The monitoring of the pressure, in terms of nodal head values, is an important task in water distribution networks, to ascertain the integrity of the components, e.g. pipes. The placement of sensors at desired locations, in realistic situations, is a challenging problem due to various practical constraints. In practice, nodal heads are estimated at locations with no sensors. In this work, we propose an algorithm, termed mean percolation head reconstruction (MPHR), for estimating the nodal heads. The iterative algorithm is inspired by concepts from graph signal processing (GSP), and consists of two stages. The first stage is equivalent to the percolation of known values across the network, and the second stage performs some form of constrained consensus computations. The algorithm is robust against uncertainty in the network parameters and suboptimal placement of sensors. Extensive simulations have demonstrated the superiority of MPHR compared to other proposed reconstruction algorithms.

Graph filter banks allow for the spectral analysis of signals defined over graph domains. We consider the construction of two channel biorthogonal filter banks with outputs that are critically sampled. A method that sharpens the frequency response of an existing filter bank will be presented. The method is based on the use of sharpening kernels, and an analytical technique for constructing the kernels will be developed. Polyphase analysis of the sharpened filters will be performed, and the relationship between the original and sharpened polyphase structures will be derived. The polyphase structure allows the filter bank to be implemented efficiently using lifting steps. We will show that the number of lifting steps of the sharpened structure is unchanged, compared to the original structure. Application to nonlinear approximation of images will also be considered.

The problem of denoising signals, defined over graph domains, using a regularization framework, is considered here. Using the$L^{2}$norm, the optimum denoising operator involves a matrix inverse. Approximation of the operator via matrix polynomial is commonly used to achieve an efficient distributed implementation. We first propose a modification to the fidelity term in the regularization framework. Based on the assumption of signal smoothness, weighting is applied to the frequency components of the noisy signal. We then propose an extension to the classical approximation using Chebyshev polynomials, by imposing linear constraints on the coefficients of the Chebyshev series. We will show that the constrained coefficients are related to the unconstrained coefficients via an affine transformation. Performance evaluation of the proposed distributed filters for denoising, using real-world datasets, is presented. Comparison with the classical filters is provided.

Graph filters are fundamental for extracting and processing signals defined over irregular domains. Most graph filters in the literature are linear, and are usually based on polynomials of the graph shift matrix. Autoregressive Moving Average (ARMA) graph filters are a generalization of polynomial filters, but are still linear. In this work, we propose a nonlinear graph filter that is an extension of the order one ARMA graph filter, to give the Median Autoregressive Graph Filter (MAF). The proposed MAF has a similar localization property to the linear counterpart, and can be implemented in a distributive manner. Though strictly nonlinear, the MAF has some linear-like properties, which will be formally proven in this work. Application of the proposed MAF to the denoising of real-world sensor network datasets will be presented. Comparisons with the linear counterpart will also be made.

Filterbanks have many applications. The orthogonal wavelet filter is widely used in filterbank design because of its advantage in energy preservation. In this work, the orthogonal wavelet filter with a given length and a prescribed number of Vanishing Moment (VM) is designed to achieve minimum Root- Mean-Square (RMS) bandwidth by using a symbolic approach.

Graph filter banks play a crucial role in the vertex and spectral representation of graph signals. The notion of two-channel nonsubsampled graph filter banks (NSGFBs) on an undirected graph was introduced recently. The absence of downsampling/upsampling operators allows greater flexibility in the design of NSGFBs that achieve perfect reconstruction. However the design of NSGFBs that take the spectral response into account has not been adequately addressed yet. Based on the polynomial/rational lifting scheme, this letter presents a simple method to design NSGFBs with good spectral response and perfect reconstruction. Experimental results will demonstrate the effectiveness of the proposed method in tailoring the spectral responses of the lifted NSGFBs. Application of the NSGFB to denoising will also be considered.

Graph signal processing on directed graphs is more challenging that on undirected graph, primarily because the graph matrices, e.g., adjacency or Laplacian, associated with the latter is non-symmetric. The eigenvalues that represent the spectral frequencies are therefore complex in general, and the design of spectral filters for complex frequencies presents more challenges. In this work we consider the design of two-channel filter banks for directed bipartite graphs. By decomposing any graph into a series of bipartite graphs, the basic two-channel system can be applied in cascade for arbitrary graphs. The graph filters are constructed using ladder structures. The design of the kernels in the ladder structures is achieved via a least-squares formulation. Analytical formulas are derived for the design of the kernel coefficients.

Two channel critically sampled filter banks for signal over graph domains were first proposed for undirected bipartite graphs by Narang and Ortega. Extension to the M-channel critically sampled case for balanced M-block cyclic graphs was then proposed by Teke and Vaidynathan but the filter bank does not achieve strict perfect reconstruction (PR), only generalized PR. In this letter, we consider the more general case of filter banks on unbalanced M-block cyclic graphs where strict PR is achieved. A polyphase analysis to derive the implementation structures in the downsampled domain is presented here. The relevant system/filter matrices have interesting cyclic properties and projection operators are needed to map signals between subgraphs.

A technique for denoising signals defined over graphs was recently proposed by Chen et al . (2014). The technique is based on a regularisation framework and denoising is achieved by solving an optimisation problem. Matrix inversion is required and an approximate solution that avoids directly calculating the inverse, by using a graph filter, was proposed by Chen et al . (2014). The technique, however, requires an eigendecomposition and the resulting filter degree is high. In this study, the authors propose a computationally efficient technique that is based on a least squares approximation of the eigenvalues of the inverse. They show that a good approximation can be achieved with a low degree graph polynomial filter without the need for any eigendecomposition. Low degree filters also have the desirable property of vertex localisation (analogous to time localisation). The filter gives denoising results that are very similar to that using the exact solution and can be implemented using distributed processing.

Wavelet filters with rational coefficients can be implemented efficiently in digital hardware using simple register shifts and adders. In this letter, a technique to construct biorthogonal filters with rational coefficients is presented. The filters have linear phase and also have very similar characteristics to orthogonal filters, while the latter cannot have linear phase. The frame bound ratio of the filters is very close to unity, i.e., almost tight. The filters are constructed via the lifting scheme with four lifting steps. The perfect reconstruction and the no-dc-leakage properties are preserved with these rational coefficients filters.

Filterbanks are widely used in many applications. In the literature, most filterbanks with irrational value coefficients were designed, while in practice, filters and filterbanks are implemented using rational coefficients. This paper introduces a powerful mathematical tool called Gröbner basis (GB)into the design of orthogonal filterbanks. Specifically, we use GB to find good rational lattice parameters for Daubechies length 6 (Db6) filterbank. We show that there does not exist any Db6 filterbank with rational coefficients and also meeting the first two vanishing moments (VM's). Moreover, we obtain several good Db6 filterbanks which meet the first VM exactly and the second VM approximately.

A new class of filter banks, that have structural perfect reconstruction, and its design is presented here. The filters are defined by four halfband filters and are constructed using the lifting scheme. The filter banks here is a generalization of the triplet halfband filter banks proposed by Ansari et. al. (1999). Filters that have linear phase response (symmetric coefficients) and are also virtually energy preserving can be constructed using the class of structure proposed.

A framework for oversampled filter banks for graph signals was recently proposed by Tanaka and Sakiyama (2014). It was shown that M-channel oversampled filter bank which is exactly orthogonal is not possible with polynomial spectral filter functions. The result is an extension of the critically sampled framework of Narang and Ortega (2012). In this work we present a solution that is nearly orthogonal which has the advantage of giving a nearly tight transform, i.e. nearly equal frame bounds. A family of target functions which satisfy the orthogonality condition is constructed using Bernstein polynomials. The design of the spectral filters is easily achieved through an approximation of the target functions. Filters with good spectral characteristics that are nearly orthogonal can be easily obtained using the proposed method.

Graph signal processing is an emerging area that has a wide variety of applications, e.g. energy networks, transportation networks and neuronal networks. Narang and Ortega (2012) proposed the critically sampled two-channel filter bank for signals on undirected graphs using spectral graph theory. The design of graph QMF (Quadrature-Mirror-Filters) by Narang and Ortega (2012) is based on the Chebyshev polynomial approximation of the ideal Meyer function. The reconstruction error using this method can be quite large especially for low degree filters and the high-pass filters suffer from DC leakage. A simple method that is analytically based is presented here for the design of the graph QMF without DC leakage and with low reconstruction error. The filters have flat spectral response at the DC and aliasing frequencies.

The processing of signal on graphs is becoming an important emerging area that has great potential in a wide variety of applications, e.g. social network. The work by Narang and Ortega (2012) laid the framework for critically sampled orthogonal two-channel filter bank for signal on undirected bipartite graphs. The design method presented by Narang and Ortega (2012) does not allow the tailoring of the filters spectral response and the control of the reconstruction error of the filter bank. This work present a method to design spectral filters that is based on Bernstein polynomial approximation and constrained optimization. The method allows the trade-off between transition band sharpness, ripple magnitude and reconstruction error.

For a time-limited sequence, the Root-Mean-Square (RMS) bandwidth is the normalized second moment of the spectrum. The RMS bandwidth is a useful and analytically tractable measure of the frequency localization of a discrete-time filter. In this work the design of orthogonal wavelet filter banks with a prescribed number of Vanishing Moment (VM) and having a minimum RMS bandwidth is considered. It is shown that the design problem can be cast as a convex optimization problem for which efficient algorithms and software for its solution exist.

The 2D separable wavelet transform offers limited directionality because it can only provide three directional subbands. The finer directional wavelet transform has been proposed to improve the directionality of the 2D separable wavelet transform. The finer directional wavelet transform employs quadrant filters on subband outputs of the 2D separable wavelet transform. It divides the three directional subband of wavelet transform into six finer directional subbands. Even though the finer directional wavelet transform has advantages of being non redundant and has efficient separable implementation, it suffers in performance due to aliasing. The aliasing occurs due to the quadrant filters' inherent frequency response characteristics and thus cannot be eliminated. This paper addresses the aliasing involved in the implementation of the finer directional wavelet transform and recommends ways to reduce the aliasing.

Orthonormal Hilbert pairs of wavelets that are time-reverse (mirror image) versions of each are termed Symmetric Self-Hilbertian wavelets and are used in the dual-tree complex wavelet transform. Previous methods for constructing the corresponding scaling low-pass filter are based on optimizing the product filter. These methods are practical only when the number of free-parameters is small due to the high computational load otherwise. An alternative method that is based on the orthogonal lattice is presented here and is practical with any number of free-parameters. Higher analytic quality Hilbert pairs can be obtained when there are more free-parameters. An effective strategy for optimizing the lattice parameters to give high quality filters is presented here.

It is a well-known fact that (compact-support) dyadic wavelets [based on the two channel filter banks (FBs)] cannot be simultaneously orthogonal and symmetric. Although orthogonal wavelets have the energy preservation property, biorthogonal wavelets are preferred in image processing applications because of their symmetric property. In this paper, a novel method is presented for the design of almost symmetric orthogonal wavelet FB. Orthogonality is structurally imposed by using the unnormalized lattice structure, and this leads to an objective function, which is relatively simple to optimize. The designed filters have good frequency response, flat group delay, almost symmetric filter coefficients, and symmetric wavelet function.

Two filter banks whose corresponding wavelets are Hilbert transforms of each other constitute a Hilbert-Pair. The common-factor technique is a simple technique proposed by Selesnick [1] for its design. The technique first requires the design of a phase factor which approximates the half-sample-delay condition. The technique then requires the computation of a factor that is common to both filter banks so that the perfect reconstruction condition is satisfied. The design of the phase factor by Selesnick [1] is based on all-pass filters which does not take the magnitude response into account. This paper proposes a direct approach to designing the phase factor that takes both the magnitude and phase into account. The new approach is more flexible and can yield better filters and wavelets.

A Hilbert-Pair is a pair of wavelets that are Hilbert transforms of each other. Previously an interesting discovery about the celebrated family of orthonormal Daubechies filters was made. It is found that if two filters whose lengths differ by four are chosen from this family, a Hilbert-Pair of reasonable approximation quality is obtained. The previous work considered only minimum phase filters. Extensions to the non-minimum phase case is considered here and a technique is presented for constructing non-minimum phase Hilbert-pairs.

A Hilbert-Pair consists of a pair of filter banks whose corresponding wavelets are Hilbert transforms of each other. Selesnick proposed the simple common-factor technique for its design. The filter transfer functions consist of the product of a factor that is common to both filter banks and a phase factor which gives the (approximate) half-sample-delay requirement. Previously the design of the phase factor has been based on designing an allpass filter approximating the half-sample-delay. This paper proposes a different approach to designing the phase factor by exploiting a basic multirate identity. The downsampling approach allows greater flexibility and can yield filters and wavelets with better properties.

The zero-pinning (ZP) was proposed by Tay as a simple technique to design orthonormal wavelets by specifying certain zeros (local minima) of a Bernstein polynomial. It was shown by Yu and Baradarani that there can be problems with this technique in situations where certain local maxima (which are not specified) exceed the value 1, thus violating the nonnegativity condition required for orthonormal filters. We present some practical rules to avoid these situations.

In this letter, we propose a sequential training scheme for multikernel support vector regression (SVR). Unlike the multistage backfitting technique; our method re-tunes, at every stage, all previously trained weights using a semiparametric algorithm in the presence of one more kernel function. In this way, local minima are avoided and any combination of arbitrary kernel functions is acceptable. By experimenting on some synthetic and real data sets, we demonstrate that our method yields a better trade-off between sparsity and accuracy in comparison with the conventional single-kernel SVR and the multikernel backfitting SVR.

A Hilbert-pair is a pair of wavelets that are Hilbert transforms of each other. A perfect reconstruction multirate filter bank defines a wavelet if the infinite product formula converges. If one chooses two filter banks arbitrarily, in general, the Hilbert transform relationship is not well approximated. This letter reports on an interesting discovery about the celebrated family of orthonormal Daubechies filters with maximum vanishing moments. It is found that if two filters whose lengths differ by four are chosen from this family, a Hilbert-pair of reasonable approximation quality is obtained. An explanation for this discovery is provided, and lessons that can be learned are discussed.

This letter develops a fast Fourier transform (FFT)-based method for estimating the impulse response of FIR single-input multiple-output (SIMO) channels driven by an unknown deterministic signal. The proposed algorithm successfully handles very short data sequences, for which the existing second-order statistics based methods, e.g., the subspace (SS), cross-relation (CR), and shifted correlation (SC) algorithms, are known to suffer performance degradation due to inaccurate statistics. The new method significantly outperforms the SS, CR, and SC methods with short sequences of observation data. This proposed method is computationally efficient for achieving good performance when data sequences are inevitably short, as in certain practical applications.

A simple yet versatile technique was recently introduced for designing FIR orthonormal wavelet filters. The technique involves pinning some of the zeros of the parametric Bernstein polynomial to ensure non-negativity of the frequency response. Filters with a high number of vanishing moments and sharper frequency response (but lower vanishing moments) than the maximally flat Daubechies filters can be easily designed. The position of the pinned zeros can be easily adjusted to give a variety of frequency response. This paper extends the previous work and presents a method to determine the zeros' position that will give a least squares error in the stopband response

A new class of biorthogonal filter banks, called the even-triplet-halfband-filter-bank (ETHFB), is introduced here. The filters have even-length, and are used to match a given odd-length filter bank such that the equivalent wavelet functions of both filter banks are approximate Hilbert transform of each other, ie. Hilbert pair. There are two versions of the ETHFB and they are modifications of the (odd-length) triplet-halfband-filter-bank. The parametric Bernstein polynomial is utilized in the construction of the three kernels that define the ETHFB. The determination of the design parameters of the filter bank is achieved through an efficient least squares method

The zero-pinning is a simple yet versatile technique that was recently introduced in the previous paper (2005) for designing FIR orthonormal wavelet filters. The technique basically involves pinning some of the zeros of the parametric Bernstein polynomial to ensure non-negativity of the frequency response. The position of the pinned zeros can be easily adjusted to give a variety of frequency response allowing trade-offs in stopband attenuation and roll-off sharpness. In this paper, we study the effect of the zeros' position on the Sobolev regularity of the equivalent wavelet function

An orthonormal Hilbert-pair consists of a pair of conjugate-quadrature-filter (CQF) banks such that the equivalent wavelet function of both banks are approximate Hilbert transforms of each other. We found that the celebrated orthonormal wavelets of Daubechies, which have maximum vanishing-moment (VM), cannot be used to construct good Hilbert-pairs. In this letter, we reduce the number of VM by one and construct a Hilbert-pair with almost maximum VM. Each pair of wavelets are time-reverse versions of each other, and the individual wavelets are of the least asymmetric type (i.e., approximate linear phase CQF)

A new class of biorthogonal wavelet filters and its design is presented in this work. The filters are even in length and are called Even-length Bernstein Filter Bank (EBFB). The new filter class is a modification of the Halfband Pair Filter Bank (HPFB, which only yields odd length filters) and is constructed using the Parametric Bernstein Polynomial. Perfect reconstruction is inherent in the structure of the filters, and the desired number of vanishing moments can be easily achieved by setting the appropriate parameters of the Bernstein Polynomial to zero. The design of the nonzero parameters is achieved through a least squares method that is noniterative. The design technique allows filters with different characteristics to be designed with ease.

A novel technique is presented for designing finite impulse response orthonormal wavelet filters. The filters are obtained from the spectral factorization of an appropriately designed parametric Bernstein polynomial. We show that by strategically "pinning" some of the zeros of the polynomial, the nonnegativity requirement on the polynomial, which is mandatory for orthonormal filter design, can be easily achieved. Filters with a high number of vanishing moments and sharper frequency response (but lower vanishing moments) than the maximally flat Daubechies filters can be easily designed. The technique is simple as it only involves solving linear equations yet is versatile as filters with different characteristics can be obtained with ease.

This paper presents a new technique for designing pairs of filter banks whose corresponding wavelet functions are approximate Hilbert transforms of each other. The filters have exact linear phase which yields biorthogonal wavelets with exact symmetry. The technique is based on matching the frequency response of a given odd-length filter bank with an even-length filter bank. The class of EBFB (even-length Bernstein filter bank) is utilized in the matching design. The EBFB has perfect reconstruction and vanishing moments properties structurally imposed and this simplifies the design process. The design is achieved through a non-iterative least squares method.

A family of biorthogonal wavelet filters for digital watermarking application is presented here. The filters are explicitly parametrized by two free parameters and can be used to provide diversity in watermarking. Diversity can be used to improve the security of the watermarking system from hostile attacks. Each filter has at least two vanishing moments which is important for ensuring some degree of smoothness in the resulting wavelet function.

In lossless image coding, it has been demonstrated that using the method of ordinary least squares (OLS) to design a linear predictor for each pixel results in better compression performance than that of the state-of-the-art. In previous studies, the order of the predictor is chosen empirically and fixed for the whole image. Since images are nonstationary signals, the order should be adapted to the local characteristics of the image. In this paper, we tackle this problem by using a model averaging approach. We show that by averaging over a group of OLS predictors, the effective number of parameter of the resultant predictor is adjusted adaptively. We show that the proposed method is robust to changes in the size of the training block. It also leads to better performance than the OLS predictor.

A study of a family of biorthogonal wavelet filters for use in digital watermarking is presented. The filters are explicitly parametrized by two free parameters and can be used to provide diversity in watermarking. Diversity can be used to improve the security of the watermarking system from hostile attacks. Each filter has at least two vanishing moments, which is important for ensuring some degree of smoothness in the resulting wavelet function. Along with robustness and security, other factors, which impact upon the successful implementation of the filters in a watermarking application are analysed. The relationship between the strength of the inserted watermark and wavelet energy is also discussed.

A class of integer wavelet transform (IWT) which are parametrized simply by one free parameter is presented . The class of IWT is obtained by a lifting based factorization on a class of 9/7 filter pair. The class includes the celebrated 9/7 filter pair of Cohen, Daubechies and Feauveau which is adopted in the upcoming JPEG2000 image compression standard. Within this class are lifting filters with simple rational coefficients which are close in characteristics to the irrational coefficient 9/7 pair employed in JPEG2000. By adjusting the free parameter, IWT with different properties and characteristics can be obtained. A study of the non-linearity of this class of IWT is also performed.

The design of non-separable 3-D biorthogonal wavelet filter banks is addressed in this paper. The sampling is on the FCO (face centered orthorhombic) lattice and the ideal low-pass filter's passband shape is the TRO (truncated octahedron). We introduce a 3-D parametric Bernstein polynomial that preserves biorthogonality and gives a good approximation to the TRO shape. Furthermore, filters with arbitrarily flat frequency response for giving regular wavelet systems are readily obtainable. The free parameters of the Bernstein polynomial can be chosen to sharpen the frequency response of the filter. A least squares approach is employed for the design of the parameters. The design process is efficient as it involves solving linear equations and is non-iterative. This approach provides a trade-off mechanism between the sharpness of roll-off and the degree of flatness.

A two-stage approach is employed for the design of a class of two-channel biorthogonal filter banks. The filter banks belong to the class of HPFB (Halfband Pair Filter Bank) and are defined by two kernels. The parametric Bernstein polynomial is used to construct the kernels. The design of the free parameters of the Bernstein polynomial is achieved through a least squares method. In the first stage, the analysis low-pass filter is designed and in the second stage, the synthesis low-pass filter is designed. With the two-stage approach, the design process is efficient and involves solving linear equations. The design techniques allows filters with different characteristics to be designed easily.

Two families of binary coefficient biorthogonal wavelet filters are presented in this paper. A binary (or dyadic) coefficient is an integer divided by a power of 2. The filters can be implemented efficiently without using any multipliers. The technique that is used to obtain the filters, hinges on the idea of freeing some of the zeros of the Lagrange Halfband Filter (LHBF) to allow some degree of freedom in choosing the coefficients. The first family is the 9/7 pairs and the second is the 6/10 pairs. Filters within the family are parametrized in a simple manner by a free parameter. By adjusting the free parameter, filters with different characteristics can be easily obtained while guaranteeing that the coefficients will always be binary.

Many wavelet filters found in the literature have irrational coefficients and thus require infinite precision implementation. One of the most popular filter pairs is the "9/7" biorthogonal pair of Cohen, Daubechies and Feauveau (1992), which is adopted in the FBI finger-print compression standard. We present a technique to rationalize the coefficients of wavelet filters that will preserve biorthogonality and perfect reconstruction. Furthermore, most of the zeros at z=-1 will also be preserved. These zeros are important for achieving regularity. The rationalized coefficients filters have characteristics that are close to the original irrational coefficients filters. Three popular pairs of filters, which include the "9/7" pair, are considered.

This letter presents a method for enhancing document images based on the multiresolution decomposition and fuzzy logic approach. The document image to be enhanced is obtained from a scanner and is a blurred binary image that is corrupted by additive noise. This type of image occurs in many situations when documents such as checks and credit card receipts become noisy and low-contrast images after scanning, thereby reducing its quality. Our task is to improve the readability of such images by reducing the noise and increasing the sharpness of the text. This is achieved using the multiresolution decomposition, fuzzy logic and contrast enhancement operator. The improvement is shown using simulation examples and compared with other enhancement techniques.

It was shown by Wei et al. (1997) that by applying the extended McClellan transformation on one-dimensional (1-D) even length linear phase perfect reconstruction (PR) filterbanks (FBs), the resulting multidimensional (M-D) FB does not have the PR property. The two types of extended McClellan transformation that were considered in Wei et al. were originally proposed by Mersereau et al. (1976) and Karam (1996), respectively, for the design of single filters. We shall show in this letter that by using a different type of transformation, PR can indeed be preserved in the M-D FB. A new class of transformation that achieves PR is presented. Furthermore, by choosing an appropriate transformation the M-D filters will have linear phase.

The design of 3-D multirate filter banks where the downsampling/upsampling is on the FCO (face centered orthorhombic) lattice is addressed. With such a sampling lattice, the ideal 3-D subband of the low-pass filter is of the TRO (truncated octahedron) shape. The transformation of variables has been shown previously to be an effective technique for designing M-D filter banks. We present a design technique for the transformation function using the multivariate Bernstein polynomial which provides a good approximation to the TRO subband shape. The method is analytically based and does not require any optimization procedure. Closed form expressions are obtained for the filters of any order. Another advantage of this technique is that it yields filters with a flat frequency response at the aliasing frequency (/spl omega//sub 1/,/spl omega//sub 2/,/spl omega//sub 3/)=(/spl pi/,/spl pi/,/spl pi/). The flatness is important for giving regular discrete wavelet transform systems.

Presents a method for enhancing document images that is based on the wavelet transform and fuzzy logic approach. The document image to be enhanced is obtained as a blurred binary image from a scanner and corrupted by additive noise. This type of image occurs in many situations when the quality of the documents including checks, hand-written text, credit card receipts become noisy and low-contrast images after scanning. Our problem is to improve such images by reducing noise and increasing the contrast of the text. This can be achieved by incorporating the wavelet transform, fuzzy logic and a contrast enhancement operator. The improvement is demonstrated by using simulation examples and compared in terms of visual enhancement with the more conventional approaches.

An approach to designing multidimensional linear-phase FIR diamond subband filters having the perfect reconstruction property is presented. It is based on a transformation of variables technique and is equivalent to the generalized McClellan transformation. Methods for designing a whole class of transformation are given. The approach consists of two parts; design of the transformation and design of the 1-D filters. The use of Lagrange halfband filters to design the 1-D filters is discussed. The modification of a particular Lagrange halfband filter which gives a pair of simple 1-D filters that are almost similar to each other in their frequency characteristics but still form a perfect reconstruction pair is presented. The design technique is extended to other types of two-channel sampling lattice and subband shapes, in particular, the parallelogram and the diagonally quadrant subband cases. Several numerical design examples are presented to illustrate the flexibility of the design method.

Structures for maximally decimated multidimensional filter banks which achieve perfect reconstruction are presented. There are no restrictions on the sampling lattice or dimensions. These are polyphase structures that can be cascaded to give finite impulse response (FIR) analysis and synthesis filters. The authors briefly review some important concepts and results of multidimensional filter banks and establish some notation. Then they present structures based on matrices whose elements are shifts. There are certain constraints that are imposed on these matrices. Next, structures based on elementary matrices that are used to effect elementary row or column operations are presented. Some useful properties of these structures are discussed.>