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Beyond the Grid: Continuous Dictionary Pursuit for Interpretable Signal Decomposition

NeurIPS 2026 · Learning theory and algorithms › Matrix and tensor methods · approach: Signal recovery and phase retrieval

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Proposes Continuous Dictionary Pursuit (CDP), an interpretable signal decomposition framework that learns continuous atom parameters to avoid grid mismatch and spectral leakage of classical matching pursuit and sparse coding.

Problem

Classical matching pursuit and sparse coding are transparent but suffer from spectral leakage and grid mismatch when signal frequencies do not align with discrete dictionary atoms, while deep models are accurate but hard to interpret.

Approach

Replaces the fixed discrete dictionary with continuous atoms whose parameters (e.g., frequencies) are learned, so decomposition is not restricted to a grid; the decomposition remains an explicit, interpretable sum of atoms.

Experimental setup

Builds on: matching pursuit sparse coding

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