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A fast algorithm for spatiotemporal signals recovery using arbitrary dictionaries with application to
S F Caracciolo1,2, C F Caiafa3, F D Martínez Pería1,4
1Instituto Argentino de Matemática 'Alberto P. Calderón', CONICET, Saavedra 15 (C1083ACA), Ciudad Autónoma de Buenos Aires, Argentina.
Biomedical Physics & Engineering Express
|July 22, 2022
Summary
This study introduces an efficient method for solving linear regression with group lasso and ridge penalties in Kronecker structured models, crucial for electrocardiography inverse problems. The approach avoids complex computations, reducing resource usage and enabling flexible dictionary use.
Area of Science:
- Computational mathematics
- Biomedical engineering
- Signal processing
Background:
- Linear regression models are fundamental in statistical analysis.
- Kronecker structured models offer efficiency for large-scale problems.
- Inverse problems in electrocardiography require robust computational methods.
Purpose of the Study:
- To develop an efficient method for linear regression with group lasso and ridge penalisation.
- To address the challenges of Kronecker structured models in inverse problems.
- To enable sparse signal representation for electrocardiography.
Main Methods:
- Application of group lasso and ridge penalisation.
- Utilisation of block coordinate descent and proximal gradient descent algorithms.
- Development of an algorithm that bypasses explicit Kronecker structure computation.
Main Results:
- Reduced space and temporal complexity compared to traditional methods.
- Successful application to the inverse problem of electrocardiography.
- Algorithm supports arbitrary dictionaries and flexible group distributions.
Conclusions:
- The proposed method provides an efficient solution for linear regression with Kronecker structures.
- This approach is well-suited for complex biomedical signal processing tasks.
- The algorithm offers flexibility and reduced computational cost.
