Investigating the Upper-Bound Performance of Sparse-Coding-Based Spectral Reconstruction from RGB Images

In Spectral Reconstruction (SR), we recover hyperspectral images from their RGB counterparts. Most of the recent approaches are based on Deep Neural Networks (DNN), where millions of parameters are trained mainly to extract and utilize the contextual features in large image patches as part of the SR process. On the other hand, the leading Sparse Coding method ‘A+’—which is among the strongest point-based baselines against the DNNs—seeks to divide the RGB space into neighborhoods, where locally a simple linear regression (comprised by roughly 102 parameters) suffices for SR. In this paper, we explore how the performance of Sparse Coding can be further advanced. We point out that in the original A+, the sparse dictionary used for neighborhood separations are optimized for the spectral data but used in the projected RGB space. In turn, we demonstrate that if the local linear mapping is trained for each spectral neighborhood instead of RGB neighborhood (and theoretically if we could recover each spectrum based on where it locates in the spectral space), the Sparse Coding algorithm can actually perform much better than the leading DNN method. In effect, our result defines one potential (and very appealing) upper-bound performance of point-based SR.

Multi-Modal Nonlinear Forced Vibrations of Circular Cylindrical Shells of Arbitrary Shapes

Large-amplitude nonlinear forced vibrations of a circular cylindrical panel with a complex base, clamped at the edges are investigated. The Sanders-Koiter and the Donnell nonlinear shell theories are used to calculate the strain energy; in-plane inertia is retained. A mesh-free technique based on classic approximate functions and the R-function theory is used to build the discrete model of the nonlinear vibrations. This allows for constructing the sequences of admissible functions that satisfy given boundary conditions in domains with complex geometries. The problem is solved in two steps: a linear analysis is conducted to identify natural frequencies and corresponding natural modes to be used in the second step as a basis for nonlinear displacements. The system of ordinary differential equations is obtained by using the Lagrange approach on both steps. Numerical responses are obtained in the spectral neighborhood of the lowest natural frequency. The convergence of nonlinear responses is investigated.

On the Nonlinear Vibrations of Clamped Oval Shells

In the present study, the nonlinear dynamic response of clamped immovable oval cylindrical shells subjected to radial harmonic excitation in the spectral neighborhood of the free vibration frequency is investigated. The formulation is based on the first order shear deformation theory. Geometric nonlinearity is inducted in the formulation considering moderately large deformation effects employing the Sanders type kinematic relations. Governing equations are discretized in space and time domains, respectively, employing computationally efficient finite-strip method and Newmark time marching scheme. Resulting nonlinear algebraic equations are solved using Newton-Raphson iterative technique. A detailed parametric study is conducted to bring out the influence of ovality parameter on the nonlinear vibration characteristics of different modes of vibrations of isotropic and angle-ply oval shells. For isotropic oval shells, it is observed that moderately oval shells show softening type nonlinearity whereas shells of large ovality show hardening type nonlinearity. The response of oval shells with large ovality reveals different temporal variation near to the semi-major axis region compared to that in the semi-minor axis region.