multidimensional directional filter banks and surfacelets in 1992 bamberger and smith proposed the directional filter bank dfb for an efficient directional decomposition of 2 d signals due to the nonseparable nature of the system extending the dfb to higher dimensions while still retaining its attractive features is a challenging and previously unsolved problem we propose a new family of filter banks named ndfb that can achieve the directional decomposition of arbitrary n dimensional nges2 signals with a simple and efficient tree structured construction in 3 d the ideal passbands of the proposed ndfb are rectangular based pyramids radiating out from the origin at different orientations and tiling the entire frequency space the proposed ndfb achieves perfect reconstruction via an iterated filter bank with a redundancy factor of n in n d the angular resolution of the proposed ndfb can be iteratively refined by invoking more levels of decomposition through a simple expansion rule by combining the ndfb with a new multiscale pyramid we propose the surfacelet transform which can be used to efficiently capture and represent surface like singularities in multidimensional data

a filter bank for the directional decomposition of images theory and design the authors introduce a directionally oriented 2 d filter bank with the property that the individual channels may be critically sampled without loss of information the passband regions of the component filters are wedge shaped and thus provide directional information it is shown that these filter bank outputs may be maximally decimated to achieve a minimum sample representation in a way that permits the original signal to be exactly reconstructed the authors discuss the theory for directional decomposition and reconstruction in addition implementation issues are addressed where realizations based on both recursive and nonrecursive filters are considered

design of directional filter banks with arbitrary number of subbands this correspondence proposes a novel method for designing directional filter banks dfbs with arbitrary number of subbands its key feature is the ability to decompose images into arbitrary directionally oriented subbands the proposed approach is based on the pseudo polar fourier transform ppft and one dimensional 1 d filter banks fbs we take some modifications on the ppft and then employ 1 d fbs to the modified ppft with these operations the two dimensional 2 d dfbs are obtained and the design of them is converted to that of 1 d fbs plus a modified ppft since the number of channels of 1 d fbs can be arbitrary the 2 d dfbs with arbitrary number of subbands can be achieved which is highly expected for directional representations of images two examples on directional feature extractions illustrate that the proposed non 2n channel dfbs can capture directional information more flexibly than the existing methods

a new family of nonredundant transforms using hybrid wavelets and directional filter banks we propose a new family of nonredundant geometrical image transforms that are based on wavelets and directional filter banks we convert the wavelet basis functions in the finest scales to a flexible and rich set of directional basis elements by employing directional filter banks where we form a nonredundant transform family which exhibits both directional and nondirectional basis functions we demonstrate the potential of the proposed transforms using nonlinear approximation in addition we employ the proposed family in two key image processing applications image coding and denoising and show its efficiency for these applications

nonuniform directional filter banks with arbitrary frequency partitioning directional filter banks dfbs are highly desired in directional representation of images in this correspondence we propose a 2 d nonsubsampled nonuniform directional filter bank nudfb and its design method the proposed nudfb has nonuniform wedge shaped subbands and allows arbitrary frequency partitioning schemes it can extract directional information according to the directional distribution of images this attractive advantage cannot be achieved by the existing directional transforms the design method of the proposed nudfb is based upon the pseudopolar fourier transform by utilizing the geometry property of the pseudopolar grid we employ a 1 d nonsubsampled nonuniform filter bank to obtain a set of nonuniform wedge shaped subbands during the design process only 1 d operations are involved and thus the difficulty encountered in the design of 2 d fan filters is avoided to demonstrate the potential of the proposed nudfb an example on image directional decomposition is given

stochastic resonance and self tuning a simple threshold system to put it in the framework of information processing stochastic resonance sr is a phenomenon in which the transfer of information from input to output signals can be significantly increased by noise with appropriate nonzero intensity the minimum requirements for sr are generally input signals nonlinearity and noise in addition to a quantifier to measure the efficiency of information transfer we study a simple threshold system and propose an adaptation mechanism for system parameters such as a threshold and noise intensity i e temperature which are held fixed in a normal sr setting our emphasis is put on parameter dynamics induced by this adaptation which we call self tuning st and on how this dynamics modifies or changes the sr picture with respect to information processing efficiency as a measure for performance of the threshold system we take mutual information and the signal to noise ratio these quantities are calculated by an analytical method and by a simulational one st of temperature results in oscillatory time variation in temperature with its average located around the temperature at which performance is maximized in the sr setting st of a threshold turns out to improve performance in the weak noise region

super camassa holm type systems associated to the kuper ramond schwarz superalgebra we describe a class of super integrable systems with a local bi super hamiltonian structure including super camassa holm type systems which can be realized as euler type systems on the dual of the kuper ramond schwarz superalgebra

the mechanism of stochastic resonance it is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance peak in the power spectrum which is absent when either the forcing or the perturbation is absent

two dimensional perfect reconstruction fir filter banks with triangular supports we present a theory and design of two dimensional 2 d perfect reconstruction pr filter banks fbs prfbs in which the supports of the analysis and synthesis filters consist of two triangulars the two triangular fb can be realized by designing an appropriate 2 d complex prototype whose passband support is a triangle that is a half of a parallelepiped shaped passband support defined by the sampling matrix then a complex prototype filter is modulated by the dft and each analysis filter is derived by taking the real part of the modulated output we show that the two triangular fb satisfies the condition of permissibility a necessary and sufficient condition for 2 d prfbs is derived moreover we present a design method of the 2 d prfb that minimizes the cost function consisting of the frequency constraint and pr condition finally a design example is presented to confirm the validity of the proposed method

bits and brains information flow in the nervous system abstract until recently there have been no convincing quantitative measurements on the rates of information transmission in real neurons here we review the theoretical basis for making such measurements together with the data which demonstrate remarkably high information rates in a variety of systems in fact these rates are within a factor of two of the absolute physical limits set by the entropy of neural spike trains theses observations lead to sharp theoretical questions about the structure of the code and the strategy for adapting the code to different ensembles of input signals

lattice structure for regular paraunitary linear phase filterbanks and m band orthogonal symmetric wavelets parauninary linear phase pulp m channel uniform filterbanks which are also known as the generalized lapped orthogonal transforms genlots can be designed and implemented using lattice structures this paper discusses how to impose regularity constraints onto the lattice structure of pulp filterbanks these conditions are expressed in term of the rotation angles of the lattice components by which the resulting filterbanks are guaranteed to have one or two degrees of regularity iterating these new regular filterbanks on the lowpass subband generates a large family of symmetric m band orthonormal wavelets design procedures with many design examples are presented smooth interpolation using regular pulp filterbanks is illustrated through image coding experiments where the novel m band wavelets consistently yield smoother reconstructed images and better perceptual quality

image coding using dual tree discrete wavelet transform in this paper we explore the application of 2 d dual tree discrete wavelet transform ddwt which is a directional and redundant transform for image coding three methods for sparsifying ddwt coefficients i e matching pursuit basis pursuit and noise shaping are compared we found that noise shaping achieves the best nonlinear approximation efficiency with the lowest computational complexity the interscale intersubband and intrasubband dependency among the ddwt coefficients are analyzed three subband coding methods i e spiht ebcot and tce are evaluated for coding ddwt coefficients experimental results show that tce has the best performance in spite of the redundancy of the transform our ddwt tce scheme outperforms jpeg2000 up to 0 70 db at low bit rates and is comparable to jpeg2000 at high bit rates the ddwt tce scheme also outperforms two other image coders that are based on directional filter banks to further improve coding efficiency we extend the ddwt to an anisotropic dual tree discrete wavelet packets addwp which incorporates adaptive and anisotropic decomposition into ddwt the addwp subbands are coded with tce coder experimental results show that addwp tce provides up to 1 47 db improvement over the ddwt tce scheme outperforming jpeg2000 up to 2 00 db reconstructed images of our coding schemes are visually more appealing compared with dwt based coding schemes thanks to the directionality of wavelets

two dimensional 2 times oversampled dft modulated filter banks and critically sampled modified dft modulated filter banks this paper investigates two dimensional 2d 2 oversampled dft modulated filter banks and 2d critically sampled modified dft mdft modulated filter banks as well as their design the structure and perfect reconstruction pr condition of 2d 2 oversampled dft modulated filter banks are presented in terms of the polyphase decompositions of prototype filters pfs in the double prototype case the part solutions of the pr condition are parameterized by imposing the 2d two channel lifting structure on each pair of the polyphase components of analysis and synthesis pfs based on the parametric structure the analysis and synthesis pfs are separately designed by constrained quadratic programs the obtained filter banks are of structurally pr moreover 2d critically sampled mdft modulated filter banks are proposed it is proved that 2d critically sampled pr mdft modulated filter banks can be rebuilt from 2d 2 oversampled pr dft modulated filter banks when the decimation matrices satisfy a permissible condition and the analysis and synthesis pfs are identical and symmetric with respect to the origin a numerical algorithm is given to design 2d critically sampled pr mdft modulated filter banks and the obtained filter banks are of numerically pr

a new class of two channel biorthogonal filter banks and wavelet bases proposes a novel framework for a new class of two channel biorthogonal filter banks the framework covers two useful subclasses i causal stable iir filter banks ii linear phase fir filter banks there exists a very efficient structurally perfect reconstruction implementation for such a class filter banks of high frequency selectivity can be achieved by using the proposed framework with low complexity the properties of such a class are discussed in detail the design of the analysis synthesis systems reduces to the design of a single transfer function very simple design methods are given both for fir and iir cases zeros of arbitrary multiplicity at aliasing frequency can be easily imposed for the purpose of generating wavelets with regularity property in the iir case two new classes of iir maximally flat filters different from butterworth filters are introduced the filter coefficients are given in closed form the wavelet bases corresponding to the biorthogonal systems are generated the authors also provide a novel mapping of the proposed 1 d framework into 2 d the mapping preserves the following i perfect reconstruction ii stability in the iir case iii linear phase in the fir case iv zeros at aliasing frequency v frequency characteristic of the filters

multiresolution direction filterbanks theory design and applications this paper presents new developments of directional filterbanks dfbs the motivation for the paper is the existence of multiresolution and multidirection orthogonal transform for two dimensional 2 d discrete signals based on the frequency supports of the ideal transform a new uniformly maximally decimated dfb with six highpass directional subbands and two lowpass subands is introduced the uniform dfb udfb can be implemented by a binary tree structure of two channel filterbanks the filterbank employed in the tree is shown to be alias free decimation and permissible the udfb is then extended to a nonuniform case nudfb which is still maximally decimated by combining the two lowpass subbands the nudfb yields nonuniform frequency division which composes of one lowpass filter with a decimation factor of one fourth and six highpass directional filters with a decimation factor of one eighth the new dfbs offer alternative image decompositions which overcome the limited directional selectivity of the separable wavelets and the limited multiresolution of the conventional dfb the lowpass subband of the nudfb can be used to obtain a multiresolution representation by simply reiterating the same nudfb decomposition on the other hand the directional subbands can also be further refined by simply applying a two channel conventional dfb at each highpass component a simple design method yielding near orthogonal uniform and nonuniform multidimensional filterbanks is presented finally the performances of the newly proposed nudfb are compared with other conventional transforms in nonlinear approximation image denoising and texture classification to demonstrate its potential

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

transport and its enhancement caused by coupling using the weiss mean field approximation theory and the particles transport theory for the spatially periodic stochastic systems we derive an exact analytical expression for the stationary probability current of a coupled lattice system driven by dichotomous noise it is shown that for this coupled lattice system the spatial asymmetry of the system the asymmetry of the dichotomous noise and the coupling among nearest neighbors are the ingredients for the stationary probability current by applying our theory to two special models we find that 1 the coupling can lead to the directional transport of the particles even when the potential and the dichotomous noise are symmetric and 2 the coupling among nearest neighbors can enhance the transport of the particles in some circumstances our results are applied to a device of two dimensional josephson junction arrays and a large protein motors cluster

flexible design of multidimensional perfect reconstruction fir 2 band filters using transformations of variables 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

stochastic resonance as dithering a direct correspondence is demonstrated between the phenomenon of stochastic resonance in static nonlinear systems and the dithering effect well known in the theory of digital waveform coding it is argued that many static systems displaying stochastic resonance are forms of dithered quantizers and that the existence or absence of stochastic resonance in such systems can be predicted from the effects of dither averaging upon their transfer characteristics also results are introduced regarding stochastic resonance in certain nonlinear systems with memory e g hysteretic systems

a computable fourier condition generating alias free sampling lattices we propose a fourier analytical condition linking alias free sampling with the fourier transform of the indicator function defined on the given frequency support our discussions center around how to develop practical computation algorithms based on the proposed analytical condition we address several issues along this line including the derivation of simple closed form expressions for the fourier transforms of the indicator functions defined on arbitrary polygonal and polyhedral domains a complete and nonredundant enumeration of all quantized sampling lattices via the hermite normal forms of integer matrices and a quantitative analysis of the approximation of the original infinite fourier condition by using finite computations combining these results we propose a computational testing procedure that can efficiently search for the optimal alias free sampling lattices for a given polygonal or polyhedral shaped frequency domain several examples are presented to show the potential of the proposed algorithm in multidimensional filter bank design as well as in applications involving the design of efficient sampling patterns for multidimensional band limited signals