A biorthogonal formulation is applied to the non-Hermite transcorrelated Hamiltonian, which treats a large amount of the dynamic correlation effects implicitly. We introduce biorthogonal canonical orbitals diagonalizing the non-Hermitian Fock operator. We also formulate many-body perturbation theory for the transcorrelated Hamiltonian. The biorthogonal self-consistent field followed by the seco...

A new implementation of the critically sampled nonperiodic real Gabor transform (GT) is presented for non-separable time-frequency (TF) plane sampling. In the propsed implementation, the quincunx sampling is used to sample the TF plane. This leads to a well localized biorthogonal function in both time and frequency. It thus overcomes the main problem of the previous implementations, which is th...

Modeling of a time-varying dynamical system provides insights into the functions of biological neural networks and contributes to the development of next-generation neural prostheses. In this paper, we have formulated a novel sparse multiwavelet-based generalized Laguerre–Volterra (sMGLV) modeling framework to identify the time-varying neural dynamics from multiple spike train data. First, the ...

We give a formula for the duals of the masks associated with trivariate box spline functions. We show how to construct trivariate nonseparable compactly supported biorthogonal wavelets associated with box spline functions. The biorthogonal wavelets may have arbitrarily high regularities.

In this paper, we describe an algorithm for computing biorthogonal compactly supported dyadic wavelets related to the Walsh functions on the positive half-line R+. It is noted that a similar technique can be applied in very general situations, e.g., in the case of Cantor and Vilenkin groups. Using the feedback-based approach, some numerical experiments comparing orthogonal and biorthogonal dyad...

(ABSTRACT) Methods for digital image compression have been the subject of much study over the past decade. Advances in wavelet transforms and quantization methods have produced algorithms capable of surpassing the existing image compression standards like the Joint Photographic Experts Group (JPEG) algorithm. For best performance in image compression, wavelet transforms require filters that com...