Kai Lu

Bio: Kai Lu is an academic researcher from National University of Defense Technology. The author has contributed to research in topics: Quantum algorithm & Quantum phase estimation algorithm. The author has an hindex of 5, co-authored 7 publications receiving 559 citations.

NEQR: a novel enhanced quantum representation of digital images

Abstract: Quantum computation is becoming an important and effective tool to overcome the high real-time computational requirements of classical digital image processing. In this paper, based on analysis of existing quantum image representations, a novel enhanced quantum representation (NEQR) for digital images is proposed, which improves the latest flexible representation of quantum images (FRQI). The newly proposed quantum image representation uses the basis state of a qubit sequence to store the gray-scale value of each pixel in the image for the first time, instead of the probability amplitude of a qubit, as in FRQI. Because different basis states of qubit sequence are orthogonal, different gray scales in the NEQR quantum image can be distinguished. Performance comparisons with FRQI reveal that NEQR can achieve a quadratic speedup in quantum image preparation, increase the compression ratio of quantum images by approximately 1.5X, and retrieve digital images from quantum images accurately. Meanwhile, more quantum image operations related to gray-scale information in the image can be performed conveniently based on NEQR, for example partial color operations and statistical color operations. Therefore, the proposed NEQR quantum image model is more flexible and better suited for quantum image representation than other models in the literature.

A novel quantum representation for log-polar images

Abstract: The power of quantum mechanics has been extensively exploited to meet the high computational requirement of classical image processing. However, existing quantum image models can only represent the images sampled in Cartesian coordinates. In this paper, quantum log-polar image (QUALPI), a novel quantum image representation is proposed for the storage and processing of images sampled in log-polar coordinates. In QUALPI, all the pixels of a QUALPI are stored in a normalized superposition and can be operated on simultaneously. A QUALPI can be constructed from a classical image via a preparation whose complexity is approximately linear in the image size. Some common geometric transformations, such as symmetry transformation, rotation, etc., can be performed conveniently with QUALPI. Based on these geometric transformations, a fast rotation-invariant quantum image registration algorithm is designed for log-polar images. Performance comparison with classical brute-force image registration method reveals that our quantum algorithm can achieve a quartic speedup.

Local feature point extraction for quantum images

Abstract: Quantum image processing has been a hot issue in the last decade. However, the lack of the quantum feature extraction method leads to the limitation of quantum image understanding. In this paper, a quantum feature extraction framework is proposed based on the novel enhanced quantum representation of digital images. Based on the design of quantum image addition and subtraction operations and some quantum image transformations, the feature points could be extracted by comparing and thresholding the gradients of the pixels. Different methods of computing the pixel gradient and different thresholds can be realized under this quantum framework. The feature points extracted from quantum image can be used to construct quantum graph. Our work bridges the gap between quantum image processing and graph analysis based on quantum mechanics.

FLPI: representation of quantum images for log-polar coordinate

Abstract: We propose an effective method, flexible log-polar image (FLPI) to represent quantum images sampled in log-polar coordinate system. Each pixel is represented by three qubit sequences and the whole image is stored into a normalized quantum superposition state. If needed, a flexible qubit sequence can be added to represent multiple images. Through elementary operations, both arbitrary rotation transformation and similarity evaluation can be realized. We also design an image registration algorithm to recognize the angular difference between two images if one is rotated from the other. It is proven that the proposed algorithm could get conspicuous improvement in performance.

A survey of quantum image representations

Abstract: Quantum image processing (QIMP) is devoted to utilizing the quantum computing technologies to capture, manipulate, and recover quantum images in different formats and for different purposes. Logically, percolating this requires that representations to encode images based on the quantum mechanical composition of any potential quantum computing hardware be conjured. This paper gathers the current mainstream quantum image representations (QIRs) and discusses the advances made in the area. Some similarities, differences, and likely applications for some of the available QIRs are reviewed. We believe this compendium will provide the readership an overview of progress witnessed in the area of QIMP while also simulating further interest to pursue more advanced research in it.

Quantum image encryption based on generalized Arnold transform and double random-phase encoding

Abstract: A quantum realization of the generalized Arnold transform is designed. A novel quantum image encryption algorithm based on generalized Arnold transform and double random-phase encoding is proposed. The pixels are scrambled by the generalized Arnold transform, and the gray-level information of images is encoded by the double random-phase operations. The keys of the encryption algorithm include the independent parameters of coefficients matrix, iterative times and classical binary sequences, and thus, the key space is extremely large. Numerical simulations and theoretical analyses demonstrate that the proposed algorithm with good feasibility and effectiveness has lower computational complexity than its classical counterpart.

Quantum image scaling using nearest neighbor interpolation

Abstract: Although image scaling algorithms in classical image processing have been extensively studied and widely used as basic image transformation methods, the quantum versions do not exist. Therefore, this paper proposes quantum algorithms and circuits to realize the quantum image scaling based on the improved novel enhanced quantum representation (INEQR) for quantum images. It is necessary to use interpolation in image scaling because there is an increase or a decrease in the number of pixels. The interpolation method used in this paper is nearest neighbor which is simple and easy to realize. First, NEQR is improved into INEQR to represent images sized $$2^{n_{1}} \times 2^{n_{2}}$$2n1×2n2. Based on it, quantum circuits for image scaling using nearest neighbor interpolation from $$2^{n_{1}} \times 2^{n_{2}}$$2n1×2n2 to $$2^{m_{1}} \times 2^{m_{2}}$$2m1×2m2 are proposed. It is the first time to give the quantum image processing method that changes the size of an image. The quantum strategies developed in this paper initiate the research about quantum image scaling.

A novel quantum representation for log-polar images

Abstract: The power of quantum mechanics has been extensively exploited to meet the high computational requirement of classical image processing. However, existing quantum image models can only represent the images sampled in Cartesian coordinates. In this paper, quantum log-polar image (QUALPI), a novel quantum image representation is proposed for the storage and processing of images sampled in log-polar coordinates. In QUALPI, all the pixels of a QUALPI are stored in a normalized superposition and can be operated on simultaneously. A QUALPI can be constructed from a classical image via a preparation whose complexity is approximately linear in the image size. Some common geometric transformations, such as symmetry transformation, rotation, etc., can be performed conveniently with QUALPI. Based on these geometric transformations, a fast rotation-invariant quantum image registration algorithm is designed for log-polar images. Performance comparison with classical brute-force image registration method reveals that our quantum algorithm can achieve a quartic speedup.

LSB Based Quantum Image Steganography Algorithm

Abstract: Quantum steganography is the technique which hides a secret message into quantum covers such as quantum images. In this paper, two blind LSB steganography algorithms in the form of quantum circuits are proposed based on the novel enhanced quantum representation (NEQR) for quantum images. One algorithm is plain LSB which uses the message bits to substitute for the pixels’ LSB directly. The other is block LSB which embeds a message bit into a number of pixels that belong to one image block. The extracting circuits can regain the secret message only according to the stego cover. Analysis and simulation-based experimental results demonstrate that the invisibility is good, and the balance between the capacity and the robustness can be adjusted according to the needs of applications.