In the context of constructive locale or frame theory (locale theory over a fixed base locale), we study some aspects of ’frame distributions’, meaning sup preserving maps from a frame to the base frame. We derive a relationship between results of Jibladze-Johnstone and Bunge-Funk, and also descriptions in distribution terms, as well as in double negation terms, of the ’interior of closure’ ope...

Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. In this paper, we introduce the notion of a sparse fusion frame, that is, a fusion frame whose subspaces are generated by orthonormal basis vectors that are sparse in a ‘uniform basis’ over all subspaces, thereby enabling low-complexity fusion frame decomposition...

The analysis sparsity model is a very effective approach in modern Compressed Sensing applications. Specifically, redundant operators can lead to fewer measurements needed for reconstruction when employing the \(l_1\)-minimization Sensing. In this paper, we pick an eigenvector of Zauner unitary matrix and –under certain assumptions on ambient dimension– build spark deficient Gabor frame. operat...

Controlled g-atomic subspace for a bounded linear operator is being presented and characterization has been given. We give an example of controlled K-g-fusion frame. construct new frame the Hilbert space H ? X using frames spaces X. Several useful resolutions identity on theory g-fusion have discussed. Frame pair Bessel sequences introduced.

We resolve a long-standing question on L completeness of the timescale (or wavelet) system generated by the Mexican hat function, when p ≥ 2. Our main result concerns frequency-scale systems generated by modulation and dilation of a single function. The mixed frame operator (analysis followed by synthesis) is shown to be bijective from L(R) to itself, for 1 ≤ q < ∞, so that the frequency-scale ...

We describe a computer program which facilitates the analysis of a series of C.T. scans made while a stereotaxic fram fixed to the patient. program has 2 modes of operation: The operator may select a region and determine the three-dimensional frame coordinate. The operator may select a set of frame coordinates and have the computer program display these at the appropriate sites on C.T. scans. I...

The consensus operator is used for cumulative belief fusion in subjective logic, and takes beliefs on binary frames of discernment as input. Coarsening to a binary state space is therefore needed in case the original frame is larger than binary. Coarsening causes information loss in general, and can lead to inconsistent results when applying the consensus operator. We presents a method for norm...

This chapter illustrates the use of Gabor frame analysis to derive results on the spectral properties of integral and pseudodifferential operators. In particular, we obtain a sufficient condition on the kernel of an integral operator or the symbol of a pseudodifferential operator which implies that the operator is trace-class. This result significantly improves a sufficient condition due to Dau...