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.
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.
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) 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(NlogN).
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.
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 least102orders in complexity.
This survey presents a comprehensive analysis of the quantum Fourier transform (QFT), a fundamental tool in quantum computing, in comparison to its classical counterpart, the fast Fourier transform (FFT). The study begins with an introduction to the classical Fourier transform, which is widely used in different disciplines such as signal and image processing. The article introduces the QFT as a quantum version of the Fourier transform, detailing how it leverages quantum parallelism and superposition to reduce the time complexity of the operation, and highlighting its crucial role in quantum algorithms like Shor’s algorithm for integer factorization. The analysis also addresses the mathematical foundations of the QFT, its implementation in quantum circuits, and the key advantages and challenges associated with its use, such as measurement precision and quantum decoherence. Finally, it concludes with an exploration of the current and potential applications of QFT in quantum computing.
Fourier Transform (FT) is an important signal processing technique that translates time-domain signals to frequency-domain forms. It is widely used in several applications, including 5G networks, image processing, & spectrum analysis. In 5G networks, efficient frequency analysis is critical for noise reduction, channel optimisation, and signal dependability.This study explores the implementation of Classical Fourier Transform, Fast Fourier Transform, and Quantum Fourier Transform using Python (NumPy, Pandas, Matplotlib) and Qiskit. The FFT significantly improves processing speed, making it suitable for real-time applications. On the other hand, QFT leverages quantum superposition and entanglement, offering promising advancements for future high-speed communication and secure data transmission. Additionally, the signal is successfully reconstructed using both the Inverse Fast Fourier Transform (IFFT) and the Inverse Quantum Fourier Transform (IQFT). While IFFT efficiently restores the original signal with minimal numerical artifacts, IQFT ensures exact reconstruction without errors. The study also includes execution on IBM Quantum’s real hardware, showcasing the practical feasibility of quantum-based signal processing.