Simulating image coaddition with the Nancy Grace Roman Space Telescope: III. Software improvements and new linear algebra strategies

TL;DR

The paper tackles the challenge of coadding Roman HLWAS undersampled images for weak lensing by refactoring IMCOM into PyImcom and introducing three linear-algebra kernels. It demonstrates substantial reductions in compute time while preserving PSF control, and provides a detailed comparison across PSF leakage, noise amplification, and point-source measurements using four Roman bands. The work reveals that the Cholesky kernel offers robust PSF fidelity but can incur postage-stamp boundary biases, the IterKernel improves noise handling with a circular input window at the cost of potential output white noise, and the EmpirKernel provides fast, geometry-based coadds suitable for quick-look analyses. These insights inform kernel choice and hyperparameter tuning for high-precision shear measurements, with broader impact on planning Roman weak-lensing surveys and PSF calibration pipelines.

Abstract

The Nancy Grace Roman Space Telescope will implement a devoted weak gravitational lensing program with its High Latitude Wide Area Survey. For cosmological purposes, a critical step in Roman image processing is to combine dithered undersampled images into unified oversampled images and thus enable high-precision shape measurements. IMCOM is an image coaddition algorithm which offers control over point spread functions in output images. This paper presents the refactored IMCOM software, featuring full object-oriented programming, improved data structures, and alternative linear algebra strategies for determining coaddition weights. Combining these improvements and other acceleration measures, to produce almost equivalent coadded images, the consumption of core-hours has been reduced by about an order of magnitude. We then re-coadd a $16 \times 16 \,{\rm arcmin}^2$ region of our previous image simulations with three linear algebra kernels in four bands, and compare the results in terms of IMCOM optimization goals, properties of coadded noise frames, and measurements of simulated stars. The Cholesky kernel is efficient and relatively accurate, yet its irregular windows for input pixels slightly bias coaddition results. The iterative kernel avoids this issue by tailoring input pixel selection for each output pixel; it yields better noise control, but can be limited by random errors due to finite tolerance. The empirical kernel coadds images using an empirical relation based on geometry; it is inaccurate, but being much faster, it provides a valid option for "quick look" purposes. We fine-tune IMCOM hyperparameters in a companion paper.

Figures (22)

• Figure 1: Diagrams for partitioning and selection of input pixels. Upper panel: Diagram showing how pixels from input exposures ( InImage instances) are partitioned into $54 \times 54$ input postage stamps ( InStamp instances). In this particular example, Paper I block (0, 0) in Y106 band, $394338$ pixels are selected from input exposure (95060, 12), and the most populous postage stamp contains $141$ of them. Lower panel: Diagram showing how input pixels are selected for output postage stamps ( OutStamp instances). Pixels from different input postage stamps (labeled as $(j_{\rm stamp}, i_{\rm stamp})$) are shown in different colors; the output postage stamp being coadded overlaps with the one in purple. Note that the dotted grid lines are offset by $-0.5$ output pixels in both directions relative to postage stamp boundaries due to the finite output pixel size.
• Figure 2: Example system matrices ( upper: ${\mathbf A}$ matrix; middle: $-{\mathbf B}/2$ matrix) in logarithmic scale and the resulting transformation matrix ( lower: ${\mathbf T}$ matrix) in linear scale. Boundaries between input postage stamps are shown as red or green dashed lines. For the ${\mathbf A}$ matrix, a threshold is set so that values close to zero (some of them are negative due to numerical errors) are uniformly shown in dark purple; the $-{\mathbf B}/2$ matrix does not have this issue. For the ${\mathbf T}$ matrix, the coloring scheme was chosen to better display structures, not to highlight significant weights (both positive and negative).
• Figure 3: An example of the trade between the PSF leakage metric $U_\alpha/C$ and noise metric $\Sigma_\alpha$, for pixel $(504,504)$ in block $(0,0)$, Y band. The solid orange curve shows the locus in $(U_\alpha/C,\Sigma_\alpha)$-space traced out as one varies the Lagrange multiplier $\kappa_\alpha$ using the "full space" search (Eq. \ref{['eq:T-AB']}). The red points labeled by $\log_{10}(\kappa_\alpha/C)$ indicate the $N_{\rm v}=3$ nodes used for this example. The dotted green curve shows the locus of linear combinations (Eq. \ref{['eq:T-LC']}) obtained with the weights of Eq. (\ref{['eq:omega']}) for 2 nodes (at $\tilde{\kappa}^{(p)}/C=10^{-4}$ and $10^{-2}$) and the dashed blue curve shows the results for 3 nodes (at $\tilde{\kappa}^{(p)}/C=10^{-4}$, $10^{-3}$, and $10^{-2}$). One sees that the 3-node curve achieves almost as good PSF leakage and noise performance as the full space search, but with reduced computational cost since only 3 Cholesky decompositions are used instead of an eigendecomposition.
• Figure 4: Locality of the transformation matrix ${\mathbf T}$. Left column: ${\mathbf T}$ entries for five specific output pixels (shown as blue dots) near the corners and the center of the postage stamp. Middle column, upper panels: ${\mathbf T}$ entries for the same output pixels, shown as a function of the distance between them and the input pixels, in units of output pixels; lower panels: output signal if we discard the contribution from input pixels outside a certain acceptance radius (but use the same ${\mathbf T}$ matrix elements for those inside), also as a function of distance. Right column: ${\mathbf T}$ entries for five specific input pixels (shown as blue dots) near the corners and the center of the postage stamp; note that these maps have a smaller scale than those in the left column.
• Figure 5: Four layers in a field of $17.5 \,{\rm arcsec}$ ($700$ output pixels) on a side, coadded by the Cholesky kernel ( left column), the iterative kernel ( middle column), and the empirical kernel ( right column). Each panel is a Y106 ( #001AA6) + J129 ( #006659) + H158 ( #596600) + F184 ( #A61A00) composite; note that these four colors have similar lightnesses and add up to white (#FFFFFF). From top row to bottom row, the four layers are: simulated science images ( ' SCI'), injected stars drawn by GalSim ( ' gsstar14'; see Section \ref{['sec:gsstar14']}), simulated white noise frames ( ' whitenoise1'; see Section \ref{['ss:whitenoise1']}), and simulated $1/f$ noise frames ( ' 1fnoise2'; see Section \ref{['ss:1fnoise2']}). The scaling is set following Paper I Fig. 8 for ' SCI' and following Paper II Fig. 1 for the other three layers.