8,811 research outputs found
Regularization matrices for discrete ill-posed problems in several space-dimensions
Many applications in science and engineering require the solution of large linear discrete ill-posed problems that are obtained by the discretization of a Fredholm integral equation of the first kind in several space dimensions. The matrix that defines these problems is very ill conditioned and generally numerically singular, and the right-hand side, which represents measured data, is typically contaminated by measurement error. Straightforward solution of these problems is generally not meaningful due to severe error propagation. Tikhonov regularization seeks to alleviate this difficulty by replacing the given linear discrete ill-posed problem by a penalized least-squares problem, whose solution is less sensitive to the error in the right-hand side and to roundoff errors introduced during the computations. This paper discusses the construction of penalty terms that are determined by solving a matrix nearness problem. These penalty terms allow partial transformation to standard form of Tikhonov regularization problems that stem from the discretization of integral equations on a cube in several space dimensions
From Rank Estimation to Rank Approximation: Rank Residual Constraint for Image Restoration
In this paper, we propose a novel approach to the rank minimization problem,
termed rank residual constraint (RRC) model. Different from existing low-rank
based approaches, such as the well-known nuclear norm minimization (NNM) and
the weighted nuclear norm minimization (WNNM), which estimate the underlying
low-rank matrix directly from the corrupted observations, we progressively
approximate the underlying low-rank matrix via minimizing the rank residual.
Through integrating the image nonlocal self-similarity (NSS) prior with the
proposed RRC model, we apply it to image restoration tasks, including image
denoising and image compression artifacts reduction. Towards this end, we first
obtain a good reference of the original image groups by using the image NSS
prior, and then the rank residual of the image groups between this reference
and the degraded image is minimized to achieve a better estimate to the desired
image. In this manner, both the reference and the estimated image are updated
gradually and jointly in each iteration. Based on the group-based sparse
representation model, we further provide a theoretical analysis on the
feasibility of the proposed RRC model. Experimental results demonstrate that
the proposed RRC model outperforms many state-of-the-art schemes in both the
objective and perceptual quality
BM3D Frames and Variational Image Deblurring
A family of the Block Matching 3-D (BM3D) algorithms for various imaging
problems has been recently proposed within the framework of nonlocal patch-wise
image modeling [1], [2]. In this paper we construct analysis and synthesis
frames, formalizing the BM3D image modeling and use these frames to develop
novel iterative deblurring algorithms. We consider two different formulations
of the deblurring problem: one given by minimization of the single objective
function and another based on the Nash equilibrium balance of two objective
functions. The latter results in an algorithm where the denoising and
deblurring operations are decoupled. The convergence of the developed
algorithms is proved. Simulation experiments show that the decoupled algorithm
derived from the Nash equilibrium formulation demonstrates the best numerical
and visual results and shows superiority with respect to the state of the art
in the field, confirming a valuable potential of BM3D-frames as an advanced
image modeling tool.Comment: Submitted to IEEE Transactions on Image Processing on May 18, 2011.
implementation of the proposed algorithm is available as part of the BM3D
package at http://www.cs.tut.fi/~foi/GCF-BM3
Shape optimization of tibial prosthesis components
NASA technology and optimal design methodologies originally developed for the optimization of composite structures (engine blades) are adapted and applied to the optimization of orthopaedic knee implants. A method is developed enabling the shape tailoring of the tibial components of a total knee replacement implant for optimal interaction within the environment of the tibia. The shape of the implant components are optimized such that the stresses in the bone are favorably controlled to minimize bone degradation, to improve the mechanical integrity of the implant/interface/bone system, and to prevent failures of the implant components. A pilot tailoring system is developed and the feasibility of the concept is demonstrated and evaluated. The methodology and evolution of the existing aerospace technology from which this pilot optimization code was developed is also presented and discussed. Both symmetric and unsymmetric in-plane loading conditions are investigated. The results of the optimization process indicate a trend toward wider and tapered posts as well as thicker backing trays. Unique component geometries were obtained for the different load cases
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