For adaptive extraction of generalized eigensubspace, Nguyen, Takahashi and Yamada proposed a scheme for solving generalized Hermitian eigenvalue problem based on nested orthogonal complement structure. This scheme can extract multiple generalized eigenvectors by combining with any algorithm designed for estimation of the first minor generalized eigenvector. In this paper, we carefully analyse the effect of a discontinuous function employed in the scheme, and show that the discontinuous function can cause unsmooth changes of the estimates by the scheme in its adaptive implementation. To remedy the weakness, we newly introduce a projection step, for smoothing, without increasing the order of the computational complexity. Numerical experiments show that the learning curves of the non-first generalized eigenvectors are improved drastically through the proposed smoothing even when the original scheme results in unexpected performance degradation.

This paper investigates the problem of simultaneous approximation of a prescribed multidimensional frequency response. The frequency responses of multidimensional IIR digital filters are used as nonlinear approximating functions. Chebyshev approximation theory and the notion of line homotopy are used to reveal the approximation properties of this set of IIR functions. A sign condition is derived to characterize a convex stable domain in this set. This sign condition can be incorporated into the optimization of the Chebyshev simultaneous approximation. The generally sufficient global Kolmogorov criterion is shown to be a necessary condition, for the characterization of best approximation, in the considered set of approximating functions. Thus, it can be incorporated, as a stopping constraint, in the design of the optimal filter. Moreover, the local Kolmogorov criterion is shown to be also necessary for the set of approximating functions. Finally, it is proved that the best approximation is a global minimum.

In this paper, we consider the problem of detecting a distributed target in unknown disturbance. The signals reflected by the target are assumed to come from the same direction. However, the exact direction is unknown and yet the signal steering vector lies in a known subspace. The disturbance consists of colored noise and deterministic interference. The interference belongs to a known subspace, linearly independent on the signal subspace. We derive the one-step Wald test and two-step Wald test. Numerical examples show that the proposed detectors can achieve better detection performance than the existing detectors.

This article addresses the problem of the Non Unitary Joint Block Diagonalization ( $$\mathsf {NU-JBD}$$ ) of a given set of complex matrices for the blind separation of convolutive mixtures of sources. We propose new different iterative optimization schemes based on Conjugate Gradient, Preconditioned Conjugate Gradient, Levenberg–Marquardt and Quasi-Newton methods. We perform also a study to determine which of these algorithms offer the best compromise between efficiency and convergence speed in the studied context. To be able to derive all these algorithms, a preconditioner has to be computed which requires either the calculation of the complex Hessian matrices or the use of an approximation to these Hessian matrices. Furthermore, the optimal stepsize is also computed algebraically to speed up the convergence of these algorithms. Computer simulations are provided in order to illustrate the behavior of the different algorithms in various contexts: when exactly block-diagonal matrices are considered but also when these matrices are progressively perturbed by an additive Gaussian noise. Finally, it is shown that these algorithms enable solving the blind separation of the convolutive mixtures of sources problem.

Multiview super resolution image reconstruction (SRIR) is often cast as a resampling problem by merging non-redundant data from multiple images on a finer grid, while inverting the effect of the camera point spread function (PSF). One main problem with multiview methods is that resampling from nonuniform samples (provided by multiple images) and the inversion of the PSF are highly nonlinear and ill-posed problems. Non-linearity and ill-posedness are typically overcome by linearization and regularization, often through an iterative optimization process, which essentially trade off the very same information (i.e. high frequency) that we want to recover. We propose a different point of view for multiview SRIR that is very much like single-image methods which extrapolate the spectrum of one image selected as reference from among all views. However, for this, the proposed method relies on information provided by all other views, rather than prior constraints as in single-image methods which may not be an accurate source of information. This is made possible by deriving explicit closed-form expressions that define how the local high frequency information that we aim to recover for the reference high resolution image is related to the local low frequency information in the sequence of views. The locality of these expressions due to modeling using wavelets reduces the problem to an exact and linear set of equations that are well-posed and solved algebraically without requiring regularization or interpolation. Results and comparisons with recently published state-of-the-art methods show the superiority of the proposed solution.

Delivery of airborne precision guided vehicles to pre-designated targets has assumed much importance in recent times. Transfer alignment is concerned with estimation of misalignment with respect to the airborne platform. During first few seconds of the post ejection phase, the trajectory deviates from intended one. Estimation of this deviation in trajectory can also be mapped to the transfer alignment problem. Large misalignment angle makes the system nonlinear while usage of mother measurements in each iteration makes it time varying. Particle filter variants can be designed to improve the quality of estimates but the time complexity increases. This work explores different resampling techniques to find a way to decrease the average time to complete an iteration. This allows more room for parallel execution with a residual evolutionary particle filter that does away with resampling by evolving through several system dynamics, thereby performing better when the knowledge of system dynamics is poor. It is observed that when the two filters are run together, the estimation accuracy improves considerably. The scheme is particularly useful in the time critical post ejection phase.

In conventional voice conversion methods, some features of a speech signal’s spectrum envelope are first extracted. Then, these features are converted so as to best match a target speaker’s speech by designing and using a set of conversions. Ultimately, the spectrum envelope of the target speaker’s speech signal is reconstructed from the converted features. The spectrum envelope reconstructed from the converted features usually deviates from its natural form. This aberration from the natural form observed in cases such as over-smoothing, over-fitting, and widening of formants is partially caused by two factors: (1) there is an error in the reconstruction of spectrum envelope from the features, and (2) the set of features extracted from the spectrum envelope of the speech signal is not closed. A method is put forward to improve the naturalness of speech by means of \(\epsilon \)-closed sets of extended vectors in voice conversion systems. In this approach, \(\epsilon \)-closed sets to reconstruct the natural spectrum envelope of a signal in the synthesis phase are introduced. The elements of these sets are generated by forming a group of extended vectors of features and applying a quantization scheme on the features of a speech signal. The use of this method in speech synthesis leads to a noticeable reduction of error in spectrum reconstruction from the features. Furthermore, the final spectrum envelope extracted from voice conversions maintains its natural form and, consequently, the problems arising from the deviation of voice from its natural state are resolved. The above method can be generally used as one phase of speech synthesis. It is independent of the voice conversion technique used and its parallel or non-parallel training method, and can be applied to improve the naturalness of the generated speech signal in all common voice conversion methods. Moreover, this method can be used in other fields of speech processing like texts to speech systems and vocoders to improve the quality of the output signal in the synthesis step.

Image inpainting in the wavelet domain refers to the recovery of an image from incomplete wavelet coefficients. In this paper, we propose a wavelet inpainting model by using fractional order total variation regularization approach. Moreover, we use a simple but very efficient primal–dual algorithm to calculate the optimal solution. In the light of saddle-point theory, the convergence of new algorithm is guaranteed. Experimental results are presented to show performance of the proposed algorithm.

Many recent studies have proposed methods for the classification of dynamic textures (DT). A method involving local binary patterns on three orthogonal planes (LBP-TOP) has shown promising results and generated considerable interest. However, LBP-TOP and most of its variants suffer from drawbacks caused by the accumulation process in the TOP technique. This process uses features from all frames in the DT sequence, including irrelevant frames, and thus disregards the distinct characteristics of each frame. To overcome this problem, we propose a codebook-based DT descriptor that aggregates salient features on three orthogonal planes. Given a DT sequence, only those frame features that are highly correlated with each cluster are selected and aggregated from the perspective of visual words. The proposed DT descriptor removes the feature from outlier frames that suddenly or rarely appear in a particular context, thus enhancing the emphasis of the salient features. Experimental results using public DT and dynamic scene datasets demonstrate the superiority of the proposed method over comparative approaches. The proposed method also yields outstanding results compared to the state-of-the-art DT representation.