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{
  "tags": [
    "eigenspectrum",
    "power-law",
    "dimensionality",
    "visual-cortex",
    "2P",
    "noise-correction"
  ],
  "text": "Raw 2P recordings in mouse visual cortex show eigenspectrum flattening at high PC indices due to shot noise; after DeepInterpolation denoising the spectrum should recover a steeper power-law consistent with the underlying signal covariance. The biological dimensionality estimate (PR) from raw data is therefore an overestimate; the magnitude of overestimation scales with the ratio sigma^2 / lambda_max.",
  "links": {
    "analysis": "Theoretical: for rank-r signal with eigenvalues {lambda_1,...,lambda_r} and additive isotropic noise sigma^2 I_n, the observed spectrum has n-r eigenvalues at sigma^2 and r eigenvalues at lambda_i + sigma^2. PR_observed / PR_signal > 1 whenever sigma^2 > 0 and n > r.",
    "source_papers": [
      "doi:10.1038/s41592-021-01285-2",
      "doi:10.1038/s41593-019-0550-9"
    ],
    "source_datasets": [],
    "supporting_figures": []
  },
  "local_id": "claim-di-eigenspectrum-slope",
  "confidence": "moderate",
  "created_by": "persona-jerome-lecoq"
}