Open Access
Table 1.
Reminder of the main notations.
| Not. | Definitions |
|---|---|
| ⊳ Constants and related indexes | |
| N | Number of pixels in a frame |
| n | Pixel index |
| L | Number of spectral frames |
| ℓ | Spectral index |
| T | Number of temporal frames |
| t | Temporal index |
| K | Number of pixels in a patch |
| ⊳ Data quantities | |
| r | Observed intensity |
| f | Background |
| h | Off-axis PSF |
| ⊳ Estimated quantities | |
| Background statistics | |
 |
Temporo-spectral weight |
 |
Temporal mean |
 |
Spatial (empirical) covariance |
 |
Spatial (shrunk) covariance |
 |
Cholesky factorization of  :  |
 |
Spectral (shrunk) covariance |
 |
Cholesky factorization of  :  |
| Source quantities | |
 |
Vector of source fluxes (spectrum) |
 |
Standard deviations of the source fluxes |
 |
Expected spectral S/N:  |
 |
Prior on the source spectrum |
 |
Expected spectral S/N if  :  |
| w | Spectral weights |
| ⊳ Detection criterions | |
| S/Nℓ | Spectral S/N at wavelength ℓ |
| x | Vector of spectral S/N: xℓ = S/Nℓ |
 |
Vector of whitened spectral  |
| wwS/N | Weighted whitened  |
| GLRTℓ | Spectral GLR:  |
| GLRT+ | Combined GLR:  |
| wGLRT | Whitened GLR:  |
| ⊳ Positions | |
| ϕ0 | 2D angular loc. of a source in a ref. frame |
| ϕℓ, t | 2D angular loc. at wavelength ℓ and time t |
 |
Closest on-grid location to ϕℓ, t |
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