Medical image encryption algorithm based on a new five-dimensional multi-band multi-wing chaotic system and QR decomposition

In Gaussian elimination and LU factorization we solve a linear system by transforming it to triangular form. These are not the only kind of transformations that can be used for such a task. Matrices with orthonormal columns, called unitary matrices can be used to reduce a square matrix to upper triangular form and more generally a rectangular matrix to upper triangular (also called upper trapezoidal) form. This lead to a decomposition of a rectangular matrix known as a QR decomposition and a reduced form which we refer to as a QR factorization. The QR decomposition and factorization will be used in later chapters to solve least squares- and eigenvalue problems.

A visually meaningful image encryption scheme with an asymmetric structure based on the discrete wavelet transform (DWT) and Schur decomposition is proposed in this study. First, the RSA algorithm is used to generate the initial values for the chaotic system to produce the random sequence. Then, both scrambling and diffusion operations are performed on the plain image to obtain the preencrypted image. Moreover, the Schur decomposition is applied on the preencrypted plain image to obtain the upper triangular and orthogonal matrices. Second, the cover image is scrambled followed by a DWT operation. Four subbands are then formed, namely, LL, HL, LH, and HH. Finally, the former upper triangular matrix and orthogonal matrix are embedded into subbands LH and HH produced by the cover image. After the application of the inverse DWT and inverse scrambling operation, the final visually meaningful cover image embedded with a secret plain image can be obtained. No one can identify any useful information about the plain image from the final embedded cover image, nor can anybody know that there is any hidden secret image. Experimental simulations show that the normalized correlation values between the original cover image and the final visually meaningful cover image are approximately 0.9997. Therefore, the proposed encryption scheme is imperceptible for secret image communications.

The protection of sensitive and confidential data become a challenging task in the present scenario as more and more digital data is stored and transmitted between the end users. The privacy is vitally necessary in case of medical data, which contains the important information of the patients. In this article, a novel biometric inspired medical encryption technique is proposed based on newly introduced parameterized all phase orthogonal transformation (PR-APBST), singular value, and QR decomposition. The proposed technique utilizes the biometrics of the patient/owner to generate a key management system to obtain the parameters involved in the proposed technique. The medical image is then encrypted employing PR-APBST, QR and singular value decomposition and is ready for secure transmission or storage. Finally, a reliable decryption process is employed to reconstruct the original medical image from the encrypted image. The validity and feasibility of the proposed framework have been demonstrated using an extensive experiments on various medical images and security analysis.

In this paper, a new nonlinear optical multi-image authentication scheme is proposed based on Kramers-Kronig digital holography and orthogonal triangular decomposition or QR decomposition. Here, the complex light field carrying the information of multiple images is modulated by random phase masks and propagated at certain distance. Afterwards, the QR decomposition is applied to the complex wavefront to generate the private keys and to add the non-linearity in the scheme. Next, the product of orthogonal matrix and upper triangular matrix is processed further. The obtained output is modulated by different phase masks and interfered with reference beam to record the encrypted image. For decryption, the Kramer-Kronig relation is utilized to extract the plaintext images directly with only the positive frequency part. A series of numerical simulations are conducted to validate the efficacy and robustness of proposed image authentication scheme.

The QR decomposition (QRD) is an implementation prerequisite for many different detection algorithms in MIMO (multiple-input multiple-output) wisely communication system. In this paper, a QR decomposition core processor which decomposes a matrix into an orthogonal and triangular matrix using Gram-Schmidt orthonormalization method is designed and implemented using a 32-bit RISC processor based on FPGA.

Overhead manipulation tasks often require collaborations between two operators, which becomes challenging in confined spaces such as in a compartment. Supernumerary Robotic Limb (SuperLimb), as a promising wearable robotic solution, can provide assistance in terms of broader workspace, wider manipulation functionalities and safer working conditions. However, the safety concerns of human-centered SuperLimb interaction mechanisms are rarely studied to date, particularly regarding human standing balance. This study proposes a balance controller by which one individual operator can accomplish overhead tasks with the assistance of SuperLimb via tunable interaction force and supporting force regulation. The SuperLimb-human interaction is modeled and a dynamics control method based on QR decomposition (also known as QR factorization, in which a matrix is factorized into an orthogonal matrix and an upper triangular matrix) is adopted to decouple joint torques of the SuperLimb and the interaction forces. Therefore, the supporting forces can be regulated independently to guarantee the operator-SuperLimb interaction forces in a safe region. Force plate is used for measuring the CoP position as an evaluation method of the standing balance. The critical horizontal push force is learned through experiment to guide the balance controller. This method is implemented on a SuperLimb prototype worn on the operator's back, to provide necessary supporting forces on overhead object while allowing the operator to move freely underneath.

We propose a data hidding technique in a stilt image. This technique is based on chaotic sequence in the transform domain of covert image. We use different chaotic random sequences multiplied by multiple sensitive images, respectively, to spread the spectrum of sensitive images. Multiple sensitive images are hidden in s covert image as a form of noise. The results of theoretical analysis and computer simulation show the new hiding technique have better properties with high security, imperceptibility and capacity for hidden information in comparison with the conventional scheme such as LSB (Least Significance Bit).

The research on the balance of chaotic sequence has important significance to spread-spectrum communication. The relationship between the balance and the parameter of four typical chaotic maps (Chebyshev, improved Logistic, Logistic and Tent) was discussed. The new numeric ranges of initial value and fractal parameter were decided, which provided reference for the generation of chaotic spread-spectrum sequence. Through the graphs of the four chaotic sequences' balance and the error-bit rate performance of these systems with the four chaotic sequences' map parameters, the new numeric ranges were validated. Both simulation results and the analysis show that the balance of Chebyshev is the best.

QR decomposition is a computationally intensive process often required for MIMO detection. A technique that allows a reduction in the computational complexity of MIMO QR detection receivers is proposed for non-stationary channel . The technique involves tracking of the upper triangular matrix and reduction of the frequency of QR decomposition. This reduction comes at the cost of increased equalization error from the outdated Q matrix that must be used between successive QR decompositions. When compared to the similar setup but with the channel matrix tracking, the proposed method yields 33% computational complexity reduction without any loss of performance.

In QR factorization of a sparse m{times}n matrix A (m {ge} n) the orthogonal factor Q is often stored implicitly as a lower trapezoidal matrix H known as the Householder matrix. This paper presents a simple characterization of the row structure of Q, which could be used as the basis for a sparse data structure that can store Q explicitly. The new characterization is a simple extension of a well known row-oriented characterization of the structure of H. Hare, Johnson, Olesky, and van den Driessche have recently provided a complete sparsity analysis of the QR factorization. Let U be the matrix consisting of the first n columns of Q. Using results from, we show that the data structures for H and U resulting from our characterizations are tight when A is a strong Hall matrix. We also show that H and the lower trapezoidal part of U have the same sparsity characterization when A is strong Hall. We then show that this characterization can be extended to any weak Hall matrix that has been permuted into block upper triangular form. Finally, we show that permuting to block triangular form never increases the fill incurred during the factorization.

A novel scheme based on QR decomposition is proposed in this paper to remove multiplicative noise, speckle noise, from medical ultrasound images. A speckle noisy image is segmented into small overlapping blocks. A global covariance matrix for the whole image is obtained by calculating the average of covariances of the corresponding blocks. QR decomposition is then applied to the global covariance matrix. Based on the principle of orthogonality of signal and noise, it is found that the first subset of orthogonal vectors of the Q matrix resulted from the QR decomposition is sufficient to construct a projection matrix capable of filtering out speckle noise. When it is applied to simulated and real medical ultrasound images, and with reasonable performance in terms of resolution and edge detection, the proposed approach has outperformed benchmark filtering schemes such as Wavelets, Wiener and Lee. It has secured the highest Signal to Noise Ratio (SNR) and Peak Signal to Noise Ratio (PSNR).

A QR decomposition aided belief propagation (QR‐BP) detector for multiple‐input multiple‐output (MIMO) systems is proposed. Before the iterative message passing process, linear transformation is performed by using the unitary matrix obtained from the QR decomposition of the original MIMO channel matrix. Then, the original MIMO channel matrix is replaced by an upper triangular channel matrix after the linear transformation and the proposed QR‐BP detector operates over the new bipartite graph from the upper triangular channel matrix. Therefore, the number of cycles in the new bipartite graph is significantly decreased when compared with the fully connected bipartite graph from the original MIMO channel matrix. In addition, since the unitary matrix is utilised for the linear transformation, there is no information loss on the likelihoods estimated from noisy observations. Simulation results verify that the proposed QR‐BP detector outperforms existing BP detectors and achieves near‐optimum performance close to the maximum‐likelihood detector in terms of bit error ratio.

This study proposes an efficient detection algorithm for double space-time block codes (DSTBCs) to improve the algorithm of Kim et al. The proposed algorithm applies QR decomposition to the channel matrix of the DSTBC to obtain an upper triangular matrix. The diagonal entries of the upper triangular matrix contain two different values. The proposed algorithm adaptively determines the number of candidates for the DSTBC according to the ratio of these two diagonal values. When their ratio is large, the number of the candidates decreases. Finally, the detection result is searched among the candidates based on a maximum-likelihood criterion. Numerical results demonstrate that the computational complexity for the search process can be reduced by 70% with little performance loss at a bit error rate (BER)of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> .

The problem of QR decomposition is considered one of the fundamental problems commonly encountered in both scientific research and engineering applications. In this paper, the QR decomposition for complex-valued time-varying matrices is analyzed and investigated. Specifically, by applying the zeroing neural dynamics (ZND) method, dimensional reduction method, equivalent transformations, Kronecker product, and vectorization techniques, a new continuous-time QR decomposition (CTQRD) model is derived and presented. Then, a novel eleven-instant Zhang et al discretization (ZeaD) formula, with fifth-order precision, is proposed and studied. Additionally, five discrete-time QR decomposition (DTQRD) models are further obtained by using the eleven-instant and other ZeaD formulas. Theoretical analysis and numerical experimental results confirmed the correctness and effectiveness of the proposed continuous and discrete ZND models.

Optical color image encryption based on computer generated hologram and chaotic theory