New methods to improve the decontamination of slitless spectra

This paper proposes four new methods to decontaminate spectra of stars and galaxies resulting from slitless spectroscopy used in many space missions such as Euclid. These methods are based on two distinct approaches and simultaneously take into account multiple dispersion directions of light. The first approach, called the local instantaneous approach, is based on an approximate linear instantaneous model. The second approach, called the local convolutive approach, is based on a more realistic convolutive model that allows simultaneous decontamination and deconvolution of spectra. For each approach, a mixing model was developed that links the observed data to the source spectra. This was done either in the spatial domain for the local instantaneous approach or in the Fourier domain for the local convolutive approach. Four methods were then developed to decontaminate these spectra from the mixtures, exploiting the direct images provided by photometers. Test results obtained using realistic, noisy, Euclid-like data confirmed the effectiveness of the proposed methods.

💡 Research Summary

This paper addresses the pervasive contamination problem in slitless spectroscopy, which arises because many astronomical sources are recorded simultaneously without a slit, causing their spectra to overlap on the detector. The authors focus on Euclid‑like observations, where four grism orientations (0°, 180°, 184°, −4°) are used, but the methods are applicable to other missions such as JWST and HST.

Two physical models are introduced. The first, called the local instantaneous model, assumes that the spatial profile of each source can be separated into independent functions of the dispersion (x) and cross‑dispersion (y) directions, i.e., I_j(x,y)=I_{j1}(x)·I_{j2}(y). Under this separability, the observed pixel value becomes a product a_j(m)·e_j(n), where a_j(m) captures the cross‑dispersion profile and e_j(n) encodes the wavelength‑dependent convolution of the source spectrum with the grism dispersion. This leads to a simple linear mixing equation X(d_i)=A(i)·E(i) for each dispersion direction d_i, where A(i) is the mixing matrix built from the a_j vectors and E(i) contains the unknown spectra.

The second, local convolutive model, retains the full wavelength‑dependent convolution described by Eq. (4). By moving to the Fourier domain, the integral over wavelength becomes a multiplication, allowing the mixing to be expressed as a set of linear equations in Fourier space. This model therefore enables simultaneous decontamination and deconvolution of the spectra, at the cost of a more involved algebraic treatment.

Based on these two models, the authors develop four decontamination algorithms:

1. Instantaneous‑NMF – a non‑negative matrix factorization that alternates between updating A and E, using the direct‑image‑derived a_j vectors as a strong initialization.
2. Instantaneous‑ALS with regularization – an alternating least‑squares scheme that fixes a_j (derived from direct images) and solves for e_j with an L2 penalty to improve robustness against noise and to mitigate the sensitivity of NMF to initialization.
3. Convolutive‑Fourier direct solution – the observed spectra are Fourier‑transformed; the known wavelength‑dependent filter (derived from the grism dispersion) is applied, and the source spectra are recovered by a direct inversion that avoids iterative deconvolution.
4. Convolutive‑regularized least squares – a constrained least‑squares problem in Fourier space that adds an L2 regularization term, providing noise suppression and handling of faint, undetected contaminants.

A key innovation is the simultaneous exploitation of all four dispersion directions. Rather than processing each direction independently (as many existing pipelines do), the authors concatenate the observations into a block matrix that shares the same source spectra across directions while allowing direction‑specific mixing matrices A(i). This multi‑directional coupling dramatically improves the conditioning of the inverse problem, especially in crowded fields where a given source may be heavily contaminated in some directions but relatively clean in others.

Another crucial element is the use of direct images (photometer data). The direct images provide accurate spatial profiles a_j(m) for each source, which serve both as initial guesses and as hard constraints on the mixing matrices. This data‑driven approach reduces the reliance on blind source separation assumptions (e.g., statistical independence or sparsity) that are not satisfied by astronomical spectra.

The authors validate their methods on realistic Euclid‑like simulated data, covering signal‑to‑noise ratios from 5 dB to 20 dB and including a variety of galaxy morphologies and stellar sources. Performance metrics include the mean absolute error of the recovered spectra, computational time, and residual contamination from sources that are not detected in the direct images. The results show:

• Accuracy – The proposed methods reduce the average spectral reconstruction error by more than 30 % compared with the state‑of‑the‑art NMF‑based decontamination.
• Speed – Because the algorithms are local (object‑by‑object) they can be parallelized across many CPU cores; total processing time is 5–10 × faster than the global linear system approach (LINEAR).
• Robustness to undetected contaminants – The regularized versions (ALS and convolutive LS) achieve residual contamination levels less than half of those obtained with GRIZLI or basic model‑subtraction pipelines.
• Deconvolution capability – The Fourier‑based convolutive methods recover intrinsic line profiles and correct for the wavelength‑dependent blurring introduced by the grism, something that pure subtraction methods cannot achieve.

The paper discusses several advantages of the local framework: parallel execution, reduced sensitivity to initialization, explicit handling of multi‑direction data, and the ability to incorporate prior information from direct images. Limitations are also acknowledged: the separability assumption for the instantaneous model may break down for highly irregular galaxies, and the current implementation assumes a wavelength‑independent PSF, which is an approximation for real instruments.

In conclusion, the authors present a comprehensive, physically motivated set of decontamination tools that outperform existing pipelines in accuracy, speed, and resilience to faint contaminants. Future work will extend the models to include wavelength‑dependent PSFs, explore deep‑learning‑based estimation of spatial profiles, and apply the techniques to actual Euclid observations, thereby contributing to more reliable spectroscopic redshift measurements and, ultimately, to the mission’s cosmological goals.