Regularized learning framework in the estimation of reflectance spectra from camera responses

For digital cameras, device-dependent pixel values describe the camera's response to the incoming spectrum of light. We convert device-dependent RGB values to device- and illuminant-independent reflectance spectra. Simple regularization methods with widely used polynomial modeling provide an efficient approach for this conversion. We also introduce a more general framework for spectral estimation: regularized least-squares regression in reproducing kernel Hilbert spaces (RKHS). Obtained results show that the regularization framework provides an efficient approach for enhancing the generalization properties of the models.     

An Error-Minimizing Approach to Regularization in Indirect Measurements

Indirect measurements often amount to the estimation of the parameters of a mathematical model that describes the object under investigation, and this process may numerically be ill conditioned. Various regularization techniques are used to solve the problem. This paper shows that popular regularization methods can be depicted as special cases of a generalized approach based on a penalty term in the minimized criterion function and how different kinds of a priori knowledge can be engaged into each of them. A new function, which depends on the estimate bias and variance, is proposed to find a regularization parameter that minimizes the error of estimation, as well as a novel approach for nonlinear estimation that results in the iterative minimization (IM) method. The superiority of IM with respect to the conventional Marquardt procedure is demonstrated. Based on analysis, it also follows that the regularization technique can be used even in the case of numerically well-conditioned indirect measurements, decreasing the total error of estimation.      

Shape-dependent regularization for the retrieval of atmospheric state parameter profiles

We present an adaptive regularization approach to retrieve vertical state parameter profiles from limb-sounding measurements with high accuracy. This is accomplished by introducing a dedicated regularization functional based on a reasonable assumption of the profile characteristics. The approach results in shape-dependent weighting during least-squares computations and relies on a Cholesky decomposition of a preselected L(T)L matrix. Our method is compared with established regularization functionals such as optimal estimation and Tikhonov with respect to errors and achievable height resolution. The results show an improved height resolution of the retrieved profiles together with a reduction of absolute and relative errors obtained by test-bed simulations.     

Wave-front recovery from two orthogonal sheared interferograms

We present a new technique for using the information of two orthogonal lateral-shear interferograms to estimate an aspheric wave front. The wave-front estimation from sheared inteferometric data may be considered an ill-posed problem in the sense of Hadamard. We apply Thikonov regularization theory to estimate the wave front that has produced the lateral sheared interferograms as the minimizer of a positive definite-quadratic cost functional. The introduction of the regularization term permits one to find a well-defined and stable solution to the inverse shearing problem over the wave-front aperture as well as to reduce wave-front noise as desired.     

Computational imaging through chromatic aberration corrected simple lenses

Modern camera lenses become increasingly more complex to optimize the light efficiency of the optical system. Recent research has combined single lens optics with complex post-capture correction methods based on computational photography. This study further improves lens design by correcting chromatic aberrations, after which a simple image deconvolution method is sufficient to produce a high-quality image. We initially estimate the point spread function with a blind image deconvolution method. We add Gaussian regularization as kernel prior to improve the accuracy of kernel estimation. A fast non-blind deconvolution method is then performed to recover a clear image. Experimental results show that the proposed method is at par with state-of-the-art deconvolution approaches. We found a better trade-off between lens design and digital image processing than previous work.     

Strong convergence of subgradient extragradient method with regularization for solving variational inequalities

The paper concerns with the two numerical methods for approximating solutions of a monotone and Lipschitz variational inequality problem in a Hilbert space. We here describe how to incorporate regularization terms in the projection method, and then establish the strong convergence of the resulting methods under certain conditions imposed on regularization parameters. The new methods work in both cases of with or without knowing previously the Lipschitz constant of cost operator. Using the regularization aims mainly to obtain the strong convergence of the methods which is different to the known hybrid projection or viscosity-type methods. The effectiveness of the new methods over existing ones is also illustrated by several numerical experiments.

     

改进的Tikhonov正则化图像重建算法

Tikhonov正则化法可以解决电容层析成像中图像重建的病态问题,同时能够平衡解的稳定性与精确性,但其有效性和成像质量受到测量数据粗差的影响。改进的Tikhonov正则化法将2范数和M-估计结合,用一个缓慢增长的Cauchy函数代替最小二乘法的平方和函数,提高了估计稳健性和适应性。利用COMSOL和MATLAB软件对方法的有效性进行验证,重建结果表明,改进的Tikhonov正则化法能够有效减少粗差影响,提高重建图像精确度及分辨率。     

Estimation of kinetic parameters of composite materials during the cure process using the combined wavelet regularization method

The limitation of the experimental methods in thermophysical characterization of composite materials leads to an increased use of inverse parameter estimation techniques. However, in some situations the convergence of the inverse algorithm is impossible due to the correlation of the involved parameters and the existing noises in measurement data. Several different approaches have been used to tackle this problem. In this article, a new approach is utilized to solve it. This new technique combines the wavelet denoising and Levenberg–Marquardt regularization method. In order to examine this technique, a highly ill-posed problem is considered as a test case, that is, the estimation of the composite kinetic parameters during the cure process.     

A practical approach for estimating illumination distribution from shadows using a single image

This article presents a practical method that estimates illumination distribution from shadows using only a single image. The shadows are assumed to be cast on a textured, Lambertian surface by an object of known shape. Previous methods for illumination estimation from shadows usually require that the reflectance property of the surface on which shadows are cast be constant or uniform, or need an additional image to cancel out the effects of varying albedo of the textured surface on illumination estimation. But, our method deals with an estimation problem for which surface albedo information is not available. In this case, the estimation problem corresponds to an underdetermined one. We show that the combination of regularization by correlation and some user‐specified information can be a practical method for solving the underdetermined problem. In addition, as an optimization tool for solving the problem, we develop a constrained Non‐Negative Quadratic Programming (NNQP) technique into which not only regularization but also multiple linear constraints induced by user‐specified information are easily incorporated. We test and validate our method on both synthetic and real images and present some experimental results. © 2005 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 15, 143–154, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.20047     

Adaptive error estimation technique of the Trefftz method for solving the over-specified boundary value problem

In this paper, numerical solutions are investigated based on the Trefftz method for an over-specified boundary value problem contaminated with artificial noise. The main difficulty of the inverse problem is that divergent results occur when the boundary condition on over-specified boundary is contaminated by artificial random errors. The mechanism of the unreasonable result stems from its ill-posed influence matrix. The accompanied ill-posed problem is remedied by using the Tikhonov regularization technique and the linear regularization method, respectively. This remedy will regularize the influence matrix. The optimal parameter λ of the Tikhonov technique and the linear regularization method can be determined by adopting the adaptive error estimation technique. From this study, convergent numerical solutions of the Trefftz method adopting the optimal parameter can be obtained. To show the accuracy of the numerical solutions, we take the examples as numerical examination. The numerical examination verifies the validity of the adaptive error estimation technique. The comparison of the Tikhonov regularization technique and the linear regularization method was also discussed in the examples.