  Citation: Cruz, H.; Véstias, M.; Monteiro, J.; Neto, H.; Duarte, R.P. A Review of Synthetic-Aperture Radar Image Formation Algorithms and Implementations. Remote Sens. 2022, 14, 1258. https://doi.org/ 10.3390/rs14051258 Academic Editor: Giampaolo Ferraioli Received: 14 January 2022 Accepted: 1 March 2022 Published: 4 March 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). remote sensing Review A Review of Synthetic-Aperture Radar Image Formation Algorithms and Implementations: A Computational Perspective Helena Cruz 1,2 , Mário Véstias 1,3, * , José Monteiro 1,2 , Horácio Neto 1,2 and Rui Policarpo Duarte 1,4 1 INESC-ID, 1000-029 Lisboa, Portugal; helena.cruz@tecnico.ulisboa.pt (H.C.); jcm@inesc-id.pt (J.M.); hcn@inesc-id.pt (H.N.); rui.duarte@tecnico.ulisboa.pt (R.P.D.) 2 Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisbon, Portugal 3 Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa, 1959-007 Lisbon, Portugal 4 Celestia Portugal, 1749-016 Lisbon, Portugal * Correspondence: mario.vestias@isel.pt Abstract: Designing synthetic-aperture radar image formation systems can be challenging due to the numerous options of algorithms and devices that can be used. There are many SAR image formation algorithms, such as backprojection, matched-filter, polar format, Range–Doppler and chirp scaling algorithms. Each algorithm presents its own advantages and disadvantages considering efficiency and image quality; thus, we aim to introduce some of the most common SAR image formation algorithms and compare them based on these two aspects. Depending on the requisites of each individual system and implementation, there are many device options to choose from, for in- stance, FPGAs, GPUs, CPUs, many-core CPUs, and microcontrollers. We present a review of the state of the art of SAR imaging systems implementations. We also compare such implementations in terms of power consumption, execution time, and image quality for the different algorithms used. Keywords: synthetic-aperture radar; SAR algorithms; SAR systems; FPGA implementations; GPU implementations; many-core implementations 1. Introduction Synthetic-aperture radar (SAR) is a radar-based technology that is capable of generat- ing images of regions or objects, regardless of time of day or weather conditions. SAR has a larger number of applications than other observation technologies, and is used to mon- itor all sorts of phenomena on the planet’s surface, from crop growth to mine detection, natural disasters, such as volcanoes or hurricanes, to climate change effects, such as the deforestation or melting of glaciers [1]. The most common deployment of SAR is usually in satellites and available through public agencies such as ESA with Copernicus, and NASA with RADARSAT. Recently, tstar- tups such as Iceye and Capella Space have provided services for high-resolution SAR images on-demand. Unlike optical observation methods, SAR pulses require intensive signal processing before rendering a visible image. Because of the very computing-intensive SAR signal processing involved, tradition- ally, SAR signals are collected during a flight and processed offline. Furthermore, with the evolution of silicon and unmanned aerial vehicle (UAV) technologies, it is feasible to equip small aircrafts and drones with SAR sensors and processors, and broadcast the compressed images in real-time. In the selection of the computing platform, it is necessary to account for a tradeoff between three constraints: the algorithm execution time, image quality, and consumed power. Moreover, highly customized hardware accelerators based on field-programmable gate array (FPGA) technology have proposed implementations of systems that achieve better power efficiency than general purpose central processing units (CPUs) [2]. This is of most relevance when considering that these systems are powered by batteries and that the total payload weight is very limited. Remote Sens. 2022, 14, 1258. https://doi.org/10.3390/rs14051258 https://www.mdpi.com/journal/remotesensing