In this paper, we will provide a simple method for starting with a given finite frame for an $n$-dimensional Hilbert space $mathcal{H}_n$ with nonzero elements and producing a frame which is $epsilon$-nearly Parseval and $epsilon$-nearly unit norm. Also, the concept of the $epsilon$-nearly equal frame operators for two given frames is presented. Moreover, we characterize all bounded invertible ...

We consider the problem of transcribing polyphonic piano music with an emphasis on generalizing to unseen instruments. We use deep neural networks and propose a novel approach that predicts onsets and frames using both CNNs and LSTMs. This model predicts pitch onset events and then uses those predictions to condition framewise pitch predictions. During inference, we restrict the predictions fro...

OBJECTIVE Right-angle dual-headed tomography has increased cardiac SPECT utility by cutting acquisition time in half which enhances gating capabilities. When gating, however, a deceleration in heart rate, due to a return to baseline rate after stress or lessened anxiety at the end of a study, may significantly affect the last step(s) of a gated study with possible frame or information loss. The...

The paper discusses discrete frames as an attractive semantics for modal logic. We study questions of completeness, persistence, duality and definability. Notions of completeness, strong global completeness and complexity of dual varieties coincide for discrete frames; moreover, they are equivalent to conservativity of minimal hybrid extensions. The paper also provides some criteria of di-persi...

Booleanization of frames or uniform frames, which is not functorial under the basic choice of morphisms, becomes functorial in the categories with weakly open homomorphisms or weakly open uniform homomorphisms. Then, the construction becomes a reflection. In the uniform case, moreover, it also has a left adjoint. In connection with this, certain dual equivalences concerning uniform spaces and u...

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...

We generalize the Second Oversampling Theorem for wavelet frames and dual wavelet frames from the setting of integer dilations to real dilations. We also study the relationship between dilation matrix oversampling of semi-orthogonal Parseval wavelet frames and the additional shift invariance gain of the core subspace.

Booleanization of frames or uniform frames, which is not functorial under the basic choice of morphisms, becomes functorial in the categories with weakly open homomorphisms or weakly open uniform homomorphisms. Then, the construction becomes a reflection. In the uniform case, moreover, it also has a left adjoint. In connection with this, certain dual equivalences concerning uniform spaces and u...

The subject of this article is the duality principle, which, well beyond its stand at the heart of Gabor analysis, is a universal principle in frame theory that gives insight into many phenomena. Its fiber matrix formulation for Gabor systems is the driving principle behind seemingly different results. We show how the classical duality identities, operator representations and constructions for ...

We introduce a new class of frames with strong symmetry properties called geometrically uniform frames (GU), that are defined over an abelian group of unitary matrices and are generated by a single generating vector. The notion of GU frames is then extended to compound GU (CGU) frames which are generated by an abelian group of unitary matrices using multiple generating vectors. The dual frame v...