Linear Image Regridding and Coaddition with Oversampled Point Spread Functions: Lessons from 1D

TL;DR

This work introduces Fast Imcom, a markedly more efficient variant of Imcom for linear image regridding and coaddition that preserves a user-specified, oversampled PSF while controlling noise. Through systematic 1D experiments, it shows that wider target PSFs improve PSF fidelity and reduce noise, compares PSF leakage and noise between Imcom and Fast Imcom, and explores two extreme meta-weight strategies (U-first and $\Sigma$-first) for coaddition. It demonstrates that Fast Imcom can reduce both computational costs and storage by about an order of magnitude for Roman HLIS, and discusses how to extend the approach to 2D, including implications for dithering patterns and survey design. The paper also addresses missing-pixel handling, error propagation, and broader applicability to other weak-lensing programs and time-domain surveys, highlighting a practical path toward scalable, PSF-controlled coadds in large surveys.

Abstract

Image regridding and coaddition have a wide range of applications in astronomical observations. {\sc Imcom}, an algorithm that provides control over point spread function (PSF) and noise in coadded images, has been found to meet the stringent requirements of weak gravitational lensing cosmology with the forthcoming Nancy Grace Roman Space Telescope. In this work, I introduce a new algorithm, Fast {\sc Imcom}, which outperforms traditional {\sc Imcom} in terms of both efficiency and quality. After explaining the underlying philosophy and mathematical formalism, I conduct systematic comparisons between {\sc Imcom} and Fast {\sc Imcom} in terms of PSF reconstruction in 1D. While a 2D implementation is beyond the scope of this paper, I demonstrate how to generalize Fast {\sc Imcom} to 2D and discuss practical issues involved. This new algorithm has the potential of reducing both the computational costs and storage requirements (current estimates are $\sim 100\,{\rm M}$ core-hours and $\sim 1.5 \,{\rm PB}$, respectively) of the Roman High Latitude Imaging Survey (HLIS) by an order of magnitude. Meanwhile, it provides implications for the dithering patterns of Roman surveys (extrapolated from 1D to 2D). I also address potential applications of Fast {\sc Imcom} beyond the Roman HLIS, with focus on other weak lensing programs and Roman time domain surveys; the actual range of use cases is likely beyond what is discussed here.

Figures (11)

• Figure 1: 1D PSFs used in this work. In each panel, the dashed blue (solid orange) curve represents the unpixelated (pixelated) input PSF, a obscured Fraunhofer single-slit diffraction pattern with $\xi \equiv \lambda / D = 1.250$ native pixels; the dash-dotted green curve represents the target output PSF, a Gaussian function with width $\sigma = 1.8685$ native pixels; the dotted red curve represents the oversampled weight field (see the text for explanation). The upper panel shows these four functions in real space; since they are all symmetric, only the $x \geq 0$ part is shown. The middle panel shows the total enclosed light (for PSFs) or weight as a function of the radius $r$; note that this includes both $x > 0$ and $x < 0$ parts. The lower panel shows the same functions in Fourier space; they are all purely real (i.e., no imaginary part), symmetric, and only non-zero at low frequencies.
• Figure 2: Imcom matrices for image regridding. Upper row: the ${\bf A}$ matrix and its inverse ${\bf A}^{-1}$. Lower row: the $-{\bf B}/2$ matrix and the resulting ${\bf T}$ matrix.
• Figure 3: Impact of target output PSF width on image regridding. Each of the first three rows shows results for a different target width. The left panel includes the oversampled weight field (solid black curve) and the discrete weights determined by Imcom (blue bars) and Fast Imcom (orange bars); note that the discrete weights can only be added to the input pixel positions, but the bars are slightly displaced for clarity. The right panel presents the PSF residuals (reconstructed minus target) resulting from Imcom (blue curve) and Fast Imcom (orange curve) weights. This figure only includes results for an output pixel overlapping with one of the input pixels (i.e., $\Delta x = 0$), hence both weights and PSF residuals are symmetric, and only the $x \geq 0$ parts are shown. The last row shows the PSF leakage $U/C$ and noise amplification $\Sigma$ as a function of target output PSF width $\sigma$; the coloring is consistent with the preceding rows, and the three widths examined therein are marked with dotted black vertical lines.
• Figure 4: Impact of the relative position of the output pixel on image regridding. Each of the first three rows shows results for a different output pixel position, and the two panels show PSF residuals in real space (left) and Fourier space (right), respectively. Like in Figure \ref{['fig:target_width']}, Imcom results are shown in blue, while Fast Imcom results are shown in orange. The last row shows the PSF leakage $U/C$ and noise amplification $\Sigma$ as a function of the relative position of the output pixel. For the former, the values reported by the Imcom matrix formalism are shown as a dashed red curve (which is close to a horizontal line).
• Figure 5: PSFs, weight field, and PSF residual involved in 2D image regridding. The upper row presents the unpixelated (left) and pixelated (middle) versions of the input PSF, an obscured Airy disk with $\xi \equiv \lambda / D = 1.250$, as well as the target output PSF, a Gaussian function with width $\sigma = 1.4014$ native pixels. All three PSFs are shown in logarithmic scale, and their half widths at half maximum are shown as radii of dashed black circles. The lower left panel presents the oversampled weight field, along with the sampling points for the output pixel at $\Delta {\boldsymbol r} = (0, 0)^{\rm T}$ shown as blue points. The other two panels of the lower row show the resulting PSF residual in real space (middle) and Fourier space (right), respectively.