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We assess the prospects for detecting the moving lens effect using cosmological surveys. The bulk motion of cosmological structure induces a small-scale dipolar temperature anisotropy of the cosmic microwave radiation (CMB), centered around halos and oriented along the transverse velocity field. We introduce a set of optimal filters for this signal, and forecast that a high significance detection can be made with upcoming experiments. We discuss the prospects for reconstructing the bulk transverse velocity field on large scales using matched filters, finding good agreement with previous work using quadratic estimators.
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Velocity fields can be reconstructed at cosmological scales from their influence on the correlation between the cosmic microwave background and large-scale structure. Effects that induce such correlations include the kinetic Sunyaev Zeldovich (kSZ) effect and the moving-lens effect, both of which will be measured to high precision with upcoming cosmology experiments. Galaxy measurements also provide a window into measuring velocities from the effect of redshift-space distortions (RSDs). The information that can be accessed from the kSZ or RSDs, however, is limited by astrophysical uncertainties and systematic effects, which may significantly reduce our ability to constrain cosmological parameters such as $fsigma_8$. In this paper, we show how the large-scale transverse-velocity field, which can be reconstructed from measurements of the moving-lens effect, can be used to measure $fsigma_8$ to high precision.
In the field of signal processing on graphs, graph filters play a crucial role in processing the spectrum of graph signals. This paper proposes two different strategies for designing autoregressive moving average (ARMA) graph filters on both directed and undirected graphs. The first approach is inspired by Pronys method, which considers a modified error between the modeled and the desired frequency response. The second technique is based on an iterative approach, which finds the filter coefficients by iteratively minimizing the true error (instead of the modified error) between the modeled and the desired frequency response. The performance of the proposed algorithms is evaluated and compared with finite impulse response (FIR) graph filters, on both synthetic and real data. The obtained results show that ARMA filters outperform FIR filters in terms of approximation accuracy and they are suitable for graph signal interpolation, compression and prediction.
This work presents a semi-analytical approach to answer the question of optimal beam filtering in the case of EDXRF measurements with an X-ray tube. A collection of programs, called xfilter, is presented that is capable to find the optimal filter material, the optimal filter thickness, and the optimal scattering angle, for all possible combinations of trace elements, target materials, and tube voltages. The concepts of the calculations are introduced in a general manner and demonstrated with a specific example, the detection of gold K_alpha1 XRF within human tissue. Comparing the calculation results and an EDXRF measurement shows excellent agreement.
In this paper we apply ideas from information theory to create a method for the design of optimal filters for photometric redshift estimation. We show the method applied to a series of simple example filters in order to motivate an intuition for how photometric redshift estimators respond to the properties of photometric passbands. We then design a realistic set of six filters covering optical wavelengths that optimize photometric redshifts for $z <= 2.3$ and $i < 25.3$. We create a simulated catalog for these optimal filters and use our filters with a photometric redshift estimation code to show that we can improve the standard deviation of the photometric redshift error by 7.1% overall and improve outliers 9.9% over the standard filters proposed for the Large Synoptic Survey Telescope (LSST). We compare features of our optimal filters to LSST and find that the LSST filters incorporate key features for optimal photometric redshift estimation. Finally, we describe how information theory can be applied to a range of optimization problems in astronomy.
Matched filters are routinely used in cosmology in order to detect galaxy clusters from mm observations through their thermal Sunyaev-Zeldovich (tSZ) signature. In addition, they naturally provide an observable, the detection signal-to-noise or significance, which can be used as a mass proxy in number counts analyses of tSZ-selected cluster samples. In this work, we show that this observable is, in general, non-Gaussian, and that it suffers from a positive bias, which we refer to as optimisation bias. Both aspects arise from the fact that the signal-to-noise is constructed through an optimisation operation on noisy data, and hold even if the cluster signal is modelled perfectly well, no foregrounds are present, and the noise is Gaussian. After reviewing the general mathematical formalism underlying matched filters, we study the statistics of the signal-to-noise with a set Monte Carlo mock observations, finding it to be well-described by a unit-variance Gaussian for signal-to-noise values of 6 and above, and quantify the magnitude of the optimisation bias, for which we give an approximate expression that may be used in practice. We also consider the impact of the bias on the cluster number counts of Planck and the Simons Observatory (SO), finding it to be negligible for the former and potentially significant for the latter.
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