fiDrizzle-MU: A Fast Iterative Drizzle with Multiplicative Updates

TL;DR

fiDrizzle-MU tackles undersampling and aliasing in co-adding dithered astronomical exposures by replacing additive corrections with multiplicative updates under a positivity constraint. The method is formulated as $F_{i+1} = F_{i} \times \left( \frac{1}{L_E} \sum_{k=1}^{N} \mathfrak{S}^k_u \left\{ \frac{I^k}{\mathfrak{S}^k_d\{ F_i \}} \right\} \right)^{\gamma}$ with $\gamma=1$, and interpreted as a Richardson-Lucy–type deconvolution across sub-dithering kernels. Across simulations and JWST data, it achieves faster convergence and higher fidelity than fiDrizzle-DC, enabling resolution of faint and extended structures and a newly identified gravitationally lensed quasar candidate. The approach offers practical benefits for upcoming deep-field surveys (e.g., CSST-MCI, Euclid, LSST) and can be integrated with PSF deconvolution and additional priors to further enhance reconstruction quality.

Abstract

We propose fiDrizzleMU, an algorithm for co-adding exposures via iterative multiplicative updates, replacing the additive correction framework. This method achieves superior anti-aliasing and noise reduction in stacked images. When applied to James Webb Space Telescope data, the fiDrizzleMU algorithm reconstructs a gravitational lensing candidate that was significantly blurred by the pipeline's resampling process. This enables the accurate recovery of faint and extended structures in high-resolution astronomical imaging.

Figures (7)

• Figure 1: Comparison between the convolution kernel derived from the pixelation blurring simulation and the theoretical prediction. Each convolution kernel in the figure corresponds to a Drizzled image pixel, derived under conditions of a dither pattern consisting solely of sub-pixel uniform random shifts along with a tenfold increase in sampling rate, delineates the flux redistribution process. The original pixel value of a target pixel, intended for restoration, is dispersed across a $21 \times 21$ pixel matrix centered at its location. The upper left panel illustrates the theoretical outcome obtained with an infinite ensemble of nearly continuous dithered frames. The subsequent five panels display the relative residuals between the convolution kernels derived from the Drizzled outcomes and the theoretical kernel. These residuals are evaluated for datasets consisting of 1,600, 10,000, 50,000, 200,000, and 1,000,000 dithered frames, respectively.
• Figure 2: Results of 1,600 dithered simulated observations of a point source located on a fine grid with $0.005^{\prime \prime}$ per pixel. Each simulated observation is sampled at the CSST-MCI pixel scale of $0.05^{\prime \prime}$, with Poisson noise corresponding to a mean background level of 500 counts per pixel applied prior to normalization. The total flux of the point source is likewise set to 500 counts before normalization. The left column shows the combined image obtained by Drizzling all 1,600 mock observational images back onto the $0.005^{\prime \prime}$ grid. The middle column presents the reconstruction result obtained with fiDrizzle-DC after 100 iterations, while the right column shows the corresponding result from fiDrizzle-MU. The top row corresponds to noise-free simulations, while the bottom row include Poisson noise.
• Figure 3: Evolution of the OCFR, defined as the normalized sum of pixel values excluding the central pixel, versus iteration number for fiDrizzle-DC and fiDrizzle-MU algorithms. Both axes are plotted on a logarithmic scale. The horizontal axis shows iteration steps, starting from iteration 1. The point at iteration “0”, representing the initial Drizzled image, is explicitly added for reference, as zero is not defined in log space. Solid lines correspond to noiseless cases, dashed lines indicate Poisson noise cases. Red curves represent fiDrizzle-MU, blue curves fiDrizzle-DC. In the noiseless case, achieves zero OCFR by iteration 850 (truncated after $\sim$150 steps for clarity). For the noisy case, fiDrizzle-MU results are shown up to 5000 iterations, whereas fiDrizzle-DC, exhibiting slower convergence, is iterated up to 35,000 steps in both noise conditions.
• Figure 4: Evolution of the PSNR versus iteration number for fiDrizzle-DC and fiDrizzle-MU. Plotting conventions (logarithmic axes, line styles, color coding, and iteration steps in each condition) are identical to those in Figure \ref{['fig_ocfr']}. The PSNR of the $0-$th iteration, i.e. the Drizzle result, is -14.035 dB. Similar trends are observed: fiDrizzle-MU exhibits significantly faster convergence in the noiseless case (curve truncated after $\sim$150 steps), and maintains superior reconstruction fidelity under Poisson noise conditions compared to fiDrizzle-DC.
• Figure 5: Evolution of the PSNR with iteration number, demonstrating the turning point behavior in iterative reconstructions under Poisson noise. The fiDrizzle-MU algorithm achieves its maximum PSNR of 79.11 dB at iteration 3023, beyond which the PSNR decreases due to noise amplification. Similarly, fiDrizzle-DC reaches its maximum PSNR of 75.05 dB at iteration 34054. This phenomenon is consistent with the typical characteristics of iterative deconvolution methods, where the iteration number serves as an implicit regularization parameter controlling the balance between reconstruction fidelity and noise suppression.