For any fixed fusion frame, its optimal dual fusion frames for reconstruction is studied in case of erasures of subspaces. It is considered that a probability distribution of erasure of subspaces is given and that a blind reconstruction procedure is used, where the erased data are set to zero. It is proved that there are always optimal duals. Sufficient conditions for the canonical dual fusion ...

Numerous human genes display dual coding within alternatively spliced regions, which give rise to distinct protein products that include segments translated in more than one reading frame. To resolve the ensuing protein structural puzzle, we identified 67 human genes with alternative splice variants comprising a dual-coding region at least 75 nucleotides in length and analyzed the structural st...

In this paper, the tangent, binormal, normal and unit Darboux vectors of the dual curve on the one–parameter dual spherical motion are obtained with respect to a unit dual orthogonal frame for dual 3–space D.

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...