Robust matched filter #138
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I just have a few general comments.
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jamesmcclain
suggested changes
May 19, 2021
| r0 = np.trace(np.dot(Ginv, S)) | ||
| return (p * math.log(2 * math.pi) + math.log(detG) | ||
| + math.log(1 - β * r0) + r0 / (1 - β * r0)) / 2 | ||
| try: |
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| X̃ = whiten(image, white_matrix=white) | ||
| s̃ = whiten(target, white_matrix=white) | ||
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| return np.divide(np.einsum('i,rci->rc', s̃, X̃), np.sqrt(np.einsum('rci,rci->rc',X̃, X̃)))/math.sqrt(np.inner(s̃, s̃)) | ||
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| def quad_form(ζ, s̃, λ, ε): |
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Some discussion/description in a comment would be welcome here. It is not clear which if any of the references this is associated with.
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It looks like you are finding the Lagrange multiplier as in equation 13 of Manolakis, et al.?
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| Minv = np.linalg.inv(Σ - (1/ζ) * np.eye(k)) | ||
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| return np.matmul(Minv, s0) / np.inner(s0, np.matmul(np.matmul(np.matmul(Minv, Σ), Minv), s0)) |
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Equation 16 from Manolakis, et. al.
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@jpolchlo I added the PRISMA notebooks to this PR branch, please feel free to remove the commit if you do not want those notebook in this branch. |
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@jpolchlo Should we try to get this merged? |
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Overview
Target detection requires a target to search for, but it may not be entirely easy to acquire a proper target spectrum that is likely to be found in a given scene. Available spectra may be lab sampled, and lack the characteristics of the target substance as they appear in the environment or as they are appear when sampled by a specific remote sensor. This can be dealt with to some extent by using a robust matched filter, which allows the detected signature to deviate from the supplied signature by a small amount (a bound is placed on ‖s - s0‖, where s0 is the supplied target spectrum and s is the true target spectrum).
This PR provides an implementation of the robust matched filter.
Closes #118
Demo
See the included notebook.
Notes
When dealing with smaller samples in the generation of a background covariance model, it is advised to use a shrinkage estimator for the covariance. There was an implementation in this library, but it hadn't been extensively used. It is not a very numerically-robust estimator, and especially seems to fail for larger-dimensional inputs, which is unfortunately our use case. The recommendation is to switch to
sklearn.covariance.LedoitWolfto access a shrunk estimate.Checklist
README.md updated if necessary to reflect the changes