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ABSTRACT: The recent developments in the theory of multivariate polynomial matrix factorization have proven to be promising for potential
applications. Attention is given here to the relevance of the described algebraic results to multidimensional filter bank
design and, consequently, also to first generation discrete wavelet construction. The recent use of such wavelets in image
sequence superresolution (high resolution) is then described in the context of the conversion of the high resolution nonuniformly
sampled raster generated from an acquired sequence of low resolution frames to the desired uniformly sampled high resolution
grid. In the future, the multivariate polynomial matrix factorization results can be profitably adapted to the problem of
multidimensional convolutional code construction, and the construction (by filter banks) and subsequent deployment of second
generation wavelets (which adapt to irregular sampled data) are expected to provide improved superresolution.
02/2011: pages 137-156;
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ABSTRACT: A constructive procedure for factoring a polynomial paraunitary matrix as a product of atomic paraunitary matrices is considered. The generic form of the paraunitary factors results from the use of projection matrices. In the univariate case, the factorization carried out in the -transform domain collapses to other univariate paraunitary matrix factorization methods. In the multivariate case, the generic factor is constructed based on the assumption of its existence. Nontrivial examples for multiband univariate, bivariate, and trivariate cases are given to illustrate the simple and straightforward algorithmic implementation.
Circuits and Systems I: Regular Papers, IEEE Transactions on 03/2008; · 1.97 Impact Factor
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N.K. Bose
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ABSTRACT: The subject of multidimensional systems, as originally conceived, is concerned with a mathematical framework for tackling a broad range of paradigms whose analysis or synthesis require the use of functions and polynomials in either several complex or real variables. Its applications, which may range from the processing of spatial and temporal signals of diverse physical origin to the design of linear continuous-discrete multidimensional control systems, are already plentiful. This paper aims to promote interaction between a broad spectrum of scientists and engineers through clear exposition and interpretation of fundamentals, albeit a daunting task, so that complex theoretical results become useful to practitioners in distinct but related disciplines. The expanding arena of theory and applications of the original aims and scopes attest to the importance and vitality of the subject-matter.
IEEE Circuits and Systems Magazine 01/2008; · 1.44 Impact Factor
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ABSTRACT: Steps are taken to design the optical system of lenslet array/photoreceptor array plexus on curved surfaces to achieve a large field of view (FOV) with each lenslet capturing a portion of the scene. An optimal sampling rate in the image plane, as determined by the pixel pitch, is found by the use of an information theoretic performance measure. Since this rate turns out to be sub-Nyquist, superresolution techniques can be applied to the multiple low-resolution (LR) images captured on the photoreceptor array to yield a single high-resolution (HR) image of an object of interest. Thus, the computational imaging system proposed is capable of realizing both the specified resolution and specified FOV.
EURASIP Journal on Advances in Signal Processing. 01/2007;
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ABSTRACT: The multidimensional generalized sampling theorem (GST) developed here provides a theoretical framework for wavelet based image superresolution, a topic of interest to the signal and image processing community during the last few years
Image Processing, 2006 IEEE International Conference on; 11/2006
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ABSTRACT: An irregularly spaced sampling raster formed from a sequence of low-resolution frames is the input to an image sequence superresolution algorithm whose output is the set of image intensity values at the desired high-resolution image grid. The method of moving least squares (MLS) in polynomial space has proved to be useful in filtering the noise and approximating scattered data by minimizing a weighted mean-square error norm, but introducing blur in the process. Starting with the continuous version of the MLS, an explicit expression for the filter bandwidth is obtained as a function of the polynomial order of approximation and the standard deviation (scale) of the Gaussian weight function. A discrete implementation of the MLS is performed on images and the effect of choice of the two dependent parameters, scale and order, on noise filtering and reduction of blur introduced during the MLS process is studied
IEEE Transactions on Image Processing 09/2006; · 3.04 Impact Factor
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ABSTRACT: An irregularly spaced sampling raster formed from a sequence of low-resolution frames is the input to an image sequence superresolution algorithm whose output is the set of image intensity values at the desired high-resolution image grid. The method of moving least squares (MLS) in polynomial space has proved to be useful in filtering the noise and approximating scattered data by minimizing a weighted mean-square error norm, but introducing blur in the process. Starting with the continuous version of the MLS, an explicit expression for the filter bandwidth is obtained as a function of the polynomial order of approximation and the standard deviation (scale) of the Gaussian weight function. A discrete implementation of the MLS is performed on images and the effect of choice of the two dependent parameters, scale and order, on noise filtering and reduction of blur introduced during the MLS process is studied.
IEEE Transactions on Image Processing 09/2006; 15(8):2239-48. · 3.04 Impact Factor
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04/2006: pages 315-326;
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Pattern Recognition Letters. 01/2006; 27:356-365.
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ABSTRACT: Wavelet coefficient thresholding is effective in reducing spatial domain noise in wavelet-based super-resolution algorithms. Here, the effect of the threshold level on reconstructed image quality in second-generation wavelet super-resolution is investigated. The choice of optimal threshold involves a tradeoff between noise filtering and blurring introduced by thresholding. A measure based on the singular values of the image matrix is employed as a reliable gauge of generated high-resolution image quality.
IEEE Signal Processing Letters 12/2005; · 1.39 Impact Factor
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ABSTRACT: Properties of wavelets with finite as well as infinite support are summarised to facilitate mother wavelet selection in a chosen application. The quantitative guidelines reduce dependence on trial-and-error schemes resorted to for selection and underscore the importance of such selection in any application of interest. In wavelet-based image sequence superresolution, studied during the last four years, the use of a B-spline mother wavelet is justified.
IEE Proceedings - Vision Image and Signal Processing 11/2005;
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ABSTRACT: Neural networks have been applied to landmine detection from data generated by different kinds of sensors. Real-valued neural networks have been used for detecting landmines from scattering parameters measured by ground penetrating radar (GPR) after disregarding phase information. This paper presents results using complex-valued neural networks, capable of phase-sensitive detection followed by classification. A two-layer hybrid neural network structure incorporating both supervised and unsupervised learning is proposed to detect and then classify the types of landmines. Tests are also reported on a benchmark data.
IEEE Transactions on Neural Networks 06/2005; 16(3):743-53. · 2.95 Impact Factor
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ABSTRACT: A constructive factorization procedure for a polynomial paraunitary matrix as a product of atomic paraunitary matrices, each of lowest degree, is given. The generic form of these paraunitary factors results from the use of projection matrices. In the univariate case, each factor is of degree 1. In the multivariate case, the generic factor is constructed based on the assumption of its existence.
Acoustics, Speech, and Signal Processing, 2005. Proceedings. (ICASSP '05). IEEE International Conference on; 04/2005 · 4.63 Impact Factor
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ABSTRACT: A system-theoretic proof for the spatiotemporal-bandwidth product (STBP) of multidimensional signals is given. Explicit formulae for the STBP of multivariate Gaussian signals and their derivatives are also supplied.
IEEE Signal Processing Letters 03/2005; · 1.39 Impact Factor
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ABSTRACT: This paper considers the fundamental problem of passive multidimensional Kirchhoff networks for linear time-varying systems that are suitable for wave digital filter discretization. An explicit solution, subject to the validity of a commutativity condition, is given in the linear time-varying case for the feasibility of representation of the coupled inductor, the crucial dynamic multiport in the network, in two equivalent forms so that the property of losslessness of the coupled inductor, and therefore, passivity of the entire network, is assured by the nonnegative definiteness of the inductance matrix for all space and time variables. The commutativity condition is expressed in an equivalent form that requires the product of two skew-symmetric matrices to be symmetric. An isomorphism is developed and proved between the spaces of skew-symmetric and orthogonal matrices of a common order. The feasibility of generalization of these results to the case of nonlinear current-controlled coupled inductor matrix is briefly explored and illustrative examples are provided throughout to facilitate comprehension of the concepts.
Circuits and Systems I: Regular Papers, IEEE Transactions on 08/2004; · 1.97 Impact Factor
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N.K. Bose
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ABSTRACT: Due to cost of hardware, size, and fabrication complexity limitations, imaging systems like CCD detector arrays or digital cameras often provide only multiple low-resolution (LR) degraded images. However, a high-resolution (HR) image is indispensable in many applications including health diagnosis and monitoring, military surveillance, and terrain mapping by remote sensing. Other intriguing possibilities include substituting expensive high-resolution instruments like scanning electron microscopes by their cruder, cheaper counterparts and then applying technical methods for increasing the resolution to that derivable with much more costly equipment. This paper presents a comparison between the various popular approaches to the attaining of superresolution following image acquisition.
Applied Imagery Pattern Recognition Workshop, 2003. Proceedings. 32nd; 11/2003
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ABSTRACT: It is proved that the multidimensional differential operator is an annihilator of the adjoint matrix associated with a Jacobian matrix. Some of the consequences of this result to other distinguished matrices are pointed out and its relevance in the derivation of a multidimensional wave digital filter structure from a passive multidimensional Kirchhoff network is confirmed.
IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications 02/2003;
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ABSTRACT: An algorithm based on spatial tessellation and approximation of each triangle patch in the Delaunay (1934) triangulation (with smoothness constraints) by a bivariate polynomial is advanced to construct a high resolution (HR) high quality image from a set of low resolution (LR) frames. The high resolution algorithm is accompanied by a site-insertion algorithm for update of the initial HR image with the availability of more LR frames till the desired image quality is attained. This algorithm, followed by post filtering, is suitable for real-time image sequence processing because of the fast expected (average) time construction of Delaunay triangulation and the local update feature.
IEEE Transactions on Image Processing 02/2002; 11(12):1427-41. · 3.04 Impact Factor
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ABSTRACT: An algorithm, based on spatial tessellation and approximation of each triangle patch in the Delaunay triangulation (with smoothness constraints) by a bivariate polynomial, is advanced to construct a high resolution (HR) high quality image from a set of low resolution (LR) frames. This algorithm, followed by post filtering, is suitable for real-time image sequence processing because of the fast expected (average) time construction of Delaunay triangulation and the local update feature.
Image Processing. 2002. Proceedings. 2002 International Conference on; 02/2002
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ABSTRACT: Subsequent to the work of Kim, Bose, and Valenzuela in 1990 on the
simultaneous filtering and interpolation of a registered sequence of
undersampled noisy and shift-invariant blur degraded images, Bose and
Boo tackled in 1998 the problem of reconstructing a high-resolution
image from multiple undersampled, shifted, degraded frames with subpixel
displacement errors. This led to a formulation involving a periodically
shift-variant system model. Lertrattanapanich and Bose advanced in 1999
a procedure for construction of a high-resolution video mosaic following
the estimation of motion parameters between successive frames in a video
sequence generated from a video camera. Current research is focused on
simultaneous blur identification and robust superresolution. The blur is
not restricted to be linear shift-invariant and could not only be of the
linear shift-variant type but also some nonlinear blurs could be
accommodated. The optimal tuning parameter may, if desired, be
calculated analytically and not by trial-and-error
Circuits and Systems, 2001. ISCAS 2001. The 2001 IEEE International Symposium on; 06/2001
