Internship proposal: Low-rank modal decompositions of laser Doppler holography spectral dynamics for robust arterio-venous choroidal angiography

Temporal laser Doppler holography signals in the choroid frequently exhibit a reversal when derived from low-frequency band power: as flow increases, the Doppler spectrum broadens and the power within a fixed low-frequency band decreases. This behavior follows from energy redistribution across Doppler frequencies when the integrated spectral energy remains approximately conserved. We discuss modal decompositions of the Doppler power spectrum $P(x,y,t,\omega)={\rm abs}({S(x,y,t,\omega)})^2$ that are designed to capture broadening---a spectral shape phenomenon---rather than raw amplitude changes. The central idea is to separate overall scale, encoded by the total spectral energy $\mathcal{E}(x,y,t)$, from normalized spectral shape descriptors such as energy-normalized spectra $p(\omega)$ and cumulative distribution function (CDF) embeddings $c_r(\omega)$. These representations make broadening dynamics low-dimensional and interpretable, enabling robust biomarkers of spectral width, signed asymmetry, beat-resolved modulation, and arterio-venous mapping in the choroidal plexuses.