Comprehensive data analysis of femtosecond transient absorption spectra: A review

Nowadays, time-resolved spectroscopy data can be routinely and accurately collected in UV-vis femtosecond transient absorption spectroscopy. However, the data analysis strategy and the postulation of a physically valid model for this kind of measurements may be tackled with many different approaches ranging from pure soft-modeling (model-free) to hard-modeling, where the elaboration of a parametric spectro-temporal model may be required. This paper reviews methods that are used in practice for the analysis of femtosecond transient absorption spectroscopy data. Model-based methods, common in photochemistry, are revisited, and soft-modeling methods, which originate from the chemometrics field and that recently disseminated in the photo(bio)chemistry literature, are presented. These soft-modeling methods are designed to suit the intrinsic nature of the multivariate (or multi-way) measurement. Soft-modeling tools do not require a priori physical or mechanistic models to provide a decomposition of the data on the time and wavelength dimensions, the only requirement being that these two (or more) dimensions are separable. Additionally, Bayesian data analysis, which provides a probabilistic framework for data analysis, is considered in detail, since it allows uncertainty quantification and validation of the model selection step.     

Estimation of the sound pressure field of a baffled uniform elliptically shaped transducer

In this paper an alternative approach to estimate the sound field of an elliptically shaped transducer in an infinite baffle is described. The method is based on a singular value decomposition of a propagating matrix which is computed through a division of the vibrating surface into a finite number of small circular piston sources flush-mounted on the elliptical surface. This decomposition is combined with the volume velocity vector on the discretized surface to obtain the sound pressure field. Numerical examples for both on-axis sound pressure and directivity are presented for the uniform elliptical piston transducer and they are in good agreement with the results given by other methods.     

Orthogonal projection regularization operators

Tikhonov regularization often is applied with a finite difference regularization operator that approximates a low-order derivative. This paper proposes the use of orthogonal projections as regularization operators, e.g., with the same null space as commonly used finite difference operators. Applications to iterative and SVD-based methods for Tikhonov regularization are described. Truncated iterative and SVD methods are also considered. Research of L. Reichel was supported in part by an OBR Research Challenge Grant. Research of F. Sgallari was supported in part by PRIN 2004 grant 2004014411-005.     

A truncated projected SVD method for linear discrete ill-posed problems

Truncated singular value decomposition is a popular solution method for linear discrete ill-posed problems. However, since the singular value decomposition of the matrix is independent of the right-hand side, there are linear discrete ill-posed problems for which this method fails to yield an accurate approximate solution. This paper describes a new approach to incorporating knowledge about properties of the desired solution into the solution process through an initial projection of the linear discrete ill-posed problem. The projected problem is solved by truncated singular value decomposition. Computed examples illustrate that suitably chosen projections can enhance the accuracy of the computed solution.     

On stabilized finite element methods for the Stokes problem in the small time step limit

Recent studies indicate that consistently stabilized methods for unsteady incompressible flows, obtained by a method of lines approach may experience difficulty when the time step is small relative to the spatial grid size. Using as a model problem the unsteady Stokes equations, we show that the semi‐discrete pressure operator associated with such methods is not uniformly coercive. We prove that for sufficiently large (relative to the square of the spatial grid size) time steps, implicit time discretizations contribute terms that stabilize this operator. However, we also prove that if the time step is sufficiently small, then the fully discrete problem necessarily leads to unstable pressure approximations. The semi‐discrete pressure operator studied in the paper also arises in pressure‐projection methods, thereby making our results potentially useful in other settings. Copyright © 2006 John Wiley & Sons, Ltd.     

SVD Analysis in Fitting Property Surfaces

Previous calculated spectral properties of Li₃⁺associated with the [6,7] vibrational band origins were rendered as uncertain, due to the exclusion of cross-terms involving the breathe mode normal co-ordinate in the analytic expansion of the dipole moment surface. However, by applying a singular value decomposition (SVD) analysis the exclusion of these terms is shown to be appropriate with respect to their negligible effect on fit (via the square root of the sum of the square of the residuals) thereby validating previous prognosis.     

Coil Combination of Multichannel Single Voxel Magnetic Resonance Spectroscopy with Repeatedly Sampled In Vivo Data

Magnetic resonance spectroscopy (MRS), as a noninvasive method for molecular structure determination and metabolite detection, has grown into a significant tool in clinical applications. However, the relatively low signal-to-noise ratio (SNR) limits its further development. Although the multichannel coil and repeated sampling are commonly used to alleviate this problem, there is still potential room for promotion. One possible improvement way is combining these two acquisition methods so that the complementary of them can be well utilized. In this paper, a novel coil-combination method, average smoothing singular value decomposition, is proposed to further improve the SNR by introducing repeatedly sampled signals into multichannel coil combination. Specifically, the sensitivity matrix of each sampling was pretreated by whitened singular value decomposition (WSVD), then the smoothing was performed along the repeated samplings’ dimension. By comparing with three existing popular methods, Brown, WSVD, and generalized least squares, the proposed method showed better performance in one phantom and 20 in vivo spectra.     

基于SVD的苹果粉质化高光谱散射图像特征提取

粉质化是影响苹果等级的重要口感参数.采用高光谱散射图像进行了苹果粉质化的无损检测研究.利用奇异值分解方法对样本600～1 000 nm 共81个波长20 mm范围内的敝射图像进行奇异值分解,将获得的奇异值作为粉质化表征参数,结介偏微分最小二乘判别分析建立苹果粉质化分类模型.结果缸示,对不同产地和不同储藏条件下的样本,其两分类模型(粉质化和非粉质化)的分类精度为76.1%～80.6%,优于平均值特征提取方法(75.3%～76.5%).分析表明,奇异值分解可以有效地提取高光谱敞射图像的特征,用此特征建立粉质化分类模型可以区分粉质化和非粉质化的苹果,但分类精度有待于进一步提高.