Quantum image processing
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Quantum image processing (QIP) is primarily devoted to using quantum computing and quantum information processing to create and work with quantum images. Due to some of the astounding properties inherent to quantum computation, notably entanglement and parallelism, it is anticipated that QIP technologies will offer capabilities and performances that are, as yet, unrivaled by their traditional equivalents. These improvements could be in terms of computing speed, guaranteed security, and minimal storage requirements, etc.,
Vlasov's work in 1997 focused on the use of a quantum system to recognize orthogonal images. This was followed by efforts using quantum algorithms to search specific patterns in binary images and detect the posture of certain targets. Notably, more optics-based interpretation for quantum imaging were initially experimentally demonstrated in  and formalized in  after seven years. Venegas-Andraca and Bose's Qubit Lattice describes quantum images in 2003. Simultaneously, Lattorre proposed another kind of representation, called the Real Ket, whose purpose was to encode quantum images as a basis for further applications in QIMP.
Technically, these pioneering efforts with the subsequent studies related to them can be classified into three main groups:
- Quantum-assisted digital image processing (QDIP): These applications aim at improving digital or classical image processing tasks and applications.
- Optics-based quantum imaging (OQI)
- Classically-inspired quantum image processing (QIP)
Quantum image manipulations
A lot of the effort in QIP has been focused on designing algorithms to manipulate the position and color information encoded using the FRQI and its many variants. For instance, FRQI-based fast geometric transformations including (two-point) swapping, flip, (orthogonal) rotations and restricted geometric transformations to constrain these operations to a specified area of an image were initially proposed. Recently, NEQR-based quantum image translation to map the position of each picture element in an input image into a new position in an output image and quantum image scaling to resize a quantum image were discussed. While FRQI-based general form of color transformations were first proposed by means of the single qubit gates such as X, Z, and H gates. Later, MCQI-based channel of interest (CoI) operator to entail shifting the grayscale value of the preselected color channel and the channel swapping (CS) operator to swap the grayscale values between two channels were fully discussed in.
To illustrate the feasibility and capability of QIP algorithms and application, researchers always prefer to simulate the digital image processing tasks on the basis of the QIRs that we already have. By using the basic quantum gates and the aforementioned operations, so far, researchers have contributed to quantum image feature extraction, quantum image segmentation, quantum image morphology, quantum image comparison, quantum image filtering, quantum image classification, quantum image stabilization, among others. In particular, QIMP-based security technologies have attracted extensive interest of researchers as presented in the ensuing discussions. Similarly, these advancements have led to many applications in the areas of watermarking, encryption, and steganography etc., which form the core security technologies highlighted in this area.
In general, the work pursued by the researchers in this area are focused on expanding the applicability of QIP to realize more classical-like digital image processing algorithms; propose technologies to physically realize the QIMP hardware; or simply to note the likely challenges that could impede the realization of some QIMP protocols.
Quantum image transform
By encoding and processing the image information in quantum-mechanical systems, a framework of quantum image processing is presented, where a pure quantum state encodes the image information: to encode the pixel values in the probability amplitudes and the pixel positions in the computational basis states. Given an image , where represents the pixel value at position with and , a vector with elements can be formed by letting the first elements of be the first column of , the next elements the second column, etc.
A large class of image operations is linear, e.g., unitary transformations, convolutions, and linear filtering. In the quantum computing, the linear transformation can be represented as with the input image state and the output image state . A unitary transformation can be implemented as a unitary evolution. Some basic and commonly used image transforms (e.g., the Fourier, Hadamard, and Haar wavelet transforms) can be expressed in the form , with the resulting image and a row (column) transform matrix . The corresponding unitary operator can then be written as . Several commonly used two-dimensional image transforms, such as the Haar wavelet, Fourier, and Hadamard transforms, are experimentally demonstrated on a quantum computer, with exponential speedup over their classical counterparts. In addition, a novel highly efficient quantum algorithm is proposed and experimentally implemented for detecting the boundary between different regions of a picture: It requires only one single-qubit gate in the processing stage, independent of the size of the picture.
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