No Arabic abstract
In the next years, several cosmological surveys will rely on imaging data to estimate the redshift of galaxies, using traditional filter systems with 4-5 optical broad bands; narrower filters improve the spectral resolution, but strongly reduce the total system throughput. We explore how photometric redshift performance depends on the number of filters n_f, characterizing the survey depth through the fraction of galaxies with unambiguous redshift estimates. For a combination of total exposure time and telescope imaging area of 270 hrs m^2, 4-5 filter systems perform significantly worse, both in completeness depth and precision, than systems with n_f >= 8 filters. Our results suggest that for low n_f, the color-redshift degeneracies overwhelm the improvements in photometric depth, and that even at higher n_f, the effective photometric redshift depth decreases much more slowly with filter width than naively expected from the reduction in S/N. Adding near-IR observations improves the performance of low n_f systems, but still the system which maximizes the photometric redshift completeness is formed by 9 filters with logarithmically increasing bandwidth (constant resolution) and half-band overlap, reaching ~0.7 mag deeper, with 10% better redshift precision, than 4-5 filter systems. A system with 20 constant-width, non-overlapping filters reaches only ~0.1 mag shallower than 4-5 filter systems, but has a precision almost 3 times better, dz = 0.014(1+z) vs. dz = 0.042(1+z). We briefly discuss a practical implementation of such a photometric system: the ALHAMBRA survey.
We propose a novel type filter for multicolor imaging to improve on the photometric redshift estimation of galaxies. An extra filter - specific to a certain photometric system - may be utilized with high efficiency. We present a case study of the Hubble Space Telescopes Advanced Camera for Surveys and show that one extra exposure could cut down the mean square error on photometric redshifts by 34% over the z<1.3 redshift range.
The determination of galaxy redshifts in James Webb Space Telescope (JWST)s blank-field surveys will mostly rely on photometric estimates, based on the data provided by JWSTs Near-Infrared Camera (NIRCam) at 0.6-5.0 {mu}m and Mid Infrared Instrument (MIRI) at {lambda}>5.0 {mu}m. In this work we analyse the impact of choosing different combinations of NIRCam and MIRI broad-band filters (F070W to F770W), as well as having ancillary data at {lambda}<0.6 {mu}m, on the derived photometric redshifts (zphot) of a total of 5921 real and simulated galaxies, with known input redshifts z=0-10. We found that observations at {lambda}<0.6 {mu}m are necessary to control the contamination of high-z samples by low-z interlopers. Adding MIRI (F560W and F770W) photometry to the NIRCam data mitigates the absence of ancillary observations at {lambda}<0.6 {mu}m and improves the redshift estimation. At z=7-10, accurate zphot can be obtained with the NIRCam broad bands alone when S/N>=10, but the zphot quality significantly degrades at S/N<=5. Adding MIRI photometry with one magnitude brighter depth than the NIRCam depth allows for a redshift recovery of 83-99%, depending on SED type, and its effect is particularly noteworthy for galaxies with nebular emission. The vast majority of NIRCam galaxies with [F150W]=29 AB mag at z=7-10 will be detected with MIRI at [F560W, F770W]<28 mag if these sources are at least mildly evolved or have spectra with emission lines boosting the mid-infrared fluxes.
In the modern galaxy surveys photometric redshifts play a central role in a broad range of studies, from gravitational lensing and dark matter distribution to galaxy evolution. Using a dataset of about 25,000 galaxies from the second data release of the Kilo Degree Survey (KiDS) we obtain photometric redshifts with five different methods: (i) Random forest, (ii) Multi Layer Perceptron with Quasi Newton Algorithm, (iii) Multi Layer Perceptron with an optimization network based on the Levenberg-Marquardt learning rule, (iv) the Bayesian Photometric Redshift model (or BPZ) and (v) a classical SED template fitting procedure (Le Phare). We show how SED fitting techniques could provide useful information on the galaxy spectral type which can be used to improve the capability of machine learning methods constraining systematic errors and reduce the occurrence of catastrophic outliers. We use such classification to train specialized regression estimators, by demonstrating that such hybrid approach, involving SED fitting and machine learning in a single collaborative framework, is capable to improve the overall prediction accuracy of photometric redshifts.
Accurate photometric redshifts are a lynchpin for many future experiments to pin down the cosmological model and for studies of galaxy evolution. In this study, a novel sparse regression framework for photometric redshift estimation is presented. Simulated and real data from SDSS DR12 were used to train and test the proposed models. We show that approaches which include careful data preparation and model design offer a significant improvement in comparison with several competing machine learning algorithms. Standard implementations of most regression algorithms have as the objective the minimization of the sum of squared errors. For redshift inference, however, this induces a bias in the posterior mean of the output distribution, which can be problematic. In this paper we directly target minimizing $Delta z = (z_textrm{s} - z_textrm{p})/(1+z_textrm{s})$ and address the bias problem via a distribution-based weighting scheme, incorporated as part of the optimization objective. The results are compared with other machine learning algorithms in the field such as Artificial Neural Networks (ANN), Gaussian Processes (GPs) and sparse GPs. The proposed framework reaches a mean absolute $Delta z = 0.0026(1+z_textrm{s})$, over the redshift range of $0 le z_textrm{s} le 2$ on the simulated data, and $Delta z = 0.0178(1+z_textrm{s})$ over the entire redshift range on the SDSS DR12 survey, outperforming the standard ANNz used in the literature. We also investigate how the relative size of the training set affects the photometric redshift accuracy. We find that a training set of textgreater 30 per cent of total sample size, provides little additional constraint on the photometric redshifts, and note that our GP formalism strongly outperforms ANNz in the sparse data regime for the simulated data set.
State estimation is critical to control systems, especially when the states cannot be directly measured. This paper presents an approximate optimal filter, which enables to use policy iteration technique to obtain the steady-state gain in linear Gaussian time-invariant systems. This design transforms the optimal filtering problem with minimum mean square error into an optimal control problem, called Approximate Optimal Filtering (AOF) problem. The equivalence holds given certain conditions about initial state distributions and policy formats, in which the system state is the estimation error, control input is the filter gain, and control objective function is the accumulated estimation error. We present a policy iteration algorithm to solve the AOF problem in steady-state. A classic vehicle state estimation problem finally evaluates the approximate filter. The results show that the policy converges to the steady-state Kalman gain, and its accuracy is within 2 %.