Image-Based Measurement of Structural Color using Spectral Camera

We perceive structural colors by optical phenomena such as light interference and diffraction caused by a fine structure of the object surface. One of the characteristics of structural colors is that a wavelength distribution of light changes depending on an incident angle of a light source and a viewing angle. Generally, for color evaluation and reproduction, it is required to acquire reflection characteristics of objects. Therefore, BRDF (Bidirectional Reflectance Distribution Function) is often used as a function that represents reflection characteristics depending on incident and viewing angles. In this study, we measured BRDF of structural colors based on a method to acquire image-based material reflection characteristics using a spectral camera. The measurement was performed by aligning an optical axis of a spectral camera with a structural color sample and changing an irradiation angle of a light source. Reflection characteristics were represented by using a radiance factor, which was a ratio between a spectral radiance of white material and that of structural color. From measurement results, we confirmed an angle-dependent radiance factor. Finally, based on a measured spectral radiance of a structural color sample, we spectrally reproduced the structural color using a spectral projector based on model fitting of spectral data.

On Asymptotics of the Density of States for Hypoelliptic Almost Periodic Systems

In this paper, we find the asymptotics of integrated density of states with remainder estimate for hypoelliptic systems with almost periodic (a.p.) coefficients. We use the approximate spectral projector method for matrix a.p. operators with continuous spectrum.

Wald Statistics in high-dimensional PCA

In this study, we consider PCA for Gaussian observations X1, …, Xn with covariance Σ = ∑iλiPi in the ’effective rank’ setting with model complexity governed by r(Σ) ≔ tr(Σ)∕∥Σ∥. We prove a Berry-Essen type bound for a Wald Statistic of the spectral projector $\hat P_r$. This can be used to construct non-asymptotic goodness of fit tests and confidence ellipsoids for spectral projectors Pr. Using higher order pertubation theory we are able to show that our Theorem remains valid even when $\mathbf{r}(\Sigma) \gg \sqrt{n}$.

Full-wave-equation depth extrapolation for migration

Most of the traditional approaches to migration by downward extrapolation suffer from inaccuracies caused by using one-way propagation, both in the construction of such propagators in a variable background and the suppression of propagating waves generated by, e.g., steep reflectors. We present a new mathematical formulation and an algorithm for downward extrapolation that suppress only the evanescent waves. We show that evanescent wave modes are associated with the positive eigenvalues of the spatial operator and introduce spectral projectors to remove these modes, leaving all propagating modes corresponding to nonpositive eigenvalues intact. This approach suppresses evanescent modes in an arbitrary laterally varying background. If the background velocity is only depth dependent, then the spectral projector may be applied by using the fast Fourier transform and a filter in the Fourier domain. In computing spectral projectors, we use an iteration that avoids the explicit construction of the eigensystem. Moreover, we use a representation of matrices leading to fast matrix-matrix multiplication and, as a result, a fast algorithm necessary for practical implementation of spectral projectors. The overall structure of the migration algorithm is similar to survey sinking with an important distinction of using a new method for downward continuation. Using a blurred version of the true velocity as a background, steep reflectors can be imaged in a 2D slice of the SEG-EAGE model.