Regularization based super-resolution (SR) methods have been widely used to improve video resolution in recent years. These methods, however, only minimize the sum of difference between acquired low resolution (LR) images and observation model without considering video local structure. In this paper, we proposed an idea, which employs adaptive kernel regression on regularization based SR methods, to improve super-resolution performance. Arbitrary motions in input video are also considered and well modeled in our work. It is shown that the proposed idea can provide better visual quality as well as higher Peak Signal-to-Noise Ratio (PSNR) than approaches using regularized scheme or adaptive kernel regression alone.

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.

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.

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.

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.

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.

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.

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.

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.

A novel robust image coding and adaptive packetization algorithm suitable for very low-bit-rate transport is suggested. This algorithm can be applied to any zerotree-based encoder, such as the embedded zerotree wavelet coder of Shapiro (1993) and set partitioning in hierarchical trees by Said and Pearlman (1996). A very explicit segmentation and packetization method of an image bitstream, where the lowest frequency subband is separately encoded from the higher frequency subbands for unequal protection over a noisy channel, is proposed. The trees in the higher frequency subbands are split, classified, and assembled for efficient image coding and packetization according to their initial threshold and subband. The use of these classified trees enables one to make robust packets, while giving priority to some packets. In practice, each packet has a different initial threshold and can be decoded independently. In spite of additional overhead bits required for packetization, the algorithm reported is comparable to the original zerotree-based image coders at low bit rates. Additionally, simulation results show that the new method is resilient under severe packet losses.

A novel spatio-temporal filter is described for monochrome image sequences with either signal-independent or signal-dependent noise by considering both spatial and temporal correlations. With the assumptions of spatio-temporal separability and temporal stationarity, it is shown that motion-compensated groups of frames can be decorrelated by using the Karhunen-Loeve transform. Practical filters that work well on a variety of image sequences are developed by first applying the Hadamard transform along the temporal direction. Subsequently, the parametric adaptive Wiener filter is applied to each of the resulting approximately decorrelated transformed images. These transformed images are classified into one average image and a remaining set of residual images, which provide interesting and useful interpretations of the type of image sequence. The filter performance is evaluated by considering different types of image sequences in the database. The procedure advanced for processing a sequence of monochrome images can be adapted for generalization to multispectral images and this possibility is currently under detailed investigation.

The need for approximating block-Toeplitz with Toeplitz block matrices by means of block-circulant with circulant block matrices with the objective of transforming an inherently ill-posed image deconvolution problem to a well-posed one motivated a surge of papers on the analysis of the quality as well as the speed of convergence of the algorithms that produce such approximants to serve as preconditioners for conjugate-gradient methods. This correspondence contributes to that surge by giving a simple proof of the fact that the sequence of eigenvalues of the Hermitian block Toeplitz with Toeplitz-block matrices are asymptotically equidistributed. To do this, Weyl's (1916) results on the distribution properties of multidimensional sequences are exploited. Inferences to related results are made.

The problem of vector quantizing the parameters of a neural network is addressed, followed by a discussion of different algorithms applicable for quantizer design. Optimal, as well as several suboptimal quantization schemes are described. Simulations involving nonlinear prediction of speech signals are presented to compare the performance of different quantization techniques. Performance evaluation conducted uncover the tradeoffs in implementational complexity. Among the three examined suboptimal quantization schemes, it is shown that the multistage quantizer offers the best tradeoff between complexity and performance.

A procedure is advanced to restore a single color image, which has been degraded by a linear shift-invariant blur in the presence of additive stationary noise. Four sensors are needed, followed by the application of the RGB-to-YIQ transformation. Subsequently, one three-dimensional (3D) Wiener filter on a sequence of two luminance component images and two two-dimensional (2D) Wiener filters on each of the two chrominance component images are needed. For the procedure to be successful, the imposition of a strongly coprime condition on the wavenumber response of two distinct sensor blur functions is necessary. The resulting well-conditioned problem is shown to provide improved restoration over the decorrelated component and the independent channel restoration methods, each of which uses one sensor for each of the three primary color components.

A procedure is advanced to restore a single color image, which has been degraded by a linear shift-invariant blur in the presence of additive noise. Four sensors are needed, followed by the application of the RGB-YIQ transformation. Subsequently, one 3-D Wiener filtration is required on a sequence of two luminance components and a 2-D Wiener filter is needed on each of the two chrominance components. For the procedure to be successful, the imposition of a strongly coprime condition on the wavenumber response of two distinct sensor blur functions is necessary. The resulting well-conditioned problem is shown to provide high-quality color images.

A theoretical analysis is proposed to evaluate the robustness of the total least square (TLS) algorithm for image reconstruction from a sequence of undersampled noisy and blurred frames in the wavenumber domain. Since the data samples in the wavenumber domain are complex-valued, the results from the TLS theory developed for the case of real-valued data are adapted to the situation at hand. It is shown that the image quality can be improved as more frames become available. In the case of blurred frames, higher resolution images may be reconstructed using the TLS algorithm with post-deblurring. Finally, computer simulation results are provided to demonstrate the robustness of the TLS algorithm for image reconstruction.>

A novel approach is proposed which determines the number of layers, the number of neurons in each layer, and their connection weights for a particular implementation of a neural network, with the multilayer feedforward topology, designed to classify patterns in the multidimensional feature space. The approach is based on construction of a Voronoi diagram over the set of points representing patterns in feature space and this finds added usefulness in deriving alternate neural network structures for realizing the desired pattern classification.

Coefficient quantization errors could adversely affect the frequency response and stability properties of both 1-D and n-D digital filters. The author provides an analytic framework for evaluating filter frequency/wavenumber response under finite arithmetic errors from a small subset of fixed extreme filters. An approach for applying boundary implication methods to the analysis of interval FIR (finite impulse response) and IIR (infinite impulse response) frequency responses is evaluated.>

Some of the key mathematical limitations encountered in multidimensional digital signal processing research, the useful general settings in which various topical investigations are facilitated, and directions for future research are summarized. The discussion covers multidimensional sampling, multidimensional signal processing over polydisc algebra, nonlinear multidimensional filtering and prediction, and nonlinear nonstationary multidimensional modelling approaches.

The authors consider the factorization of the 1-D and 2-D spectral density functions (z-transforms of real-valued autocorrelation sequences), S(z) and S(z/sub 1/, z/sub 2/) in the forms Sz=F(z)F(z/sup -1/) and S(z/sub 1/, z/sub 2/)=F(z/sub 1/, z/sub 2/) F(z/sub 1//sup -1/, z/sub 2//sup -1/), respectively where the coefficient of polynomials F(z) and F(z/sub 1/, z/sub 2/) are constrained to be nonnegative. The problem is solved only in special cases. In the general situation, the scopes for adapting and generalizing the iterative techniques available for the classical 1-D spectral factorization problem to tackle the nonnegativity constrained spectral factorization problem under study have been analyzed.>

An analysis of the quadratic-linear (QL) filter, for improving signal detection capability and facilitating image segmentation, is carried out. The principal results are the solutions for QL filters under the generalized deflection criterion and Gaussian input assumptions; the establishment of mapping order properties for two-dimensional implementations of linear, pure quadratic, and QL filters; and the definition of regions of superior performance for the QL filter as compared to linear and quadratic filters under Gaussian assumptions when the input has separated means and separated variances.>

This paper considers the generalization of 1-D iterative methods to the 2-D case in order that 2-D spectral factorization may be iteratively implemented. The 2-D Bauer generalization has been proposed by other authors. The authors of this paper have obtained meaningful generalizations of Wilson's and Arp's algorithms. Comparisons of the proposed generalizations bring out the advantages of the 2-D Wilson scheme in terms of guaranteed stability of the spectral factor coupled with accuracy and speed of convergence.