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arXiv:2504.20811

A Quantum Range-Doppler Algorithm for Synthetic Aperture Radar Image Formation

Alessandro Giovagnoli, Sigurd Huber, Gerhard Krieger

Published Apr 29, 2025• 0 citations
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Abstract

Synthetic aperture radar (SAR) is a well established technology in the field of Earth remote sensing. Over the years, the resolution of SAR images has been steadily improving and the pixel count increasing as a result of advances in the sensor technology, and so have the computational resources required to process the raw data to a focused image. Because they are a necessary step in the study of the retrieved data, new high-resolution and low-complexity focusing algorithms are constantly explored in the SAR literature. The theory of quantum computing proposes a new computational framework that might allow to process a vast amount of data in a more efficient way. Relevant to our case is the advantage proven for the quantum Fourier transform (QFT), the quantum counterpart of a fundamental element of many SAR focusing algorithms. Motivated by this, in this work we propose a quantum version of the range-Doppler algorithm. We show how in general reference functions, a key element in many SAR focusing algorithms, can be mapped to quantum gates; we present the quantum circuit performing the SAR raw data focusing and we discuss in detail its computational complexity. We find that the core of the quantum range-Doppler algorithm has a computational complexity, namely the number of single- and two-qubit gates, of $O(N)$, less than its classical counterpart with computational complexity $O(N \log N)$.

DOI
10.48550/arxiv.2504.20811

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Synthetic aperture radar (SAR) is a well established technology in the field of Earth remote sensing. Over the years, the resolution of SAR images has been steadily improving and the pixel count increasing as a result of advances in the sensor technology, and so have the computational resources required to process the raw data to a focused image. Because they are a necessary step in the study of the retrieved data, new high-resolution and low-complexity focusing algorithms are constantly explored in the SAR literature. The theory of quantum computing proposes a new computational framework that might allow to process a vast amount of data in a more efficient way. Relevant to our case is the advantage proven for the quantum Fourier transform (QFT), the quantum counterpart of a fundamental element of many SAR focusing algorithms. Motivated by this, in this work we propose a quantum version of the range-Doppler algorithm. We show how in general reference functions, a key element in many SAR focusing algorithms, can be mapped to quantum gates; we present the quantum circuit performing the SAR raw data focusing and we discuss in detail its computational complexity. We find that the core of the quantum range-Doppler algorithm has a computational complexity, namely the number of single- and two-qubit gates, of O(N)O(N)O(N), less than its classical counterpart with computational complexity O(Nlog⁡N)O(N \log N)O(NlogN).
Synthetic Aperture Radar (SAR) has played an important role in Earth observation, with applications in disaster monitoring, agriculture, forestry, ice surveillance, defense, and planetary exploration. The reconstruction of SAR images is a costly operation that uses Fourier Transform, while quantum computing has some key advantages that potentially enhance the algorithm to make it faster. Therefore, in the first part of the thesis, a major image processing method used in SAR systems is studied, known as the Range Doppler Algorithm (RDA). RDA is implemented on a simulated data set and a real data set from ICEYE Oy. In the second half of the thesis, quantum computing basic is studied and reviewed, including qubits, 1-qubit gate and 2-qubits gates, as well as the Quantum Fourier Transform (QFT) that are specific to replace the classical Fourier Transform. A framework for implementing the Range Doppler Algorithm (RDA) on a quantum computer, referred to as the Quantum Range Doppler Algorithm (QRDA), is proposed. In addition, the required resources under ideal quantum-computing assumptions are analyzed, including time complexity (algorithmic scaling) and space complexity (the number of qubits required). Lastly, the potential applicability of the proposed. QRDA in the context of current quantum device, Noisy Intermediate-Scale Quantum (NISQ) machine, is discussed.
Synthetic aperture radar (SAR) data processing is crucial for high-resolution Earth observation and remote sensing applications, one of the most commonly used algorithms for this task is the Range Doppler Algorithm (RDA). Using the Fast Fourier Transform (FFT), the collected signal is transformed to the frequency domain and then goes through the processing steps of this algorithm. However, when it comes to large datasets, this process can be computationally expensive. This paper explores the implementation of a Quantum Range Doppler Algorithm (QRDA), relying on the Quantum Fourier Transform (QFT) as a speedup tool over the classical FFT. Additionally, it proposes a quantum version of the Range Cell Migration Correction (RCMC) in the Fourier domain, one of the key correctional steps of the RDA algorithm, and compares it with its classical counterpart.
In accord with imaging mechanism, by tackling the integrated quantum circuit without multiple preparations and measurements, a quantum algorithm with remarkable speedup for synthetic aperture radar (SAR) imaging is proposed to decrease the data storage and time consuming in this letter. First, the quantum algorithms for 2-D matched filtering and range cell migration correction (RCMC) are presented. Then, the relevant quantum circuits are designed and bonded together as an integrated quantum circuit for SAR imaging. It would be further applied to wide-swath imaging and sparse-driven radar imaging to form the corresponding quantum algorithm from quantum data to quantum data. The polynomial speedup in computational complexity is analyzed theoretically, and the needed quantum data are reduced exponentially compared to classical data. Experimental results obtained by computer simulation of quantum algorithm demonstrate that the proposed method can obtain the high-resolution SAR image and decrease at least10210^{2}102orders in complexity.
Synthetic Aperture Radar (SAR) imaging is crucial in remote sensing due to its ability to produce high-resolution images regardless of weather conditions or daylight. However, SAR images often suffer from various types of noise, especially speckle noise, which degrades image quality and complicates data analysis. Traditional noise reduction techniques face challenges in balancing noise suppression with the preservation of image details. Recent deep learning approaches, such as U-Net architectures, have made strides in addressing these issues. Simultaneously, quantum computing has emerged as a promising field that can potentially enhance computational methods in image processing. We propose a hybrid classical-quantum U-Net framework that integrates quantum-classical algorithms with tensor networks for improved noise reduction in SAR images. Leveraging the representational capacity of tensor networks and the computational strengths of quantum algorithms, our method aims to surpass the limitations of classical techniques in managing complex noise patterns. In our architecture, certain layers of the U-Net are implemented using quantum circuits specifically optimized for noise suppression. The inclusion of tensor networks enables efficient handling of high-dimensional data within the hybrid model. The idea is to perform extensive experiments on standard SAR datasets to demonstrate that our hybrid U-Net outperforms traditional denoising methods and purely classical deep learning models in both noise reduction and detail preservation. Quantitative assessments using metrics like Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM) would be used for comparison. Moreover, we will evaluate the computational efficiency of our approach, underscoring the potential of quantum computing to expedite complex image processing tasks. This work aims to highlight the feasibility and benefits of integrating quantum computing into practical remote sensing applications. Our hybrid quantum-classical U-Net architecture with tensor networks paves the way for advanced noise reduction techniques in SAR imaging and potentially other domains. Future research will focus on optimizing quantum circuit designs for specific noise types and exploring the scalability of our approach alongside advancements in quantum hardware.
The 3D range-migration algorithm (RMA) and its 2D equivalent, the omega-k algorithm, are employed in a wide range of applications where reconstruction of synthetic aperture data is required, from satellite radar imaging of planets over seismic imaging of the earth crust, down to phased-array ultrasound and ultrasonic application, and recently in-line synthetic aperture radar for non-destructive testing. These algorithms are based on Fourier transforms and share their time-complexity. This limits highly-resolved measurement data to be processed at high speeds which would be advantageous for modern production feed lines. In this publication, we present the development and implementation of the RMA on a quantum computer that scales favourably compared to the time complexity of the classical RMA. We compare reconstruction results of simulated and measured data of the classical and quantum RMA. Hereby, the quantum RMA is run on a quantum simulator backend as well as on IBM's Q System One quantum computer. The results show that real world applications and testing tasks may benefit from future quantum computers.