From 0fb7af77ce286bf05e2bd28eb445778b1f2dc27a Mon Sep 17 00:00:00 2001 From: Jeremy Karst Date: Sat, 12 Sep 2026 22:35:48 -0400 Subject: [PATCH] Added clarification about sparse sampling shortcomings. --- findings.md | 15 +++++++++++---- 1 file changed, 11 insertions(+), 4 deletions(-) diff --git a/findings.md b/findings.md index 49d0626..c3c70d7 100644 --- a/findings.md +++ b/findings.md @@ -79,10 +79,17 @@ cells. The ergodic pattern costs about 1.6 times the error here. That cost is th premium for insurance that pays out on the Fourier-sparse truth, where half the signal varies too fast for the sparse grid: there the sparse grid garbles the fast waves into false slow ones (this is aliasing, and is destructive; compare the sparse-grid and ergodic columns of -figure 2). THIS CASE IS MOSTLY THEORETICAL: If we knew that there was no small-scale variation -to capture, the sparse grid would be the right choice outright; in practice that is rarely known -before sampling, which is exactly what motivates the signal-agnostic ergodic pattern. See -the "Potential Future Work" section for some related thoughts. +figure 2). THIS CASE IS MOSTLY THEORETICAL: sparse sampling's win here does not carry over to +real applications, for two reasons. First, the rough scale of variation is always a known prior +in practice (it is how any sample spacing gets chosen at all), but acting on that prior does not +lead to a comfortably dense regular grid: any scale at which we knew there were no spatial +frequencies beyond what uniform spacing resolves would be better served by sensing the same area +with fewer, ergodically spaced samples. The regular grid's win in this column is really a +statement that its sample budget was larger than the known field scale required. Second, for +potential fields in particular, variation much finer than the survey scale reflects shallow +sources rather than the deep signal of interest, which is why this ground truth is generated +with a source-depth attenuation term. See the "Potential Future Work" section for some related +thoughts. ![Figure 2](plt1a.png)