2025 Theses Doctoral

Decoupling Compression and Demixing: A Modular Penalized Matrix Decomposition Framework for Calcium and Voltage Imaging Data

Kinsella, Ian

Calcium and voltage imaging produce high-dimensional fluorescence movies in which neural activity must be recovered from low-SNR measurements and is often obscured by structured backgrounds and acquisition artifacts. The objective is to recover and demix signals attributable to distinct sources. Most pipelines attempt this in a single stage; in practice, joint formulations are sensitive to initialization and hyperparameters and are computationally demanding. This thesis develops a modular alternative: perform compression and denoising first to obtain a compact, noise-reduced representation, and then demix on that representation.

First, the thesis introduces a patch-wise Penalized Matrix Decomposition (PMD) that constructs a structured, low-rank representation aligned with characteristics shared across modalities, without requiring modality-specific assumptions. Framing the initial stage as signal approximation rather than source separation yields robust compression and denoising without parameter tuning and compares favorably with standard dimensionality reduction baselines. This positions PMD as a general-purpose tool and a foundation from which to revisit the design of demixing.

Second, the thesis turns to demixing through targeted case studies, using the PMD representation as the substrate for redesigned, modality-adapted algorithms. Working directly in the compressed space improves conditioning, enables more stable and data-driven initialization, and reduces computational cost. These designs are translated into usable software and reproducible pipelines, and deployed in collaborative settings, illustrating how the modular framework supports scalable, routine analysis.