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Quantum image processing has become a significant aspect within the field of quantum information processing because the image is an essential carrier of information, and quantum computation has powerful image processing ability. Image scrambling algorithms are often required as initial image operations in quantum image processing applications such as quantum image encryption and watermarking. However, the efficiency of existing quantum image scrambling algorithms needs to be improved urgently, especially in terms of periodicity. Therefore, a novel quantum image scrambling algorithm based on discrete Baker map is proposed in this paper, which can be implemented by swapping qubits with low circuit complexity. The quantum version of discrete Baker map is deduced and the corresponding quantum circuit is designed. The simulation results show that the scrambling algorithm has the characteristic of long period, which can further enhance the security of quantum image encryption algorithms. Besides, for generalized discrete Baker maps, the conditions that they can be implemented by swapping qubits are given. Moreover, the number of discrete Baker maps satisfying the conditions is also calculated.

With the development of quantum computing, the application of it to image processing has lots of advantages compared to classical image processing. In this paper, we propose a scheme to extract the interest point in quantum images. Interest point is a kind of feature point which can help to identify the target object in the image. Our scheme is based on the idea of Luminance Contrast (LC) algorithm. The scheme computes the absolute value of gray level differences between a pixel and the others, and then adds all these differences together. The sum is defined as a saliency. After computing the saliency of every pixel, we label the pixels with the maximal saliency as the interest points. The algorithm has pretty good performance and its time complexity is much better than the classical algorithm in same conditions, which provides a new idea for the extraction of image interest point.

The classical image segmentation algorithm based on local adaptive threshold can effectively segment images with uneven illumination, but with the increase of the image data, the real-time problem gradually emerges. In this paper, a quantum segmentation algorithm based on local adaptive threshold for NEQR image is proposed, which can use quantum mechanism to simultaneously compute local thresholds for all pixels in a gray-scale image and quickly segment the image into a binary image. In addition, several quantum circuit units, including median calculation, quantum binarization, etc. are designed in detail, and then a complete quantum circuit is designed to segment NEQR images by using fewer qubits and quantum gates. For a $2^n\times 2^n$ image with $q$ gray-scale levels, the complexity of our algorithm can be reduced to O$(n^2+q)$, which is an exponential speedup compared to the classic counterparts. Finally, the experiment is conducted on IBM Q to show the feasibility of our algorithm in the noisy intermediate-scale quantum (NISQ) era.

The quantum adder is a vital arithmetic operation for quantum algorithms. However, the existing quantum floating-point adders only considered the case of two normal numbers. In this paper, we propose an enhanced quantum floating-point adder based on IEEE 754 standard. First, we divide quantum floating-point adders into four cases: the normal case, subnormal case, mixed case, and special case. Then, we propose a result-sign and mantissa-sign determining unit to avoid conversion from sign-magnitude to two complements. Moreover, we design a new quantum leading zero detector with the optimized T-depth and T-count. Comparison results reveal that the proposed floating-point adder has lower circuit width, T-depth, and T-count than the current works.

Reviewing past researches on quantum image scaling, only 2D images are studied. And, in a quantum system, the processing speed increases exponentially since parallel computation can be realized with superposition state when compared with classical computer. Consequently, this paper proposes quantum multidimensional color image scaling based on nearest-neighbor interpolation for the first time. Firstly, flexible representation of quantum images (FRQI) is extended to multidimensional color model. Meantime, the nearest-neighbor interpolation is extended to multidimensional color image and cycle translation operation is designed to perform scaling up operation. Then, the circuits are designed for quantum multidimensional color image scaling, including scaling up and scaling down, based on the extension of FRQI. In addition, complexity analysis shows that the circuits in the paper have lower complexity. Examples and simulation experiments are given to elaborate the procedure of quantum multidimensional scaling.

Quantum machine learning is expected to be one of the potential applications that can be realized in the near future. Finding potential applications for it has become one of the hot topics in the quantum computing community. With the increase of digital image processing, researchers try to use quantum image processing instead of classical image processing to improve the ability of image processing. Inspired by previous studies on the adversarial quantum circuit learning, we introduce a quantum generative adversarial framework for loading and learning a quantum image. In this paper, we extend quantum generative adversarial networks to the quantum image processing field and show how to learning and loading an classical image using quantum circuits. By reducing quantum gates without gradient changes, we reduced the number of basic quantum building block from 15 to 13. Our framework effectively generates pure state subject to bit flip, bit phase flip, phase flip, and depolarizing channel noise. We numerically simulate the loading and learning of classical images on the MINST database and CIFAR-10 database. In the quantum image processing field, our framework can be used to learn a quantum image as a subroutine of other quantum circuits. Through numerical simulation, our method can still quickly converge under the influence of a variety of noises.

To reduce the time complexity of quantum morphology operations, two kinds of improved quantum dilation and erosion operations are proposed. Quantum parallelism is well used in the design of these operations. Consequently, the time complexity is greatly reduced compared with the previous quantum dilation and erosion operations. The neighborhood information of each pixel is needed in the process of designing quantum dilation and erosion operations. In order to get the neighborhood information, quantum position shifting transformation is utilized, which can make the neighborhood information store in a quantum image set. In this image set, the neighborhood information of pixel at location ($j$, $i$) is stored at the same location ($j$, $i$) of other images in the image set. All the pixels will be processed simultaneously, which is the performance of quantum parallelism. The time complexity analysis shows that these quantum operations have polynomial-time complexity which is much lower than the exponential-time complexity of the previous version.

One of the most considering matters in the field of quantum information processing is quantum data hiding including quantum steganography and quantum watermarking. This field is an efficient tool for protecting any kind of digital data. In this paper, three quantum color images steganography algorithms are investigated based on Least Significant Bit (LSB). The first algorithm employs only one of the image’s channels to cover secret data. The second procedure is based on LSB XORing technique, and the last algorithm utilizes two channels to cover the color image for hiding secret quantum data. The performances of the proposed schemes are analyzed by using software simulations in MATLAB environment. The analysis of PSNR, BER and Histogram graphs indicate that the presented schemes exhibit acceptable performances and also theoretical analysis demonstrates that the networks complexity of the approaches scales squarely.

To address quantum description for color images, an improved FRQI model called FRQCI is proposed in this paper. In our model, the qubit has two-phase parameters $\theta$ and $\varphi$, and the primary color R is stored in $\theta$, the primary colors G and B are stored in $\varphi$. We provide several simple image processing operators, including color change and geometric transformation. Next, we focus on an encryption algorithm, which includes two parts: position scrambling and color transformation. All operations involved in this paper are implemented by the rotation of the qubit on the Bloch sphere. The simulation results on classical computer show the effectiveness of the proposed method.

In quantum image steganography, embedding capacity and security are two important issues. This paper presents a novel quantum steganography scheme using color images as cover images. First, the secret information is divided into 3-bit segments, and then each 3-bit segment is embedded into the LSB of one color pixel in the cover image according to its own value and using Gray code mapping rules. Extraction is the inverse of embedding. We designed the quantum circuits that implement the embedding and extracting process. The simulation results on a classical computer show that the proposed scheme outperforms several other existing schemes in terms of embedding capacity and security.

Image scaling is the basic operation that is widely used in classic image processing, including nearest-neighbor interpolation, bilinear interpolation, and bicubic interpolation. In quantum image processing (QIP), the research on image scaling is focused on nearest-neighbor interpolation, while the related research of bilinear interpolation is very rare, and that of bicubic interpolation has not been reported yet. In this study, a new method based on quantum Fourier transform (QFT) is designed for bilinear interpolation of images. Firstly, some basic functional modules are constructed, in which the new method based on QFT is adopted for the design of two core modules (i.e. addition and multiplication), and then these modules are used to design quantum circuits for the bilinear interpolation of images, including scaling-up and down. Finally, the complexity analysis of the scaling circuits based on the elementary gates is deduced. Simulation results show that the scaling image using bilinear interpolation is clearer than that using the nearest-neighbor interpolation.

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.

Quantum edge detection is one of the important part of quantum image processing. In this paper, a quantum edge detection algorithm is designed for the quantum representation of multi-wavelength image (QRMW) model. The algorithm includes all stages of filtering, enhancement and detection. The proposed algorithm is also designed to apply any filtering operation to QRMW images, not only for a particular filtering operation. The proposed algorithm aims to solve the problems that quantum edge detection algorithms in the literature have processing only for a particular operator and noise reduction. Moreover, the algorithm aims to perform operations more efficiently by using less resources. Low-pass filter (LPF) smoothing operators are applied in the filtering stage for the noise reduction problem. In order to apply all filtering operations to the image, arithmetic operators that can operate with all signed integers are used in the algorithm. The operators Sobel, Prewitt and Scharr in the enhancement stage and the gradient method in the detection stage are used for both verification of the proposed algorithm and comparisons with the existing algorithms. A method with quantitative outcomes is shown to evaluate the performance of the edge detection algorithms. Analysis of the simulations performed on sample images with different operators. The circuit complexity of the algorithm is presented and the comparisons are made with the existing studies. The superiority of the proposed algorithm and its flexibility to be used in other studies are clearly demonstrated by analysis.

Quantum image representation is an important research direction of quantum image processing, which mainly studies the use of quantum properties to encode and store images. At present, most quantum image representation models store image grayscale-related information, but lack histogram-related information. A few quantum representation models that store image histogram information cannot accurately retrieve the image, resulting in the difficulty of quantum image histogram processing. Therefore, this paper proposes an improved order-encoded quantum image representation model ONEQR, which uses the quantum basis state sequence to store the grayscale information, real position information and ascending position information of the image, which can not only solve the problem of inability to accurately retrieve the image, but also store the histogram information of the image, which is convenient for the implementation of the histogram processing algorithm of quantum image; In addition, based on ONEQR, a quantum image representation model MULTI-ONEQR that stores multiple images is proposed, and based on this model, a quantum image histogram specification (HS) algorithm is proposed, which can use quantum properties to complete image HS in parallel. Finally, the simulation experiment of the HS algorithm based on the ONEQR model is carried out to verify the effectiveness of the algorithm.

The development of new quantum watermarking is in full swing, and it is crucial to test the robustness of these proposed watermarking schemes. In this paper, different quantum circuits are introduced to realize geometric transformations on quantum images, which serve as a means of simulating geometric attacks on quantum watermark images. Receivers may get distorted images, and the extracted watermark images may also be disrupted. To recover the geometric order of the quantum watermark images, a strategy is proposed to identify the trajectory of qubit alterations. Quantum circuits can be designed accordingly to restore the original order of the watermark images, which receivers could use before the extraction process to mitigate the impact of geometric attacks. Experimental simulations demonstrate how attacks affect the quantum watermark images and the extracted watermark images. Additionally, it illustrates how quantum recovery circuits step by step act on images that have been geometrically attacked. An analysis of the complexity of geometric restoration circuits reveals that quantum circuits exhibit better performance compared to classical circuits.