This note is concerned with the generalization of the continuous shearlet transform to higher dimensions. Quite recently, a first approach has been derived in [4]. We present an alternative version which deviates from [4] mainly by a different generalization of the shear component. It turns out that the resulting integral transform is again associated with a square-integrable group representation.

Based on analyzing the related technologies of the original video retrieval, we proposed an algorithm of adaptive dual-threshold shot boundary detection for the game video of TV. At the beginning, we convert each frame to the HSV space, set high and low ratio of threshold according to the frame difference. Then, the average value of frame difference in the sliding window is calculated to receiv...

We show that there exists a frame wavelet ψ with fast decay in the time domain and compact support in the frequency domain generating a wavelet system whose canonical dual frame cannot be generated by an arbitrary number of generators. On the other hand, there exists infinitely many alternate duals of ψ generated by a single function. Our argument closes a gap in the original proof of this fact...

The variety of Heyting algebras has a nice property that HS = SH. Heyting algebras are the algebraic dual of intuitionistic descriptive frames. The goal of this paper is to define proper dual notions so as to formulate this algebraic properties in the frame language, and to give a frame-based proof of this property and some other duality theorems.

Frames are the foundation of the linear operators used in the decomposition and reconstruction of signals, such as the discrete Fourier transform, Gabor, wavelets, and curvelet transforms. The emergence of sparse representation models has shifted of the emphasis in frame theory toward sparse l1-minimization problems. In this paper, we apply frame theory to the sparse representation of signals i...

OBJECTIVES We assessed the comparability of self-reported smoking prevalence estimates from a dual-frame survey with those from two large-scale, national surveys. METHODS The Social Climate Survey of Tobacco Control (SCS-TC) obtained self-reported current smoking status via a dual-frame methodology in the fall of 2010. One frame used random digit dialling procedures and consisted of household...

Identifying and characterizing flame fronts is the most common task in the computer-assisted analysis of data obtained from imaging techniques such as planar laser-induced fluorescence (PLIF), laser Rayleigh scattering (LRS), or particle imaging velocimetry (PIV). We present Complex Shearlet-Based Ridge and Edge Measure (CoShREM), a novel edge and ridge (line) detection algorithm based on compl...

We design alternative dual frames for linearly reconstructing signals from Sigma-Delta (Σ∆) quantized finite frame coefficients. In the setting of sampling expansions for bandlimited functions, it is known that a stable rth order Sigma-Delta quantizer produces approximations where the approximation error is at most of order 1/λ , and λ > 1 is the oversampling ratio. We show that the counterpart...

In allusion to remove Racian noise while lessen the loss of details as low as possible, this paper proposed an filter algorithm which comprehensive utilize Multi-Objective Genetic Algorithm (MOGA) and Shearlet transform based on a Multi-scale Geometric Analysis (MGA) theory. First, it performs a wavelet multi-scale decomposition of image. Then, it builds target function in MOGA by several evalu...