For good image quality using ultrasound inverse scattering, one alternately solves the well-posed forward scattering equation for an estimated total field and the ill-posed inverse scattering equation for the desired object property function. In estimating the total field, error or noise contaminates the coefficients of both matrix and data of the inverse scattering equation. Previous work on i...

Classification based on Low-Rank Representation (LRR) has been a hot-topic in the field of pattern classification. However, LRR may not be able to fuse the local and global information of data completely and fail to represent nonlinear samples. In this paper, we propose a kernel locality preserving low-rank representation with Tikhonov regularization (KLP-LRR) for face recognition. KLP-LRR is a...

We consider the problem of Tikhonov regularization with a general convex loss function: this formalism includessupport vector machines and regularized least squares. For a family of kernels that includes the Gaussian, parameterized by a “bandwidth” parameter σ, we characterize the limiting solution as σ → ∞. In particular, we show that if we set the regularization parameter λ = λ̃σ, the regulari...

In this paper we consider the inverse problem of image deblurring with Neumann boundary conditions. Regularization is incorporated by using Gaussian Markov random fields (GMRFs) to model an appropriate prior on the image pixel values. We provide a linear algebraic framework for GMRFs, and we establish an important connection between GMRFs studied in the statistical literature, and negative-Lapl...

In parallel imaging, the signal-to-noise ratio (SNR) of sensitivity encoding (SENSE) reconstruction is usually degraded by the ill-conditioning problem, which becomes especially serious at large acceleration factors. Existing regularization methods have been shown to alleviate the problem. However, they usually suffer from image artifacts at high acceleration factors due to the large data incon...

The main goal of our paper is to study the regularization problems which occur in predictive control of systems with severely ill-posed inverse model. We propose a new formulation of predictive control where the future controls are obtained as a solution of certain ill-posed inverse problem. This formulation leads to a possibility of closed loop on-line control of complex systems with ill-posed...

Classification based on Low-Rank Representation (LRR) has been a hot-topic in the field of pattern classification. However, LRR may not be able to fuse the local and global information of data completely and fail to represent nonlinear samples. In this paper, we propose a kernel locality preserving low-rank representation with Tikhonov regularization (KLP-LRR) for face recognition. KLP-LRR is a...

Tikhonov regularization with the regularization parameter determined by the discrepancy principle requires the computation of a zero of a rational function. We describe a cubically convergent zero-finder for this purpose. AMS subject classification: 65F22, 65H05, 65R32.

In this paper, we study the multi-parameter Tikhonov regularization method which adds multiple different penalties to exhibit multi-scale features of the solution. An optimal error bound of the regularization solution is obtained by a priori choice of multiple regularization parameters. Some theoretical results of the regularization solution about the dependence on regularization parameters are...

We report on a new iterative method for regularizing a nonlinear operator equation in Hilbert spaces. The proposed algorithm is a combination of Tikhonov regularization and a fixed point algorithm for the minimization of the Tikhonov–functional. Under the assumptions that the operator F is twice continuous Fréchet–differentiable with Lipschitz– continuous first derivative and that the solution ...