In order to solve the high complexity of classical image processing, a quantum scheme for image sharpness estimation based on the Laplacian operator is proposed. The mean of grayscale gradients of all pixels is regarded as the sharpness estimation metric. A new quantum image representation model is presented by extending the Novel Enhanced Quantum Representation (NEQR) model, which is greatly useful for quantum image convolution. In quantum platforms, it has been shown that the mean calculation of numbers is rather difficult because the numbers are stored in a quantum superposition state. In order to solve this problem, we put forward an algorithm which essential idea is cyclically shifting the superposition state and iteratively calculating the mean of the new one and the original state. The mean can be obtained from the superposition state by only one quantum measurement. By analyzing the space complexity and time complexity, the scheme is far superior to classical ones in terms of resource consumption and execution speed. In addition, the results of simulation experiments show that for noiseless images, the performance of the scheme is consistent with subjective visual perception of images sharpness.
In order to solve the high complexity of classical image processing, a quantum scheme for image sharpness estimation based on the Laplacian operator is proposed. The mean of grayscale gradients of all pixels is regarded as the sharpness estimation metric. A new quantum image representation model is presented by extending the Novel Enhanced Quantum Representation (NEQR) model, which is greatly useful for quantum image convolution. In quantum platforms, it has been shown that the mean calculation of numbers is rather difficult because the numbers are stored in a quantum superposition state. In order to solve this problem, we put forward an algorithm which essential idea is cyclically shifting the superposition state and iteratively calculating the mean of the new one and the original state. The mean can be obtained from the superposition state by only one quantum measurement. By analyzing the space complexity and time complexity, the scheme is far superior to classical ones in terms of resource consumption and execution speed. In addition, the results of simulation experiments show that for noiseless images, the performance of the scheme is consistent with subjective visual perception of images sharpness.
Abstract With the increase in the quantity and quality of images that need to be processed, there are higher requirements for the speed of image processing. Thus, it is necessary to speed-up the image processing algorithms. In this paper, we design a quantum image edge detection algorithm based on Laplacian of Gaussian (LoG) operator, which has significant acceleration due to the quantum parallelism. Firstly, the quantum circuit of the novel enhanced quantum image representation (NEQR) model is improved to represent multiple quantum images simultaneously with lower time complexity. Secondly, the quantum subtractor and quantum comparator are optimized. Thirdly, quantum adder, quantum multiplier, quantum comparator, and quantum subtractor are adopted to design the quantum circuit of LoG operator and zero-crossing detector, which constitute the quantum edge detection algorithm. Finally, the algorithm is simulated on the IBM Quantum Experience (IBM Q) platform to verify its feasibility. Compared with the existing state-of-the-art algorithms, the proposed quantum image edge detection algorithm has significant improvement in time complexity.
This work introduces a novel quantum algorithm for gradient-based edge detection that operates entirely within the quantum circuit model. Grayscale images are encoded using the Novel Enhanced Quantum Representation (NEQR), allowing exact arithmetic on pixel intensities. Directional gradients are computed by generating superpositions of neighboring pixels via cyclic shift operations and performing subtraction with an exact quantum arithmetic circuit. To refine accuracy, we introduce a direction-aware shifting mechanism that aligns edges with the darker side of intensity transitions. Our novel Quantum Partitioning Algorithm enables efficient in-place thresholding of edge candidates. This work exhibits polynomial-time improvements and optimizes the ancilla count compared to previous NEQR-based quantum edge detection algorithms. These results demonstrate a resource-efficient and fully quantum approach to edge detection, highlighting a practical quantum advantage in image processing.
Abstract Quantum Image Representation (QIR) is a fundamental concept in quantum image processing. It describes how classical images are converted into quantum states for processing on quantum computers. Researchers proposed several QIR models, with FRQI and NEQR being the most popular ones. These models show the possibilities of the quantum image encoding. Nevertheless, they are also limited in some way. Mostly, pixel intensity accuracy, the required number of qubits, and circuit complexity have trade-offs. Their application to Noisy Intermediate-Scale Quantum (NISQ) devices becomes challenging, the quantum resources being small in such devices, due to this. In the following paper, we introduce our own approach, which is the Intensity-Preserving Quantum image Representation (IP-QIR). The key aim of IP-QIR is to maintain the information about the grayscale intensities and decrease the amount of quantum resources. IP-QIR quantifies pixel intensities by a controlled rotation scheme. The measurement statistics of a single qubit hold the intensity information and the position qubits represent the spatial information. The strategy uses small patches of images rather than complete images to make it easy to implement. This will decrease the depth of circuit design and makes the approach less advanced to the near-term quantum hardware. IBM Qiskit simulations are used in assessing the performance of IP-QIR. The three types of grayscale images of which experiments are run are the synthetic image patches, SAR images and medical TB chest X-ray images. It is revealed that IP-QIR maintains the intensity information compared to the FRQI and NEQR. SAR and medical data can reach values of fidelity of 84.12\%. The other notable point is that the size of a 4 x 4 image patch only needs five qubits which are much lower than in NEQR. Meanwhile, good reconstruction accuracy is achieved. These findings demonstrate the fact that IP-QIR is an effective and realistic approach to quantum image representation on the NISQ-era quantum devices.
Quantum image representation (QIR) is the basic idea behind quantum image processing. It explains how a normal image is converted into quantum states so that it can be processed using quantum computers. The commonly used models for QIR are Flexible Representation of Quantum Images (FRQIs) and Novel Enhanced Quantum Representation (NEQR). Though these approaches highlight the potential of quantum-based image encoding, the limitation of practical applicability on Noisy Intermediate-Scale Quantum (NISQ) devices exists. In this paper, we propose an intensity-preserving quantum image representation (IP-QIR) scheme that aims to maintain accurate grayscale intensity information while significantly reducing quantum resource usage. The proposed method employs a controlled rotation-based encoding strategy, where pixel intensities are embedded into the measurement probability of a single intensity qubit, and spatial information is represented using position qubits. To further enhance feasibility on near-term quantum hardware, the framework operates on small image patches instead of full-resolution images, thereby reducing circuit depth and overall complexity. The performance of the proposed IP-QIR approach is evaluated through IBM Qiskit simulations on three types of grayscale images: synthetic image patches, synthetic aperture radar (SAR) images, and medical tuberculosis (TB) chest X-ray images. Experimental results demonstrate that IP-QIR achieves better intensity preservation than FRQIs and NEQR, with fidelity values reaching up to 84.12% for both SAR and medical datasets. In addition, IP-QIR represents a 4×4 image patch using only five qubits, which significantly reduces the qubit requirement when compared to NEQR, while still preserving high reconstruction accuracy.
Abstract Color images (i.e. RGB) contain rich visual information essential for object recognition, spatial context analysis, and decision-making across fields such as medical imaging, remote sensing, and computer vision. Processing such data efficiently requires significant computational resources, which can be addressed by the parallelism and speed of quantum computing. Representing RGB image data within quantum states enables efficient and scalable processing compared to classical methods. In recent years, various quantum image representation techniques have been developed based on probabilistic and basis state encoding. Probabilistic encoding methods are efficient for representing quantum binary images but face challenges in accurately reconstructing RGB images. This is due to the randomness introduced by measurement. To overcome this limitation, several basis state encoding approaches have been proposed. These methods map classical pixel values directly to quantum basis states. Thus enabling accurate grayscale and RGB image representation. However, they often require a larger number of qubits and complex gate operations, leading to higher circuit preparation costs. So, there exists substantial potential for quantum probabilistic RGB image representation using randomized measurements. Hence, our objective is to develop a probabilistic quantum image representation, capable of representing RGB images using fewer qubits. This method aims to reconstruct the classical image with high accuracy using randomized measurements, thereby addressing the major limitations of probabilistic methods. To balance image quality with resource efficiency, we propose an Improved Probabilistic Quantum Image Representation (IPQIR) method based on equal superposition states. This approach utilizes a quantum circuit with Hadamard Gate to encode classical pixel values into equal superposition states. The original image is then reconstructed by performing multiple quantum measurements and applying expectation value estimation to average the outcomes. To align with existing research in quantum image representation, quantum state tomography and different applications are utilized as standard evaluation methods to assess the effectiveness of the proposed algorithm. The tomography achieved a fidelity of 97.51%. In addition, various parametric and non-parametric statistical tests were performed to verify the accuracy of the reconstructed classical image. The high Pearson (0.9983) and Spearman (0.9959) correlation coefficients indicate a nearly perfect linear and monotonic relationship between the original and reconstructed images.
Quantum image processing is a system where both quantum computing and image processings are key. Now it is required to investigate how to apply image processing concepts such as image edge detection and improved Sobel operator, to quantum image processing. Just as traditional image processing helps to image manipulation, our efforts in quantum image processing contribute to the further development of quantum algorithm and quantum information theory. Edge detection is an important problem in traditional image processing, and image edge detection algorithm can filter image edge features and retain important attributes. We proposed a quantum edge detection algorithm, which employs improved Sobel operator to improve the performance, so as to solve the problem of unsatisfactory traditional image edge detection methods. In practical application, the amount of image data to be processed increases sharply, and the computing power of classical computer becomes a limitation. Quantum information processing can effectively accelerate many classical problems by virtue of quantum mechanical characteristics, such as quantum superposition, entanglement, parallelism. Our proposed method uses the novel enhanced quantum representation to store quantum images, which stores all the pixels in the image in a superimposed state, realizing parallel computation. The improved eight-direction Sobel operator is used to calculate the gray gradient, and the quantum circuit is designed to realize quantum edge detection. Simulation results have shown that our algorithm can extract edge with dimension 2n× 2nwhen the computational complexity is O(n2+ 2q+3). The improved algorithm can detect more edge details and has strong adaptability.