Showing papers in "Multidimensional Systems and Signal Processing in 2013"
TL;DR: A full reference metric for quality assessment of stereoscopic images based on the binocular fusion process characterizing the 3D human perception is proposed and the difference of binocular energy has shown a high correlation with the human judgement for different impairments and is used to build the Binocular Energy Quality Metric (BEQM).
Abstract: Stereoscopic imaging is becoming very popular and its deployment by means of photography, television, cinema. . .is rapidly increasing. Obviously, the access to this type of images imposes the use of compression and transmission that may generate artifacts of different natures. Consequently, it is important to have appropriate tools to measure the quality of stereoscopic content. Several studies tried to extend well-known metrics, such as the PSNR or SSIM, to 3D. However, the results are not as good as for 2D images and it becomes important to have metrics dealing with 3D perception. In this work, we propose a full reference metric for quality assessment of stereoscopic images based on the binocular fusion process characterizing the 3D human perception. The main idea consists of the development of a model allowing to reproduce the binocular signal generated by simple and complex cells, and to estimate the associated binocular energy. The difference of binocular energy has shown a high correlation with the human judgement for different impairments and is used to build the Binocular Energy Quality Metric (BEQM). Extensive experiments demonstrated the performance of the BEQM with regards to literature.
131 citations
TL;DR: This paper deals with the problem of delay-dependent robust H∞ filtering for uncertain two-dimensional (2-D) continuous systems described by Roesser state space model with time-varying delays, with the uncertain parameters assumed to be of polytopic type.
Abstract: This paper deals with the problem of delay-dependent robust \(H_{\infty }\) filtering for uncertain two-dimensional (2-D) continuous systems described by Roesser state space model with time-varying delays, with the uncertain parameters assumed to be of polytopic type. A sufficient condition for \(H_{\infty }\) noise attenuation is derived in terms of linear matrix inequalities, so a robust \(H_{\infty }\) filter can be obtained by solving a convex optimization problem. Finally, some examples are provided to illustrate the effectiveness of the proposed methodology.
63 citations
TL;DR: The 2-D fuzzy system model is established based on the Fornasini–Marchesini local state-space model, and a control design procedure is proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used.
Abstract: This paper investigates the problem of stability analysis and stabilization for two-dimensional (2-D) discrete fuzzy systems. The 2-D fuzzy system model is established based on the Fornasini---Marchesini local state-space model, and a control design procedure is proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, nonquadratic stability conditions are derived by means of linear matrix inequality (LMI) technique. Then, by introducing an additional instrumental matrix variable, the stabilization problem for 2-D fuzzy systems is addressed, with LMI conditions obtained for the existence of stabilizing controllers. Finally, the effectiveness and advantages of the proposed design methods based on basis-dependent Lyapunov functions are shown via two examples.
56 citations
TL;DR: The Cramér-Rao Bound (CRB), which is widely spread in signal processing to characterize the estimation performance will be used here as a useful tool to find the optimal configuration of a 3D antenna array under both conditional, and unconditional observation models.
Abstract: In the context of passive sources localization using antenna array, the estimation accuracy of elevation, and azimuth are related not only to the kind of estimator which is used, but also to the geometry of the considered antenna array. Although there are several available results on the linear array, and also for planar arrays, other geometries existing in the literature, such as 3D arrays, have been less studied. In this paper, we study the impact of the geometry of a family of 3D models of antenna array on the estimation performance of elevation, and azimuth. The Cramer-Rao Bound (CRB), which is widely spread in signal processing to characterize the estimation performance will be used here as a useful tool to find the optimal configuration. In particular, we give closed-form expressions of CRB for a 3D antenna array under both conditional, and unconditional observation models. Thanks to these explicit expressions, the impact of the third dimension to the estimation performance is analyzed. Particularly, we give criterions to design an isotropic 3D array depending on the considered observation model. Several 3D particular geometry antennas made from uniform linear array (ULA) are analyzed, and compared with 2D antenna arrays. The isotropy condition of such arrays is analyzed. The presented framework can be used for further studies of other types of arrays.
44 citations
TL;DR: The proposed method can achieve the unambiguous direction estimates with enhanced accuracy by setting the vector sensors to space much farther apart than a half-wavelength, and it is also suitable for the case of spatially nonuniform noise, which may be more realistic scenario for the sparsely placed sensors.
Abstract: This paper proposes a computationally efficient two-dimensional (2-D) direction-of-arrival (DOA) estimation algorithm based extended-aperture for acoustic coherent signals impinging on a sparse acoustic vector-sensor array. The coherency of incident signals is decorrelated through matrix averaging and the signal/noise subspaces are reconstructed through a linear operation of a matrix formed from the cross-correlations between some sensor data, where the effect of additive noise is eliminated. Consequently, DOAs can be estimated without performing eigen-decomposition (into signal/noise subspaces), and there is no need to evaluate all correlations of the array data. The derived estimates are automatically matched by translating eigenvalues into real-valued ones, furthermore, the proposed method can achieve the unambiguous direction estimates with enhanced accuracy by setting the vector sensors to space much farther apart than a half-wavelength, and it is also suitable for the case of spatially nonuniform noise, which may be more realistic scenario for the sparsely placed sensors. The performance of the proposed method is demonstrated through numerical examples.
38 citations
TL;DR: The experimental results on bi-level and multilevel thresholding for synthetic and real-world images demonstrate the success of the proposed image thresholding scheme, as compared with the Otsu method, the two-dimensional OTSu method and the minimum class variance thresholding method.
Abstract: Variance-based thresholding method is a very effective technology for image segmentation. However, its performance is limited in traditional one-dimensional and two-dimensional scheme. In this paper, a novel two-dimensional variance thresholding scheme to improve image segmentation performance is proposed. The two-dimensional histogram of the original and local average image is projected to one-dimensional space in the proposed scheme firstly, and then the variance-based criterion is constructed for threshold selection. The experimental results on bi-level and multilevel thresholding for synthetic and real-world images demonstrate the success of the proposed image thresholding scheme, as compared with the Otsu method, the two-dimensional Otsu method and the minimum class variance thresholding method.
32 citations
TL;DR: A new edge detection technique is proposed to deal with the noisy image using fuzzy derivative and bacterial foraging algorithm that can detect the edges in an image in the presence of impulse noise up to 30%.
Abstract: Bio-inspired edge detection using fuzzy logic has achieved great attention in the recent years. The bacterial foraging (BF) algorithm, introduced in Passino (IEEE Control Syst Mag 22(3):52---67, 2002) is one of the powerful bio-inspired optimization algorithms. It attempts to imitate a single bacterium or groups of E. Coli bacteria. In BF algorithm, a set of bacteria forages towards a nutrient rich medium to get more nutrients. A new edge detection technique is proposed to deal with the noisy image using fuzzy derivative and bacterial foraging algorithm. The bacteria detect edge pixels as well as noisy pixels in its path during the foraging. The new fuzzy inference rules are devised and the direction of movement of each bacterium is found using these rules. During the foraging if a bacterium encounters a noisy pixel, it first removes the noisy pixel using an adaptive fuzzy switching median filter in Toh and Isa (IEEE Signal Process Lett 17(3):281---284, 2010). If the bacterium does not encounter any noisy pixel then it searches only the edge pixel in the image and draws the edge map. This approach can detect the edges in an image in the presence of impulse noise up to 30%.
32 citations
TL;DR: A novel scheme for generalized minor subspace extraction is proposed by extending an idea of dimension reduction technique to that for extracting the first minor generalized eigenvector of a matrix pencil of lower dimensionality.
Abstract: The contribution of this paper is three-fold: first, we propose a novel scheme for generalized minor subspace extraction by extending an idea of dimension reduction technique. The key of this scheme is the reduction of the problem for extracting the ith (i ? 2) minor generalized eigenvector of the original matrix pencil to that for extracting the first minor generalized eigenvector of a matrix pencil of lower dimensionality. The proposed scheme can employ any algorithm capable of estimating the first minor generalized eigenvector. Second, we propose a pair of such iterative algorithms and analyze their convergence properties in the general case where the generalized eigenvalues are not necessarily distinct. Third, by using these algorithms inductively, we present adaptive implementations of the proposed scheme for estimating an orthonormal basis of the generalized minor subspace. Numerical examples show that the proposed adaptive subspace extraction algorithms have better numerical stability than conventional algorithms.
28 citations
TL;DR: A detailed investigation of the relationship between the Fisher information matrices of the two problems for the different experimental approaches considered here, which shows that the distance estimation problem is in fact related to the localization accuracy problem, the latter being a distinct problem that deals with how accurately the location of an object can be determined.
Abstract: Optical microscopy is an invaluable tool to visualize biological processes at the cellular scale. In the recent past, there has been significant interest in studying these processes at the single molecule level. An important question that arises in single molecule experiments concerns the estimation of the distance of separation between two closely spaced molecules. Presently, there exists different experimental approaches to estimate the distance between two single molecules. However, it is not clear as to which of these approaches provides the best accuracy for estimating the distance. Here, we address this problem rigorously by using tools of statistical estimation theory. We derive formulations of the Fisher information matrix for the underlying estimation problem of determining the distance of separation from the acquired data for the different approaches. Through the Cramer-Rao inequality, we derive a lower bound to the accuracy with which the distance of separation can be estimated. We show through Monte-Carlo simulations that the bound can be attained by the maximum likelihood estimator. Our analysis shows that the distance estimation problem is in fact related to the localization accuracy problem, the latter being a distinct problem that deals with how accurately the location of an object can be determined. We have carried out a detailed investigation of the relationship between the Fisher information matrices of the two problems for the different experimental approaches considered here. The paper also addresses the issue of a singular Fisher information matrix, which presents a significant complication when calculating the Cramer-Rao lower bound. Here, we show how experimental design can overcome the singularity. Throughout the paper, we illustrate our results by considering a specific image profile that describe the image of a single molecule.
28 citations
TL;DR: This paper addresses the problems of delay-range-dependent stability and robust stability for uncertain two-dimensional (2-D) state-delayed systems in the Fornasini–Machesini second model, with the uncertainty assumed to be of norm bounded form.
Abstract: This paper addresses the problems of delay-range-dependent stability and robust stability for uncertain two-dimensional (2-D) state-delayed systems in the Fornasini---Machesini second model, with the uncertainty assumed to be of norm bounded form. A generalized Lyapunov function candidate is introduced to prove the stability condition and some free-weighting matrices are used for less conservative conditions. The resulting stability and robust stability conditions in terms of linear matrix inequalities are delay-range-dependent. Some numerical examples are given to illustrate the method.
24 citations
TL;DR: This paper is dedicated to the study of robust stability and controller synthesis for discrete linear repetitive processes with polytopic uncertainty in the robust control domain, where conditions based on parameter dependent Lyapunov functions are proposed in order to reduce the conservatism related to uncertainty problems.
Abstract: This paper is dedicated to the study of robust stability and controller synthesis for discrete linear repetitive processes with polytopic uncertainty. In the robust control domain, conditions based on parameter dependent Lyapunov functions are proposed in order to reduce the conservatism related to uncertainty problems. The solution is a class of Lyapunov functions that depends in a polytopic way on the uncertain parameters and that can be derived from linear matrix inequality conditions. Nevertheless, in many cases in practice, the frequency range of reference signals, noises and disturbances are known beforehand. Therefore, performing controller synthesis in the full frequency range is not practically suited and may introduce conservatism to some extent. Based on generalized Kalman–Yakubovich–Popov Lemma, a finite frequency controller is derived for uncertain discrete linear repetitive processes which are the most investigated class of 2D systems. Hence, the designer can specify a frequency range where the prescribed control performance is required, where, for example, this range could be determined by inspection of frequency spectrums of the available signals.
TL;DR: A computationally feasible characterisation of spatially distributed controllers stabilising a linear spatially invariant system, that is, a system described by linear partial differential equations with coefficients independent on time and location, is given.
Abstract: The paper gives a computationally feasible characterisation of spatially distributed controllers stabilising a linear spatially invariant system, that is, a system described by linear partial differential equations with coefficients independent on time and location. With one spatial and one temporal variable such a system can be modelled by a 2-D transfer function. Stabilising distributed feedback controllers are then parametrised as a solution to the Diophantine equation ax + by = c for a given stable bi-variate polynomial c. The paper is built on the relationship between stability of a 2-D polynomial and positiveness of a related polynomial matrix on the unit circle. Such matrices are usually bilinear in the coefficients of the original polynomials. For low-order discrete-time systems it is shown that a linearising factorisation of the polynomial Schur-Cohn matrix exists. For higher order plants and/or controllers such factorisation is not possible as the solution set is non-convex and one has to resort to some relaxation. For continuous-time systems, an analogue factorisation of the polynomial Hermite-Fujiwara matrix is not known. However, for low-order systems and/or controller, positivity conditions on the closed-loop polynomial coefficients can be invoked. Then the computational framework of linear matrix inequalities can be used to describe the stability regions in the parameter space using a convex constraint.
TL;DR: A low-complexity algorithm is presented for the estimation of the nominal direction-of-arrivals (DOAs) of incoherently distributed (ID) sources by a novel propagator method which makes use of the approximate rotational invariance relationship between two closely spaced identical uniform linear arrays.
Abstract: A low-complexity algorithm is presented for the estimation of the nominal direction-of-arrivals (DOAs) of incoherently distributed (ID) sources. The presented algorithm estimates the nominal DOAs of ID sources by a novel propagator method which makes use of the approximate rotational invariance relationship between two closely spaced identical uniform linear arrays. Without any search and the eigendecomposition of the sample covariance matrix, our algorithm can provide lower computational complexity than other known methods. In addition, it can be applied to the multisource scenario with different angular distribution shapes. Simulation results prove the effectiveness of the presented algorithm.
TL;DR: Two 2-D based algorithms are presented for the weighted least squares (WLS) design of quadrantally symmetric 2- D FIR filters with arbitrary weighting functions, based on matrix iterative techniques with guaranteed convergence and design time.
Abstract: The impulse response coefficients of a two-dimensional (2-D) finite impulse response (FIR) filter naturally constitute a matrix. It has been shown by several researchers that, two-dimension (2-D) based algorithms that retain the natural matrix form of the 2-D filter's coefficients are computationally much more efficient than the conventional one-dimension (1-D) based algorithms that rearrange the coefficient matrix into a vector. In this paper, two 2-D based algorithms are presented for the weighted least squares (WLS) design of quadrantally symmetric 2-D FIR filters with arbitrary weighting functions. Both algorithms are based on matrix iterative techniques with guaranteed convergence, and they solve the WLS design problems accurately and efficiently. The convergence rate, solution accuracy and design time of these proposed algorithms are demonstrated and compared with existing algorithms through two design examples.
TL;DR: Repetitive processes are a class of 2D systems where information propagation in one direction is of finite duration and such a theory is advanced through the development of new control law design algorithms.
Abstract: Repetitive processes are a class of 2D systems where information propagation in one direction is of finite duration. These processes make a series of sweeps, termed passes, through a set of dynamics and on completion of each pass resetting to the starting position occurs ready for the start of the next pass. The control problem is that the previous pass output, termed the pass profile, acts as a forcing function on the current pass and can result in oscillations that increase in amplitude from pass-to-pass. In the case of discrete dynamics, these processes have structural links with 2D systems described by the well known Roesser and Fornasini–Marchesini state-space models but some applications require updating structures that cannot be represented by these models. This requirement arises either in adequately modeling the dynamics or as a result of the control law structure and requires the development of a systems theory for eventual use in applications. In this paper such a theory is advanced through the development of new control law design algorithms.
TL;DR: This work proposes a new mathematical expression of energy operators linked to Teager-Kaiser energy operator (TKEO) using directional derivatives along any n-D vector and Kronecker powers and introduces a new scalar function using the directional derivative along a vector to recover the “sign” of the frequency components.
Abstract: This work aims at introducing some energy operators linked to Teager-Kaiser energy operator (TKEO) (Kaiser in On a simple algorithm to calculate the energy of a signal, pp 381---384, 1990), its associated higher order versions and expanding them to multi-dimensional signals. These operators are very useful for analysing oscillatory signals with time-varying amplitude and frequency (AM---FM). We first propose a new mathematical expression of these operators using directional derivatives along any n-D vector and Kronecker powers (Proposition 1, Sect. 3). This mathematical formulation allows us to extend to n-D case some properties of the classical TKEO such as tracking of AM envelope and instantaneous frequency of a multi-dimensional AM---FM signal. In addition, we have introduced a new scalar function using the directional derivative along a vector to recover the "sign" of the frequency components. Applications of this model to a local n-D AM---FM signal and the related demodulation errors are presented. To show the effectiveness and the robustness of the new class of operators in term of envelope and frequency tracking, results obtained on synthetic and real data are compared to multi-dimensional energy separation algorithm (Maragos and Bovik in J Opt Soc Am A 12:1867---1876, 1995) and to our previously developed method (Salzenstein and Boudraa in Signal Process 89(4):623---640, 2009). Finally, the performances of these methods are investigated in the presence of an additive noise.
TL;DR: This paper derives a novel implementation of a very computationally demanding matched filter-bank based a spectral estimator, namely the multi-dimensional Capon spectral estimators, and proposes to use the discrete Zhang neural network for the online covariance matrix inversion.
Abstract: The minimum variance spectral estimator, also known as the Capon spectral estimator, is a high resolution spectral estimator used extensively in practice. In this paper, we derive a novel implementation of a very computationally demanding matched filter-bank based a spectral estimator, namely the multi-dimensional Capon spectral estimator. To avoid the direct computation of the inverse covariance matrix used to estimate the Capon spectrum which can be computationally very expensive, particularly when the dimension of the matrix is large, we propose to use the discrete Zhang neural network for the online covariance matrix inversion. The computational complexity of the proposed algorithm for one-dimensional (1-D), as well as for two-dimensional (2-D) and three-dimensional (3-D) data sequences is lower when a parallel implementation is used.
TL;DR: An improved iterative algorithm is put forward to maximize the signal-to-clutter-plus-noise ratio (SCNR) under the constant modulus constraint to strengthen the detection performance in the presence of clutter and white Gaussian noise.
Abstract: This paper proposes a novel method of unimodular transmitting waveforms design for multiple-input multiple-output (MIMO) radar to strengthen the detection performance in the presence of clutter and white Gaussian noise. An improved iterative algorithm is put forward to maximize the signal-to-clutter-plus-noise ratio (SCNR) under the constant modulus constraint. During iterations, the optimization of unimodular waveforms with filters fixed is a nonconvex fractional quadratically constrained quadratic program problem, which is NP-hard and not able to be solved in polynomial time. An algorithm based on semidefinite programming relaxation combined with bisection and Gaussian randomization is introduced to provide the high-quality suboptimal solutions with a polynomial time computational complexity. The analysis on the approximation bound is given to prove the tightness of the semidefinite programming relaxation and so the correctness of the proposed algorithm. The simulation results show that the improved method is efficient in designing unimodular waveforms for MIMO radar to achieve a better SCNR performance.
TL;DR: It is shown that each dimension can nearly be regarded as an uncertain parameter and the other way around and their influence on the conservatism of the obtained condition is very similar.
Abstract: This paper aims at proposing a general framework for the establishement of LMI conditions to analyse the robust stability of a singular hybrid Roesser model subject to parametric uncertainties. The uncertain parameters are involved through implicit Linear Fractional Representations (LFR). Special focus is put on the influence of the number of uncertain parameters and the dimensionality of the model. More precisely it is shown that each dimension can nearly be regarded as an uncertain parameter and the other way around. Therefore, their influence on the conservatism of the obtained condition is very similar.
TL;DR: A systematic method is presented for the design of UIOs using a linear matrix inequality technique and an example is provided to illustrate the effectiveness of the proposed design method.
Abstract: This paper considers the analysis and design of asymptotic unknown input observers (UIOs) for a class of two-dimensional (2-D) nonlinear systems. A sufficient condition for the existence of an asymptotic UIO such that the observer estimation error asymptotically converges to zero is first given in terms of a rank condition on the given system matrices. A systematic method is then presented for the design of UIOs using a linear matrix inequality technique. An example is provided to illustrate the effectiveness of the proposed design method.
TL;DR: The design and analysis of two-channel two-dimensional (2D) nonseparable nearly-orthogonal symmetric wavelet filter banks with quincunx decimation is studied and methods for analyzing the correlation of the semi-orthogsonal filter banks are proposed.
Abstract: The design and analysis of two-channel two-dimensional (2D) nonseparable nearly-orthogonal symmetric wavelet filter banks with quincunx decimation is studied. The basic idea is to impose multiple zeros at the aliasing frequency to a symmetric filter and minimize the deviation of the filter satisfying the orthogonal condition to obtain a nearly-orthogonal FIR filter bank. Since multiple zeros are imposed, a scaling function may be generated from the minimized filter. With this filter, a semi-orthogonal filter bank is constructed. Methods for analyzing the correlation of the semi-orthogonal filter banks are proposed. The integer translates of the wavelet and scaling function are nearly-orthogonal. The integer translates of the wavelet at different scale are completely orthogonal. The semi-orthogonal filter bank can be efficiently implemented using the corresponding nearly-orthogonal FIR filter bank.
TL;DR: A new view on uncertain system parameters is presented considering them in the same way as other independent variables, e.g., time or space variables, and how to extend the well known theory of designing optimal controllers with quadratic criterion to cover the reduction of uncertainties in systems described by a class of linear partial differential equations.
Abstract: A new view on uncertain system parameters is presented considering them in the same way as other independent variables, e.g., time or space variables. After re-interpreting the well known equations for the sensitivities of a system to parameter changes, we consider the problem of optimal control that takes into account not only the quality of control itself, but also a reduction in the influence of parameter changes. Firstly, we re-derive and elucidate known results for systems described by linear ordinary differential equations in the state-space form. Then, it is shown how to extend the well known theory of designing optimal controllers with quadratic criterion so as to cover the reduction of uncertainties in systems described by a class of linear partial differential equations. As a result, we obtain a controller that has a new modal structure in space. Furthermore, the controller incorporates additional sensitivity signals for each mode.
TL;DR: This paper proposes a new direction-of-arrival estimation technique as well as a beamformer with the spatial domain IIR array implementation which potentially can offer more degrees of freedom to control the performance of the array and reduce the complexity of the system for a desired performance.
Abstract: Various array processing techniques applied to uniform linear arrays are involuntarily realized using structures that are analogous to finite impulse response filters. This observation leads to the following question: "can we extend infinite impulse response (IIR) filtering to array processing?". In this paper, we introduce the concept of IIR array in spatial domain. Note that IIR array here does not mean time-domain IIR filtering for array beamforming which is commonly understood. This paper is dedicated to the study of an alternate approach for array signal processing which defines IIR structure in spatial domain. To illustrate the applicability of the concept of IIR array, we propose a new direction-of-arrival estimation technique as well as a beamformer with the spatial domain IIR array implementation. The performance of the proposed methods are comparable to the existing techniques. These illustrations are intended to introduce a new approach which potentially can offer more degrees of freedom to control the performance of the array and reduce the complexity of the system for a desired performance.
TL;DR: The new concept of 2D structured system is defined and characterizations of global reachability are obtained, extending well known results for the 1D case.
Abstract: The new concept of 2D structured system is defined and characterizations of global reachability are obtained. This paper extends well known results for the 1D case, according to which a structured system (A ?, B ?) is (generically) reachable if and only if its graph is spanned by a cactus, or, equivalently, if and only if the pair (A ?, B ?) is full generically row rank and irreducible.
TL;DR: This paper investigates a realization of a three-dimensional (3-D) adaptive notch filter based on adaptive line enhancer on infinite impulse response (IIR) lattice structure and shows how to remove a sinusoidal interference superimposed on a 3-D image.
Abstract: This paper investigates a realization of a three-dimensional (3-D) adaptive notch filter. The procedures are mainly divided into two parts: frequency-detecting and sinusoidal interference removal. The detections are based on adaptive line enhancer on infinite impulse response (IIR) lattice structure. In the interference removal part, a non-separable version of a 3-D notch filter is effectively applied. The magnitude response of a 3-D adaptive IIR notch filter is illustrated. At the end of the paper, the implementation of an IIR notch filter on a 3-D image is also conducted in order to show how to remove a sinusoidal interference superimposed on a 3-D image.
TL;DR: The existence of a solution to an optimization problem under appropriate assumptions is the main result of this paper.
Abstract: In the paper the optimization problem described by some nonlinear hyperbolic equation being continuous counterpart of the Fornasini-Marchesini model is considered. A theorem on the existence of at least one solution to this hyperbolic PDE is proved and some propertiesofthesetofallsolutionsareestablished.Theexistenceofasolutiontoanoptimiza- tionproblemunderappropriateassumptionsisthemainresultofthispaper.Someapplication of the obtained results to the process of gas filtration is also presented. Ft ,ϕ � (t) ,ϕ �� (t) ,ψ � (t) ,ψ �� (t) � dt + g � ϕ (0) ,ϕ � (0) ,ψ � (0) � ,
TL;DR: A characterisation of robust stability in terms of the stability of several other polynomials yields a test for robust stability based on stability tests, and some fundamental results on robustly stable polynomial results are developed.
Abstract: We consider stability and robust stability of polynomials with respect to a given arbitrary disjoint decomposition $${{\mathbb C}^{n} = \Gamma \uplus \Lambda }$$ . A polynomial is called stable if it has no zeros in the region of instability ? and robustly stable if it is stable and remains so under small variations of its coefficients. Inspired by the article Robust stability of multivariate polynomials. Part 1: Small coefficient perturbations by Kharitonov et al. (Multidimens Syst Signal Process 10(1):21---32, 1999), we generalise some of their results to arbitrary stability decompositions and develop some fundamental results on robustly stable polynomials. The central one of them is a characterisation of robust stability in terms of the stability of several other polynomials, which yields a test for robust stability based on stability tests. Finally, we consider the special situation that the region of instability is a Cartesian product and recover some results for the standard stability decompositions for linear partial differential resp. difference equations with constant coefficients.
TL;DR: The definitions of controlled and conditioned invariance introduced, along with the corresponding output-nulling and input-containing subspaces, are shown to be richer than the one-dimensional counterparts.
Abstract: Geometric tools are developed for two-dimensional (2-D) models in an implicit Fornasini–Marchesini form. In particular, the structural properties of controlled and conditioned invariance are defined and studied. These properties are investigated in terms of quarter-plane causal solutions of the implicit model given compatible boundary conditions. The definitions of controlled and conditioned invariance introduced, along with the corresponding output-nulling and input-containing subspaces, are shown to be richer than the one-dimensional counterparts. The analysis carried out in this paper establishes necessary and sufficient conditions for the solvability of 2-D disturbance decoupling problems and unknown-input observation problems. The conditions obtained are expressed in terms of output-nulling and input-containing subspaces, which can be computed recursively in a finite number of steps.
TL;DR: This paper establishes a multiscale-multiband autoregresive model (MMAM) to characterize the inter-band, the spatial and the band-spatial correlation in hyperspectral data simultaneously and has the corresponding multiscales- multiband likelihood ratio (MMLR) test.
Abstract: There are often demands for region target detection such as air pollution detection and oil spill monitoring, even though small target detection has gained much attention in the field of hyperspectral detection. In this paper, we present a long-tail distribution based multiscale-multivariate autoregressive hyperspectral detector to handle such region targets. We establish a multiscale-multiband autoregresive model (MMAM) to characterize the inter-band, the spatial and the band-spatial correlation in hyperspectral data simultaneously and have the corresponding multiscale-multiband likelihood ratio (MMLR) test. Due to the long tail property of MMAM noise, we treat the statistical characteristics of MMAM noise as multivariate t distribution. Then, alternating projection involving fixed-point iteration and gradient based searching (APFPGS) are utilized to fit this statistical distribution. Experimental results on the real hyperspectral imagery recorded with A series of Environmental Probe System (EPS-A) show that our approach has better performance in hyperspectral region target detection than the other four detectors.
TL;DR: A frame-compatible top-bottom packing with a horizontal line offset is proposed, where the vertical resolutions of the stereoscopic left and right images are reduced by half, and the proposed algorithm improves the PSNR as much as 1.5–3dB comparing to conventional interpolation filters.
Abstract: As a transition stage from a conventional 2D TV to a full stereoscopic 3D TV system, a frame-compatible format of fitting stereoscopic left and right images to a single frame of the existing 2D TV is required to utilize existing codec and transmission infrastructure. To meet this requirement, a frame-compatible top-bottom packing with a horizontal line offset is proposed, where the vertical resolutions of the stereoscopic left and right images are reduced by half. Then, the optimal interpolation mode for each line segment of the sub-sampled horizontal line is determined by exploiting parallax-compensated data as well as undeleted neighboring upper and lower horizontal lines. At the receiver, the discarded horizontal lines for the left and right images are reconstructed by the interpolation modes provided by the sender. Experimental results show that the proposed algorithm improves the PSNR as much as 1.5---3dB comparing to conventional interpolation filters.