Prescribed Performance Tracking Control of Lower-Triangular Systems with Unknown Fractional Powers

Xu, Kai-Di; Zhang, Jin-Xi

doi:10.3390/fractalfract7080594

Cited by 3 publications

(2 citation statements)

References 50 publications

(246 reference statements)

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“…Therefore, images processed by fractional differentials are clearer and have higher contrast [48]. This approach is widely used in image processing [5][6][7][8]49,50]. These works have shown that the fractional-order derivative performs well in achieving a satisfactory compromise between avoiding staircasing and preserving important fine-scale features such as edges and textures.…”

Section: Fractional-order Derivative In Image Deblurringmentioning

confidence: 99%

Preconditioning Technique for an Image Deblurring Problem with the Total Fractional-Order Variation Model

Al-Mahdi

2023

MCA

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Total fractional-order variation (TFOV) in image deblurring problems can reduce/remove the staircase problems observed with the image deblurring technique by using the standard total variation (TV) model. However, the discretization of the Euler–Lagrange equations associated with the TFOV model generates a saddle point system of equations where the coefficient matrix of this system is dense and ill conditioned (it has a huge condition number). The ill-conditioned property leads to slowing of the convergence of any iterative method, such as Krylov subspace methods. One treatment for the slowness property is to apply the preconditioning technique. In this paper, we propose a block triangular preconditioner because we know that using the exact triangular preconditioner leads to a preconditioned matrix with exactly two distinct eigenvalues. This means that we need at most two iterations to converge to the exact solution. However, we cannot use the exact preconditioner because the Shur complement of our system is of the form S=K*K+λLα which is a huge and dense matrix. The first matrix, K*K, comes from the blurred operator, while the second one is from the TFOV regularization model. To overcome this difficulty, we propose two preconditioners based on the circulant and standard TV matrices. In our algorithm, we use the flexible preconditioned GMRES method for the outer iterations, the preconditioned conjugate gradient (PCG) method for the inner iterations, and the fixed point iteration (FPI) method to handle the nonlinearity. Fast convergence was found in the numerical results by using the proposed preconditioners.

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Section: Fractional-order Derivative In Image Deblurringmentioning

confidence: 99%

Preconditioning Technique for an Image Deblurring Problem with the Total Fractional-Order Variation Model

Al-Mahdi

2023

MCA

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“…The histogram-based approach successfully achieves capacity increase and distortion control by fully utilizing the image redundancy. However, for histogram-based methods, the same distortion is introduced for each pixel in the same bin and cannot integrate adaptive embedding with the Human Visual System (HVS) [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

High-Quality Reversible Data Hiding Based on Multi-Embedding for Binary Images

Li,

Xiao

et al. 2023

Mathematics

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Unlike histogram-based reversible data hiding (RDH), the general distortion-based framework considers pixel-by-pixel distortions, which is a new research direction in RDH. The advantage of the general distortion-based RDH method is that it can enhance the visual quality of the marked image by embedding data into visually insensitive regions (e.g., edges and textures). In this paper, following this direction, a high-capacity RDH approach based on multi-embedding is proposed. The cover image is decoupled to select the embedding sequence that can better utilize texture pixels and reduce the size of the reconstruction information, and a multi-embedding strategy is proposed to embed the secret data along with the reconstruction information by matrix embedding. The experimental results demonstrate that the proposed method provides a superior visual quality and higher embedding capacity than some state-of-the-art RDH works for binary images. With an embedding capacity of 1000 bits, the proposed method achieves an average PSNR of 49.45 dB and an average SSIM of 0.9705 on the test images. This marks an improvement of 1.1 dB in PSNR and 0.0242 in SSIM compared to the latest state-of-the-art RDH method.

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Prescribed Time Tracking Controller for a Class of Nonholonomic Systems: Theory and Experiment

Xu,

Cong,

Xing

et al. 2024

IEEE Trans. Ind. Inf.

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Prescribed Performance Tracking Control of Lower-Triangular Systems with Unknown Fractional Powers

Cited by 3 publications

References 50 publications

Preconditioning Technique for an Image Deblurring Problem with the Total Fractional-Order Variation Model

Preconditioning Technique for an Image Deblurring Problem with the Total Fractional-Order Variation Model

High-Quality Reversible Data Hiding Based on Multi-Embedding for Binary Images

Prescribed Time Tracking Controller for a Class of Nonholonomic Systems: Theory and Experiment

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