Showing papers on "Biorthogonal system published in 1998"
06 Apr 1998
TL;DR: In this paper, a series of explicit expressions for the correlation functions in the scaling limit (as the number of points goes to infinity) are given by certain new kernels which are described in terms of the Wright's generalized Bessel function and can be viewed as a generalization of the well-known sine and Bessel kernels.
Abstract: One object of interest in random matrix theory is a family of point ensembles (random point configurations) related to various systems of classical orthogonal polynomials The paper deals with a one--parametric deformation of these ensembles, which is defined in terms of the biorthogonal polynomials of Jacobi, Laguerre and Hermite type Our main result is a series of explicit expressions for the correlation functions in the scaling limit (as the number of points goes to infinity) As in the classical case, the correlation functions have determinantal form They are given by certain new kernels which are described in terms of the Wright's generalized Bessel function and can be viewed as a generalization of the well--known sine and Bessel kernels In contrast to the conventional kernels, the new kernels are non--symmetric However, they possess other, rather surprising, symmetry properties Our approach to finding the limit kernel also differs from the conventional one, because of lack of a simple explicit Christoffel--Darboux formula for the biorthogonal polynomials
264 citations
TL;DR: The HLBT has a significantly lower computational complexity than the lapped orthogonal transform (LOT), essentially no blocking artifacts, and fewer ringing artifacts than the commonly used discrete cosine transform (DCT).
Abstract: New lapped transforms are introduced. The lapped biorthononal transform (LBT) and hierarchical lapped biorthogonal transform (HLBT) are appropriate for image coding, and the modulated HLBT biorthogonal transform (MMLBT) and nonuniform modulated lapped biorthogonal transform (NMLBT) are appropriate for audio coding. The HLBT has a significantly lower computational complexity than the lapped orthogonal transform (LOT), essentially no blocking artifacts, and fewer ringing artifacts than the commonly used discrete cosine transform (DCT). The LBT and HLBT have transform coding gains that are typically between 0.5 and 1.2 dB higher than that of the DCT. Image coding examples using JPEG and embedded zerotree coders demonstrate the better performance of the LET and HLBT. The NMLBT has fewer ringing artifacts and better reproduction of transient sounds than the MLT, as shown in audio coding examples. Fast algorithms for both the HLBT and the NMLBT are presented.
230 citations
TL;DR: Conditions are presented under which optimal orthonormal subband coders yield as much coding gain as biorthogonal ones for a fixed number of subbands.
Abstract: The theory of the orthogonal transform coder and methods for its optimal design have been known for a long time. We derive a set of necessary and sufficient conditions for the coding-gain optimality of an orthonormal subband coder for given input statistics. We also show how these conditions can be satisfied by the construction of a sequence of optimal compaction filters one at a time. Several theoretical properties of optimal compaction filters and optimal subband coders are then derived, especially pertaining to behavior as the number of subbands increases. Significant theoretical differences between optimum subband coders, transform coders, and predictive coders are summarized. Finally, conditions are presented under which optimal orthonormal subband coders yield as much coding gain as biorthogonal ones for a fixed number of subbands.
174 citations
TL;DR: A frequency domain identification procedure is proposed where the model parameters are computed by DFT of appropriately transformed data and bounds on the the partial sum operators and on the L ∞ norm of the approximation error are derived.
78 citations
TL;DR: In this paper, a vector filter bank of biorthogonal Hermite cubic multi-wavelets with short, smooth duals is presented, and numerical experiments in signal denoising and image compression using multi-filters are discussed.
Abstract: This paper presents new vector filter banks, in particular biorthogonal Hermite cubic multiwavelets with short, smooth duals. We study different preprocessing techniques and the covariance structure of corresponding transforms. Results of numerical experiments in signal denoising and image compression using multi-filters are discussed.We compare the performance of several multi-filters with the performance of standard scalar wavelets such as Daubechies orthogonal external phase and least asymmetric ones and biorthogonal 9- 7 pair. Often multiwavelet scheme turn out to be better. We analyze these results.
58 citations
TL;DR: Experimental results show that the Daubechies orthonormal basis perform well in recognizing transformed textures, followed by the Haar basis, and the concept of multiresolution representation and orthogonality are shown to be useful for invariant texture classificaiton.
54 citations
TL;DR: An analogue of the Hahn theorem for Laurent biorthogonal polynomials (LBP) Pn(z) is studied in this article, where necessary and sufficient conditions (criterion) for derivatives P n (z) = (n + 1) −1 P′ n+1 (z).
49 citations
TL;DR: In this article, the authors briefly review the orthonormal case, and then present several new results for the biorthogonal case, all discussions pertain to the infinite order (ideal filter) case.
Abstract: Optimization of filter banks for specific input statistics has been of interest in the theory and practice of subband coding. For the case of orthonormal filter banks with infinite order and uniform decimation, the problem has been completely solved in recent years. For the case of biorthogonal filter banks, significant progress has been made recently, although a number of issues still remain to be addressed. In this paper we briefly review the orthonormal case, and then present several new results for the biorthogonal case. All discussions pertain to the infinite order (ideal filter) case. The current status of research as well as some of the unsolved problems are described.
47 citations
TL;DR: In this article, it is shown that the dynamics of waves in open systems can be cast exactly into this form, thus providing a wellfounded realization of the phenomenological description and at the same time placing these open systems into a well-known framework.
Abstract: Dissipative quantum systems are sometimes phenomenologically described in terms of a non-Hermitian Hamiltonian H, with different left and right eigenvectors forming a biorthogonal basis. It is shown that the dynamics of waves in open systems can be cast exactly into this form, thus providing a well-founded realization of the phenomenological description and at the same time placing these open systems into a well-known framework. The formalism leads to a generalization of norms and inner products for open systems, which in contrast to earlier works is finite without the need for regularization. The inner product allows transcription of much of the formalism for conservative systems, including perturbation theory and second quantization.
42 citations
TL;DR: The construction method takes a point of view opposite to the one of Cohen-Daubechies-Feauveau (1992, which starts from a well-choosen pair of biorthogonal discrete filters), where the necessary and sufficient condition is the nonperpendicularity of the multiresolutions.
Abstract: Starting from any two given multiresolution analyses of L/sub 2/, {V/sub j//sup 1/}/sub j/spl isin/Z/ and {V/sub j//sup 2/}/sub j/spl isin/Z/, we construct biorthogonal wavelet bases that are associated with this chosen pair of multiresolutions. Thus, our construction method takes a point of view opposite to the one of Cohen-Daubechies-Feauveau (1992), which starts from a well-choosen pair of biorthogonal discrete filters. In our construction, the necessary and sufficient condition is the nonperpendicularity of the multiresolutions.
33 citations
12 May 1998
TL;DR: A lattice structure based on the singular value decomposition (SVD) is introduced that can be proven to use a minimal number of delay elements and to completely span a large class of M-channel linear phase perfect reconstruction filter banks (LPPRFB).
Abstract: A lattice structure based on the singular value decomposition (SVD) is introduced. The lattice can be proven to use a minimal number of delay elements and to completely span a large class of M-channel linear phase perfect reconstruction filter banks (LPPRFB): all analysis and synthesis filters have the same FIR length of L=KM, sharing the same center of symmetry. The lattice also structurally enforces both linear phase and perfect reconstruction properties, is capable of providing fast and efficient implementation, and avoids the costly matrix inversion problem in the optimization process. From a block transform perspective, the new lattice represents a family of generalized lapped biorthogonal transforms (GLBT) with arbitrary integer overlapping factor K. The relaxation of the orthogonal constraint allows the GLBT to have significantly different analysis and synthesis basis functions which can then be tailored appropriately to fit a particular application. Several design examples are presented along with a high-performance GLBT-based progressive image coder to demonstrate the superiority of the new lapped transforms.
04 Oct 1998
TL;DR: This work designs the entire class of antisymmetric biorthogonal coiflet systems, whose filterbanks have even lengths and are linear phase, and shows that one of the novel filterbanks achieves noticeably better rate-distortion performance than several state-of-the-art filterbanks in image coding.
Abstract: Wavelet techniques have achieved a tremendous success in image data compression. In designing wavelet coding algorithms, the choice of wavelet systems is of great importance for compression performance. We design the entire class of antisymmetric biorthogonal coiflet systems, whose filterbanks have even lengths and are linear phase. We show that one of the novel filterbanks achieves noticeably better rate-distortion performance than several state-of-the-art filterbanks in image coding.
TL;DR: In this article, the authors show that imposing a certain number of vanishing moments on a scaling function (e.g., coiflets) leads to fairly small phase distortion on its associated filter bank in the neighborhood of DC.
Abstract: We show that imposing a certain number of vanishing moments on a scaling function (e.g., coiflets) leads to fairly small phase distortion on its associated filter bank in the neighborhood of DC. However, the phase distortion at the other frequencies can be much larger. We design a new class of real-valued, compactly supported, orthonormal, and nearly symmetric wavelets (we call them generalized coiflets) with a number of nonzero-centered vanishing moments equally distributed on scaling function and wavelet. Such a generalization of the original coiflets offers one more free parameter, the mean of the scaling function, in designing filter banks. Since this parameter uniquely characterizes the first several moments of the scaling function, it is related to the phase response of the lowpass filter at low frequencies. We search for the optimal parameter to minimize the maximum phase distortion of the filter bank over the lowpass half-band. Also, we are able to construct nearly odd-symmetric generalized coiflets, whose associated lowpass filters are surprisingly similar to those of some biorthogonal spline wavelets. These new wavelets can be useful in a broad range of signal and image processing applications because they provide a better tradeoff between the two desirable but conflicting properties of the compactly supported and real-valued wavelets, i.e., orthonormality versus symmetry, than the original coiflets.
04 Oct 1998
TL;DR: This work assesses whether the added orthogonality of the new balanced multiwavelets yields a performance gain compared to traditional biorthogonal transforms, and re-establishs the rule of thumb that strict orthog onality is not a key factor in image transform coding.
Abstract: Biorthogonal wavelets have been used with great success in most of the recent transform image coders. By using the new balanced multiwavelets, one can now easily design fully orthogonal linear phase FIR transform schemes. The aim of our work is to assess whether the added orthogonality yields a performance gain compared to traditional biorthogonal transforms. As comparison platform we use the well-known SPIHT codec, which is based on the significance tree quantization (STQ) principle. Without any particular fine-tuning the multiwavelet codec performs within 0.5 dB of SPIHT. A closer inspection shows however that it is hard to improve on this, therefore re-establishing the rule of thumb that strict orthogonality is not a key factor in image transform coding. More details can be obtained on the [WEB] at http://lcavwww.epfl.ch/~weidmann/mwcoder.
05 Jun 1998
TL;DR: In this paper, the orthogonal and biorthogonal modulated lapped transforms (MLTs) were obtained by combining the MLT window operators with stages from a previously introduced structure for the type-IV discrete cosine transform (DCT-IV).
Abstract: New algorithms for the computation of orthogonal and biorthogonal modulated lapped transforms (MLTs) are presented. The new structures are obtained by combining the MLT window operators with stages from a previously introduced structure for the type-IV discrete cosine transform (DCT-IV). The net result is fewer multiplications and additions than previously reported algorithms. For the orthogonal MLT, in particular, the new structure requires the computation of a slightly modified DCT-IV and some extra additions, but no further multiplications; so it demonstrates that the multiplicative complexity of the orthogonal MLT is the same as that of the DCT-IV.
04 Oct 1998
TL;DR: This paper presents shape adaptive wavelet transforms for object-based image coding and methods for recovering moment properties that are valid for the original filters and wavelets, but that get lost in the boundary regions of shape adaptive transforms.
Abstract: This paper presents shape adaptive wavelet transforms for object-based image coding. Methods for recovering moment properties that are valid for the original filters and wavelets, but that get lost in the boundary regions of shape adaptive transforms, are presented. Furthermore, methods for equalizing the energies of the boundary wavelets are shown. This equalization allows one to avoid the white quantization noise (introduced in the subbands) that appears as highly colored noise in the reconstructed image.
01 Jun 1998
TL;DR: New algorithms for the computation of orthogonal and biorthogonal modulated lapped transforms (MLTs) are presented and it is demonstrated that the multiplicative complexity of the Orthogonal MLT is the same as that of the DCT-IV.
Abstract: New algorithms for the computation of orthogonal and biorthogonal modulated lapped transforms(MLTs) are presented. The new structures are obtained by combining the MLT window operators with stages from a previously introduced structure for the type-IV discrete cosine transform (DCT-IV). The net result is fewer multiplications and additions than previously reported algorithms. For the orthogonal MLT, in particular, the new structure requires the computation of a slightly modified DCT-IV and some extra additions, but no further multiplications; so it demonstrates that the multiplicative complexity of the orthogonal MLT is the same as that of the DCT-IV.
TL;DR: It is shown that the construction of biorthogonal M- channel wavelet bases is equivalent to the design of a M-channel perfect reconstruction filter bank with some added regularity conditions.
Abstract: We generalize the theory of compactly supported biorthogonal two-channel wavelet bases to M-channel. A sufficient condition for the M-channel perfect reconstruction filter banks to construct M-channel biorthogonal bases of compactly supported wavelets is derived. It is shown that the construction of biorthogonal M-channel wavelet bases is equivalent to the design of a M-channel perfect reconstruction filter bank with some added regularity conditions. A family of M-channel biorthogonal wavelet bases based on the cosine-modulated filter bank (CMFB) is proposed. It has the advantages of simple design procedure, efficient implementation, and good filter quality. A new method fur imposing the regularity on the CMFBs is also introduced, and several design examples are given.
TL;DR: The paper develops algorithms for the design of orthogonal and biorthogonal compact support scaling functions that are robust to translations and obtains expedite algorithms by decoupling the optimization from the constraints on the scaling function.
Abstract: The discrete wavelet transform (DWT) is popular in a wide variety of applications. Its sparse sampling eliminates redundancy in the representation of signals and leads to efficient processing. However, the DWT lacks translation invariance. This makes it ill suited for many problems where the received signal is the superposition of arbitrarily shifted replicas of a transmitted signal as when multipath occurs, for example. The paper develops algorithms for the design of orthogonal and biorthogonal compact support scaling functions that are robust to translations. Our approach is to maintain the critical sampling of the DWT while designing multiresolution representations for which the coefficient energy redistributes itself mostly within each subband and not across the entire time-scale plane. We obtain expedite algorithms by decoupling the optimization from the constraints on the scaling function. Examples illustrate that the designed scaling function significantly improves the robustness of the representation.
12 May 1998
TL;DR: A previously unpublished nearly coiflet 17/11 biorthogonal wavelet filter pair is constructed, and Simulation results with the SPIHT algorithm confirm that the new 17/ 11 wavelet basis outperforms the others for still image compression.
Abstract: The selection of the filter bank in wavelet compression is crucial, affecting the image quality and system design. The biorthogonal coiflet (cooklet) family of wavelet filters has been constructed, and explicit frequency domain formulae have been developed in the Bernstein polynomial basis. We use the Bernstein basis for the frequency domain design and construction of biorthogonal nearly coiflet wavelet bases. In particular, we construct a previously unpublished nearly coiflet 17/11 biorthogonal wavelet filter pair. Key filter quality evaluation metrics due to Villasenor (see IEEE Trans. on Image Proc., vol.4, no.8, p.1053-1060, 1995) demonstrate this filter pair to be well suited for image compression. Comparison is made to the 17/11 biorthogonal coiflet (cooklet), Villasenor 10/18, Odegard 9/7, and classical CDF 9/7 wavelet bases. Simulation results with the SPIHT algorithm due to Said and Pearlman (see IEEE Trans. on Circ. and Systems, vol.6, no.3, p.243-250, 1996), and with our SR/sub SFQ/, confirm that the new 17/11 wavelet basis outperforms the others for still image compression.
TL;DR: In this paper, the constructions of biorthogonal basis of compactly supported wavelets in Sobolev spaces of integer order were studied, using techniques of [1] and [2].
Abstract: This article is concerned with constructions of biorthogonal basis of compactly supported wavelets in Sobolev spaces of integer order. Using techniques of [1] and [2], the results presented here generalize to Sobolev spaces some constructions of Cohen et al. [7] and Chui and Wang [5] established in L2(ℝ).
04 Oct 1998
TL;DR: This paper introduces a class of linear phase lapped biorthogonal transforms with basis functions of variable length (VLGLBT), characterized by a lattice which structurally enforces both linear phase and perfect reconstruction properties as well as provides a fast and efficient transform implementation.
Abstract: This paper introduces a class of linear phase lapped biorthogonal transforms with basis functions of variable length (VLGLBT). The transform can be characterized by a lattice which structurally enforces both linear phase and perfect reconstruction properties as well as provides a fast and efficient transform implementation. Our main motivation of the new transform is its application in image coding. The VLGLBT has several long overlapped basis functions for representing smooth signals to avoid blocking artifacts. The rest of the bases covering high-frequency bands are constrained to be short to limit ringing artifacts. The relaxation of the orthogonal constraint allows the VLGLBT to have significantly different analysis and synthesis banks which can be tailored appropriately to obtain high-quality reconstructed images. Most importantly, the variable-length property allows us to design very fast and low-complexity transforms. Comparing to the popular DCT, a fast VLGLBT named FLT only requires 6 more multiplications and 8 more additions. Yet, image coding examples show that the FLT is far superior than the DCT and is close to the 9/7-tap biorthogonal wavelet in both objective and subjective coding performance.
25 Sep 1998
TL;DR: A general algorithm is given to convert a discrete biorthogonal wavelet transform into lifting steps, so that one version of the transform can support both the lossy and lossless coding to facilitate the region of interest based image compression.
Abstract: This paper concentrates on two issues related to wavelet- based image coding. At first, an algebra method is proposed to select biorthogonal wavelets for higher compression ratio and better quality of the reconstructed image. Then, a general algorithm is given to convert a discrete biorthogonal wavelet transform into lifting steps, so that one version of the transform, which maps integers to integers, can support both the lossy and lossless coding to facilitate the region of interest based image compression.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
TL;DR: In this article, the authors extended the method of Dubuc and Deslauriers on symmetric interpolatory subdivision to study the relationship between interpolation processes and wavelet construction.
TL;DR: In this article, an implementation of a biorthogonal approach to modern valence bond calculations is presented, emphasizing the problems associated with larger numbers of active electrons, and a restricted-step second-order algorithm is proposed which may be of use also for other non-symmetrical optimization problems.
Abstract: An implementation of a biorthogonal approach to modern valence bond calculations is presented, emphasizing the problems associated with larger numbers of active electrons. A full treatment of up to 20 active electrons seems feasible within this strategy. A restricted-step second-order algorithm is proposed which may be of use also for other non-symmetrical optimization problems. Applications to the ground states of methylene and naphthalene are presented, highlighting the difference between a biorthogonal approach and the analogous variational calculations.
12 May 1998
TL;DR: A new method is presented for designing two channel biorthogonal IIR filter banks, which satisfy both the perfect reconstruction and causal stable conditions and are based on the formulation of a generalized eigenvalue problem by using the Remez multiple exchange algorithm.
Abstract: This paper presents a new method for designing two channel biorthogonal IIR filter banks, which satisfy both the perfect reconstruction and causal stable conditions. The proposed method is based on the formulation of a generalized eigenvalue problem by using the Remez multiple exchange algorithm. Therefore, the filter coefficients can be computed by solving the eigenvalue problem, and the optimal solution is easily obtained through a few iterations. One example is designed to demonstrate the effectiveness of the proposed method.
06 Oct 1998
TL;DR: In this article, an efficient method is presented to cope with the need of phase linear filters in orthonormal wavelet transform for image processing, which can be obtained in two dimensions by using Cohen/Daubechies biorthogonal wavelets.
Abstract: In this paper an efficient method is presented to cope with the need of phase linear filters in orthonormal wavelet transform for image processing. Phase linear filtering can be obtained in two dimensions by using Cohen/Daubechies biorthogonal wavelets. But as orthogonal analysis is preferable, a new method to construct orthonormal bidimensional wavelet base in the quincunx scheme is proposed. These filters are designed by applying the McClellan Transform on 1D B-spline filters in order to get 2D orthonormal quincunx non-separable ones. This method takes advantage of the orthogonality of the analysis and of the quincunx scheme, indeed these filters lead to only one approximation image and only one detail image. The interscale resolution given by this analysis is twice more accurate than in the case of a separable analysis and the wavelet functions have better isotropic and frequency properties than those previously proposed by Feauveau.
TL;DR: An image model based on Hermite spline multiresolution analysis ins considered and the algorithm of fast biorthogonal multiwavelet transform is used to compute image representations.
Abstract: An image model based on Hermite spline multiresolution analysis ins considered. To compute image representations, the algorithm of fast biorthogonal multiwavelet transform is used. The transform depends on the choice of multi-scaling functions biorthogonal to Hermite splines. An algorithm for the construction of such functions is given and examples for cubic Hermite splines are shown.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
04 Oct 1998
TL;DR: A large class of generalized lapped biorthogonal transforms with integer coefficients (IGLBT) is presented, which yields comparable objective and subjective performance to those of popular state-of-the-art transforms with floating-point coefficients.
Abstract: Invertible transforms with integer coefficients are highly desirable because of their fast, efficient, VLSI-suitable implementations and their lossless coding capability. In this paper, a large class of generalized lapped biorthogonal transforms with integer coefficients (IGLBT) is presented. The IGLBT also possesses a fast and efficient lattice that structurally enforces both linear phase and exact reconstruction properties. Preliminary image coding experiments show that the IGLBT yields comparable objective and subjective performance to those of popular state-of-the-art transforms with floating-point coefficients.