Learned Interferometric Imaging for the SPIDER Instrument

TL;DR

This work addresses the challenge of reconstructing high-quality images from SPIDER's sparse interferometric measurements while enabling real-time imaging. It introduces two data-driven reconstruction approaches that integrate measurement models with learned priors: a fast post-processing network (U-Net) and a learned iterative network (GU-Net) that uses multiscale gradient information. By modeling SPIDER's forward operator with NUFFT and a Radon-based NU-Radon alternative, the authors achieve dramatic reductions in reconstruction time (down to ~10 ms) while preserving or improving image fidelity, and they demonstrate transfer learning to domain-specific datasets with limited training data. The results indicate that learned methods can outperform traditional primal-dual variational approaches in both reconstruction quality and speed, making real-time SPIDER imaging practically feasible and suggesting broader applicability to radio interferometry.

Abstract

The Segmented Planar Imaging Detector for Electro-Optical Reconnaissance (SPIDER) is an optical interferometric imaging device that aims to offer an alternative to the large space telescope designs of today with reduced size, weight and power consumption. This is achieved through interferometric imaging. State-of-the-art methods for reconstructing images from interferometric measurements adopt proximal optimization techniques, which are computationally expensive and require handcrafted priors. In this work we present two data-driven approaches for reconstructing images from measurements made by the SPIDER instrument. These approaches use deep learning to learn prior information from training data, increasing the reconstruction quality, and significantly reducing the computation time required to recover images by orders of magnitude. Reconstruction time is reduced to ${\sim} 10$ milliseconds, opening up the possibility of real-time imaging with SPIDER for the first time. Furthermore, we show that these methods can also be applied in domains where training data is scarce, such as astronomical imaging, by leveraging transfer learning from domains where plenty of training data are available.

Figures (15)

• Figure 1: A diagram of a SPIDER instrument design proposed with 37 PICs with lenslets attached to them. Image credit: kendrickFlatPanelSpaceBasedSpace2013.
• Figure 2: (Left) The physical locations of the lenslets of the 2D interferometer as detailed in the design proposed in kendrickFlatPanelSpaceBasedSpace2013. The lenslets on each of the radial spokes are mounted to their respective PIC. (Right) The measured baselines of the interferometric measurements between pairs of lenslets on the PICs of the SPIDER instrument. The amount of baselines is increased by measuring at different spectral frequencies. Note that the measurements all lie in the same direction as the directions of the spokes, since measurements are only made using pairs of lenslets on 1 PIC.
• Figure 3: Generating a dirty reconstruction by applying the adjoint of the measurement operator, using the NUDFT, to interferometric measurements of the SPIDER instrument (left), compared to accelerated methods for approximation of the adjoint operation using the NUFFT (centre) and the NU-Radon (right) approaches as detailed in sections \ref{['sec:nufft']} and \ref{['sec:nu-radon']} respectively. The MSE of the two accelerated approaches compared to the NUDFT is shown, where the error is only calculated inside the circular aperture that limits the NU-Radon method.
• Figure 4: Measurements are simulated from the original image from the COCO dataset of natural images shown in the left-most image, using a NUFFT with the SPIDER sampling pattern. Generating images by applying adjoint NUFFT operation, the pseudo-inverse NUFFT operation, and the pseudo-inverse NU-Radon operation are shown respectively from left to right.
• Figure 5: The learned post-processing approach takes the interferometric measurements and uses the telescope model to create an initial reconstruction, in our case the dirty image. This is then passed through the learned post-processing network to create the final reconstruction.