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Scientific Reports

Quantum range-migration-algorithm for synthetic aperture radar applications

Erik Hagen Waller, Andreas Keil, Fabian Friederich

Published Jul 15, 2023• 6 citations
Publisher

Abstract

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.

DOI
10.1038/s41598-023-38611-x

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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.
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) 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).
The field of quantum computing, especially quantum machine learning (QML), has been the subject of much research in recent years. Leveraging the quantum properties of superposition and entanglement promises exponential decrease in computation costs. With the promises of increased speed and accuracy in the quantum paradigm, many classical machine learning algorithms have been adapted to run on quantum computers, typically using a quantum-classical hybrid model. While some work has been done to compare classical and quantum classification algorithms in the Electro-Optical (EO) image domain, this paper will compare the performance of classical and quantum-hybrid classification algorithms in their applications on Synthetic Aperture Radar (SAR) data using the MSTAR dataset. We find that there is no significant difference in classification performance when training with quantum algorithms in ideal simulators as compared to their classical counterparts. However, the true performance benefits will become more apparent as the hardware matures.
Phase unwrapping is the reconstruction of an absolute phase given its values modulo 2π. It is a commonly applied post-processing technique in synthetic aperture radar interferometry applications, such as topographic height and deformation estimation. Established InSAR phase unwrapping approaches focus on large scene phase retrieval, aiming for good overall performance and relying on auxiliary data, such as additional acquisitions, to correct the resulting large local deviations. Given recent progress in quantum algorithm development for optimization problems and phase unwrapping, we are further exploring the feasibility of leveraging gate-based quantum computers and hybrid quantum algorithms to improve small-scale high-accuracy phase unwrapping. We consider a new quantum approach to L1-norm phase unwrapping and a multistage combined approach leveraging the potential advantages of L0quantum and L1phase unwrapping.