The 2024' Interferometric Imaging Contest

For the 2024' Interferometric Imaging Contest held in Japan, the objective of the contest is to reconstruct multi-wavelength images. Following the 2016' Interferometric Imaging Beauty Contest^{[Sanchez2016]}, the metric is the sum of scores in the different spectral channels and such that it is insensitive to irrelevant differences due to:

• orientation: image axes may be inverted, notably the E-W axis;
• translation: there may be an arbitrary shift between images, the shift $\Vt$ is however the same in all spectral channels because this is expected for scientific analysis of the images;
• brightness: not all entries are normalized according to the channel-wise flux given in OI_FLUX data-block so a correction factor $α_λ > 0$ is allowed for the restored image in each spectral channel;
• out-of-field values: after all geometric transformations, the fields of view of the reference and reconstructed images may be different, it is assumed that missing pixel values are equal to zero: $β = η = 0$;
• angular resolution: the expected angular resolution is set by the resolution limit of the interferometer with some amount of super-resolution.

The image distance is computed for reference and restored images convolved with a an effective Point Spread Function (PSF) whose Full Width at Half Maximum (FWHM) is given by:

\[\omega_λ = \frac{λ}{ζ\,B_{\mathrm{max}}}\]

with $ζ ≥ 2$ the level of super resolution and $B_{\mathrm{max}}$ the maximal baseline. Following Gomes et al.^[Gomes2016], the distance is given by the sum of the absolute value of the pixel-wise difference with no brightness correction, i.e. $p = 1$ and $\Gamma(x) = x$. The score for a multi-spectral restored image $\Vx$ is thus given by:

\[\Score(\Vx) = \max\limits_{\Vt}\sum_λ\left( 1 - \frac{ \min\limits_{α_λ}\sum_{j \in Ω_λ} \bigl|α_λ\,[\MR_{\Vtheta_λ}\cdot\Vx_λ]_j - [\Vy_λ]_j\bigr| }{ \sum_{j \in Ω_λ} \bigl|[\Vy_λ]_j\bigr| } \right)\]

with

\[\Vtheta_λ = \{\rho_λ,\Vt,\omega_λ\}\]

the settings for resampling the restored image in spectral channel $λ$. The magnification $\rho_λ$ is computed as the ratio of the known pixel sizes of $\Vx_λ$ and $\Vy_λ$ and, usually, does not depend on $λ$.

Since there is no closed-form expression of the best scaling factors $α_λ$, for each translation $\Vt$, the score is numerically optimized in the chromatic scaling factors. Since this optimization is separable in the spectral channels, we used Brent's fmin algorithm to find the scaling factors.

To find the best shift $\Vt$, the score is computed of a coarse grid of offsets and then continuously maximized starting from the best coarse offset.