# Wiener filter reloaded: fast signal reconstruction without preconditioning

## TL;DR

This paper introduces a dual messenger algorithm for Wiener filtering that efficiently reconstructs signals from large, complex datasets without preconditioning, outperforming existing methods in speed while maintaining accuracy.

## Contribution

The paper presents a novel dual messenger algorithm that improves computational efficiency in Wiener filtering for complex data, without requiring preconditioning.

## Key findings

- Matches the performance of the PCG method in reconstruction accuracy.
- Runs 2 to 4 times faster than standard messenger and PCG methods.
- Successfully applied to simulated CMB temperature data.

## Abstract

We present a high performance solution to the Wiener filtering problem via a formulation that is dual to the recently developed messenger technique. This new dual messenger algorithm, like its predecessor, efficiently calculates the Wiener filter solution of large and complex data sets without preconditioning and can account for inhomogeneous noise distributions and arbitrary mask geometries. We demonstrate the capabilities of this scheme in signal reconstruction by applying it on a simulated cosmic microwave background (CMB) temperature data set. The performance of this new method is compared to that of the standard messenger algorithm and the preconditioned conjugate gradient (PCG) approach, using a series of well-known convergence diagnostics and their processing times, for the particular problem under consideration. This variant of the messenger algorithm matches the performance of the PCG method in terms of the effectiveness of reconstruction of the input angular power spectrum and converges smoothly to the final solution. The dual messenger algorithm outperforms the standard messenger and PCG methods in terms of execution time, as it runs to completion around 2 and 3-4 times faster than the respective methods, for the specific problem considered.