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2018.

## Built on by (most cited first, 11 of 11)

- [Understanding approximate and unrolled dictionary learning for pattern recovery](https://mlsanity.com/paper/2106.06338/) (2021)
- [FaDIn: Fast Discretized Inference for Hawkes Processes with General Parametric Kernels](https://mlsanity.com/paper/2210.04635/) (2022)
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- [DriPP: Driven Point Processes to Model Stimuli Induced Patterns in M/EEG Signals](https://mlsanity.com/paper/2112.06652/) (2021)
- [Personalized Convolutional Dictionary Learning of Physiological Time Series](https://mlsanity.com/paper/2503.07687/) (2025)
- [Searching for waveforms on spatially-filtered epileptic ECoG](https://mlsanity.com/paper/2103.13853/) (2021)
- [Unmixing Noise from Hawkes Process to Model Learned Physiological Events](https://mlsanity.com/paper/2406.16938/) (2024)
- [Spectral Differential Network Analysis for High-Dimensional Time Series](https://mlsanity.com/paper/2412.07905/) (2024)
- [Unsupervised Complex Semi-Binary Matrix Factorization for Activation Sequence Recovery of Quasi-Stationary Sources](https://mlsanity.com/paper/2310.02295/) (2023)
- [RoseCDL: Robust and Scalable Convolutional Dictionary Learning for Rare event and Anomaly Detection](https://mlsanity.com/paper/2509.07523/) (2025)
- [Interpretable EEG biomarkers with bag-of-waves: Spatial and temporal waveform dictionaries for low-data regimes](https://mlsanity.com/paper/2607.22508/) (2026)

## Abstract (arXiv)

Frequency-specific patterns of neural activity are traditionally interpreted as sustained rhythmic oscillations, and related to cognitive mechanisms such as attention, high level visual processing or motor control. While alpha waves (8-12 Hz) are known to closely resemble short sinusoids, and thus are revealed by Fourier analysis or wavelet transforms, there is an evolving debate that electromagnetic neural signals are composed of more complex waveforms that cannot be analyzed by linear filters and traditional signal representations. In this paper, we propose to learn dedicated representations of such recordings using a multivariate convolutional sparse coding (CSC) algorithm. Applied to electroencephalography (EEG) or magnetoencephalography (MEG) data, this method is able to learn not only prototypical temporal waveforms, but also associated spatial patterns so their origin can be localized in the brain. Our algorithm is based on alternated minimization and a greedy coordinate descent solver that leads to state-of-the-art running time on long time series. To demonstrate the implications of this method, we apply it to MEG data and show that it is able to recover biological artifacts. More remarkably, our approach also reveals the presence of non-sinusoidal mu-shaped patterns, along with their topographic maps related to the somatosensory cortex.