We present two computationally inexpensive techniques for estimating the numerical rank of a matrix, combining powerful tools from computational linear algebra. These techniques exploit three key ingredients. The first is to approximate the projector on the non-null invariant subspace of the matrix by using a polynomial filter. Two types of filters are discussed, one based on Hermite interpolat...

A multivariate polynomial matrix-factorization algorithm is introduced and discussed. This algorithm and another algorithm for computing a globally minimal generating matrix of the syzygy of solutions associated with a polynomial matrix are both associated with a zero-coprimeness constraint that characterizes perfect-reconstruction filter banks. Generalizations, as well as limitations of recent...

This paper derives a square-root information-type filtering algorithm for nonlinear multi-sensor fusion problems using the cubature Kalman filter theory. The resulting filter is called the square-root cubature Information filter (SCIF). The SCIF propagates the square-root information matrices derived from numerically stable matrix operations and is therefore numerically robust. The SCIF is appl...

In this paper, the design problem of two-channel linear-phase finite-impulse response perfect reconstruction filter banks in which both the filters are of even length (which are known as type filter banks) is addressed. The condition on the determinant of the polyphase matrix is translated in terms of well-known convolution matrices. The perfect reconstruction condition is obtained as a system ...

We investigate a special class of N-channel oversampled linearphase perfect reconstruction filter banks with a smaller decimation factor M than N. We deal with systems in which all analysis and synthesis filters have the same FIR length and share the same center of symmetry. We provide the general lattice factorization of a polyphase matrix of a particular class of these oversampled filter bank...

This paper presents a sensor fusion method based on the combination of cubature Kalman filter (CKF) and fuzzy logic adaptive system (FLAS) for the integrated navigation systems, such as the GPS/INS (Global Positioning System/inertial navigation system) integration. The third-degree spherical-radial cubature rule applied in the CKF has been employed to avoid the numerically instability in the sy...

This letter introduces the frequency structure matrix as a new representation of color filter arrays (CFAs). The matrix records the frequency components of CFA filtered images and their positions in the spectrum. The matrix can be conveniently obtained by applying the symbolic DFT to the CFA pattern. With this new representation, it is easy to analyze the characteristics of CFAs and to formulat...

Discrete wavelet coefficients of input and output of a Linear Time Invariant system, respectively, are shown to be related by a transformation matrix whose elements depend upon characteristics of the system and choice of wavelet bases. A filter bank implementation of the matrix using digital filters, Upand Down-samplers is also given.

In dynamic contrast enhanced (DCE) MRI, temporal and spatial resolution can be improved by timeresolved angiography with interleaved stochastic trajectories (TWIST). However, due to view sharing, the temporal resolution of TWIST is not a true one. To overcome this limitation, we employ recently proposed annihilating filter-based low rank Hankel matrix approach (ALOHA) that interpolates the miss...