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In this paper, a design method of quantum circuits for threshold segmentation of gray-scale image is proposed, which is a quantum counterpart of classical optimum global thresholding using Otsu's method. First, we design a quantum circuit to obtain the histogram of the pixels distribution. Then, on this basis, we design the quantum circuits of some sub-modules, such as the cumulative histogram, cumulative mean, multiplication, division, the between-class variance and so on. Finally, all the between-class variances corresponding to each gray-level are sorted. At this time, the gray-level corresponding to the maximum of the between-class variance is the Otsu's threshold. For all the operations involved in the classical Otsu's threshold selection, we designed the corresponding quantum circuits, analyzed the computational complexity, and verified the correctness of these circuits by simulations on classical computers. [ABSTRACT FROM AUTHOR]

In this paper, we design a quantum associative classifier, which includes pattern storage and pattern classification. For pattern storage, we present a method to construct quantum superposition states with arbitrary number of basis states. The method employs three groups of qubits to encode the sequence number, category, and value of each sample respectively. Firstly, according to the total number of samples N to be stored, the number of sequence number qubits needed by associative classifier is calculated. Then, some quantum rotation gates and Hadamard gates are used to transform the sequence number qubits with initial state of | 0 ⟩ into the quantum equilibrium superposition state which contains exactly N basis states. Finally, according to the category and value of the sample to be stored, the remaining two groups of qubits with initial state of | 0 ⟩ are converted into corresponding quantum basis states by some controlled operations. For associative classification, we design a classification method based on quantum minimum search. Firstly, the Hamming distances between the input sample and all the stored samples are calculated, and then Grover’s algorithm with fixed phase is used to search the minimum value of these Hamming distances. At this time, the category of the stored sample corresponding to the minimum value is the category of the input sample. The specific classification results can be obtained through the measurement of quantum state in the register. The number of iterations of the search is exponentially lower than that of its classical counterpart, so that pattern classification can be realized quickly. [ABSTRACT FROM AUTHOR]

This paper presented a quantum representation and some basic operations for one-dimensional finite length digital signal. For the representation, similar to the existing flexible representation of quantum audio (FRQA), two sets of qubits are used to represent the amplitudes and positions of the signal, respectively, wherein the amplitude is represented by an (n + 1)-bit signed number in twos complement, including one sign bit, m integer bits and n − m fractional bits. The basic operations include the addition, subtraction, multiplication, division, and circular convolution of two digital signals. We designed the quantum circuits that implements these basic operations, analyzed the computational complexity, and verified the correctness of these circuits by simulations on classical computers. [ABSTRACT FROM AUTHOR]

At present, the classical least-significant-bit (LSB) based image steganography has been extended to quantum image processing. For the existing LSB-based quantum image steganography schemes, the embedding capacity is no more than 3 bits per pixel. Therefore, it is meaningful to study how to improve the embedding capacity of quantum image steganography. This work presents a novel LSB-based steganography using reflected Gray code for colored quantum images, and the embedding capacity of this scheme is up to 4 bits per pixel. In proposed scheme, the secret qubit sequence is considered as a sequence of 4-bit segments. For the four bits in each segment, the first bit is embedded in the second LSB of B channel of the cover image, and and the remaining three bits are embedded in LSB of RGB channels of each color pixel simultaneously using reflected-Gray code to determine the embedded bit from secret information. Following the transforming rule, the LSB of stego-image are not always same as the secret bits and the differences are up to almost 50%. Experimental results confirm that the proposed scheme shows good performance and outperforms the previous ones currently found in the literature in terms of embedding capacity. [ABSTRACT FROM AUTHOR]

In this paper we investigate the use of quantum Fourier transform (QFT) in the field of image processing. We consider QFT-based color image filtering operations and their applications in image smoothing, sharpening, and selective filtering using quantum frequency domain filters. The underlying principle used for constructing the proposed quantum filters is to use the principle of the quantum Oracle to implement the filter function. Compared with the existing methods, our method is not only suitable for color images, but also can flexibly design the notch filters. We provide the quantum circuit that implements the filtering task and present the results of several simulation experiments on color images. The major advantages of the quantum frequency filtering lies in the exploitation of the efficient implementation of the quantum Fourier transform. [ABSTRACT FROM AUTHOR]

In this paper, we investigated the quantum image spatial filtering, and focused on the design method of quantum weighted averaging filter and its application in image de-noising. To this end, we first designed the quantum circuits for some auxiliary modules, such as swapping two numbers, comparing two numbers, computing the weighted average of some integers, etc. Next, we constructed a weighted averaging filter of size 3 × 3 using auxiliary modules. The spatial filtering directly on the image itself can be accomplished by using designed filter. We provided the quantum circuits that implements the filtering task and presented the results of several simulation experiments on some gray images with different noises. The significance of this paper is to explore the quantum realization method of image filtering in spatial domain. [ABSTRACT FROM AUTHOR]

In this paper, a simple encryption scheme for quantum color image is proposed. Firstly, a color image is transformed into a quantum superposition state by employing NEQR (novel enhanced quantum representation), where the R,G,B values of every pixel in a 24-bit RGB true color image are represented by 24 single-qubit basic states, and each value has 8 qubits. Then, these 24 qubits are respectively transformed from a basic state into a balanced superposition state by employed the controlled rotation gates. At this time, the gray-scale values of R, G, B of every pixel are in a balanced superposition of 2 multi-qubits basic states. After measuring, the whole image is an uniform white noise, which does not provide any information. Decryption is the reverse process of encryption. The experimental results on the classical computer show that the proposed encryption scheme has better security. [ABSTRACT FROM AUTHOR]