embedded image coding using zerotrees of wavelet coefficients the embedded zerotree wavelet algorithm ezw is a simple yet remarkably effective image compression algorithm having the property that the bits in the bit stream are generated in order of importance yielding a fully embedded code the embedded code represents a sequence of binary decisions that distinguish an image from the null image using an embedded coding algorithm an encoder can terminate the encoding at any point thereby allowing a target rate or target distortion metric to be met exactly also given a bit stream the decoder can cease decoding at any point in the bit stream and still produce exactly the same image that would have been encoded at the bit rate corresponding to the truncated bit stream in addition to producing a fully embedded bit stream the ezw consistently produces compression results that are competitive with virtually all known compression algorithms on standard test images yet this performance is achieved with a technique that requires absolutely no training no pre stored tables or codebooks and requires no prior knowledge of the image source the ezw algorithm is based on four key concepts 1 a discrete wavelet transform or hierarchical subband decomposition 2 prediction of the absence of significant information across scales by exploiting the self similarity inherent in images 3 entropy coded successive approximation quantization and 4 universal lossless data compression which is achieved via adaptive arithmetic coding

rank minimization code aperture design for spectrally selective compressive imaging a new code aperture design framework for multiframe code aperture snapshot spectral imaging cassi system is presented it aims at the optimization of code aperture sets such that a group of compressive spectral measurements is constructed each with information from a specific subset of bands a matrix representation of cassi is introduced that permits the optimization of spectrally selective code aperture sets furthermore each code aperture set forms a matrix such that rank minimization is used to reduce the number of cassi shots needed conditions for the code apertures are identified such that a restricted isometry property in the cassi compressive measurements is satisfied with higher probability simulations show higher quality of spectral image reconstruction than that attained by systems using hadamard or random code aperture sets

nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for r sup n new results on multidimensional filter banks and their connection to multidimensional nonseparable wavelets are presented among the topics discussed are sampling in multiple dimensions multidimensional perfect reconstruction filter banks the two channel case in multiple dimensions the synthesis of multidimensional filter banks and the design of compactly supported wavelets

entropy based algorithms for best basis selection adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals it permits efficient compression of a variety of signals such as sound and images the predefined libraries of modulated waveforms include orthogonal wavelet packets and localized trigonometric functions and have reasonably well controlled time frequency localization properties the idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost the method relies heavily on the remarkable orthogonality properties of the new libraries all expansions in a given library conserve energy and are thus comparable several cost functionals are useful one of the most attractive is shannon entropy which has a geometric interpretation in this context

optimization of integer wavelet transforms based on difference correlation structures in this paper a novel lifting integer wavelet transform based on difference correlation structure dccs liwt is proposed first we establish a relationship between the performance of a linear predictor and the difference correlations of an image the obtained results provide a theoretical foundation for the following construction of the optimal lifting filters then the optimal prediction lifting coefficients in the sense of least square prediction error are derived dccs liwt puts heavy emphasis on image inherent dependence a distinct feature of this method is the use of the variance normalized autocorrelation function of the difference image to construct a linear predictor and adapt the predictor to varying image sources the proposed scheme also allows respective calculations of the lifting filters for the horizontal and vertical orientations experimental evaluation shows that the proposed method produces better results than the other well known integer transforms for the lossless image compression

arens regularity of banach algebras and the geometry of banach spaces we show that a banach algebra a such that a has the property v of a pelczynski is arens regular a strong uniqueness property of the extension of the product on a unital c algebra a to a is proved the algebraic structure of the bidual of a c algebra can be obtained through the local reflexivity principle we give examples which show that the results are sharp

hyperspectral image compression adapting spiht and ezw to anisotropic 3 d wavelet coding hyperspectral images present some specific characteristics that should be used by an efficient compression system in compression wavelets have shown a good adaptability to a wide range of data while being of reasonable complexity some wavelet based compression algorithms have been successfully used for some hyperspectral space missions this paper focuses on the optimization of a full wavelet compression system for hyperspectral images each step of the compression algorithm is studied and optimized first an algorithm to find the optimal 3 d wavelet decomposition in a rate distortion sense is defined then it is shown that a specific fixed decomposition has almost the same performance while being more useful in terms of complexity issues it is shown that this decomposition significantly improves the classical isotropic decomposition one of the most useful properties of this fixed decomposition is that it allows the use of zero tree algorithms various tree structures creating a relationship between coefficients are compared two efficient compression methods based on zerotree coding ezw and spiht are adapted on this near optimal decomposition with the best tree structure found performances are compared with the adaptation of jpeg 2000 for hyperspectral images on six different areas presenting different statistical properties

tilings of the time frequency plane construction of arbitrary orthogonal bases and fast tiling algorithms the authors consider expansions which give arbitrary orthonormal tilings of the time frequency plane these differ from the short time fourier transform wavelet transform and wavelet packets tilings in that they change over time they show how this can be achieved using time varying orthogonal tree structures which preserve orthogonality even across transitions the method is based on the construction of boundary and transition filters these allow us to construct essentially arbitrary tilings time varying modulated lapped transforms are a special case where both boundary and overlapping solutions are possible with filters obtained by modulation they present a double tree algorithm which for a given signal decides on the best binary segmentation in both time and frequency that is it is a joint optimization of time and frequency splitting the algorithm is optimal for additive cost functions e g rate distortion and results in time varying best bases the main application of which is for compression of nonstationary signals experiments on test signals are presented

nonlinear harten s multiresolution on the quincunx pyramid multiresolution transforms provide useful tools for image processing applications for an optimal representation of the edges it is crucial to develop nonlinear schemes which are not based on tensor product this paper links the nonseparable quincunx pyramid and the nonlinear discrete harten s multiresolution framework in order to obtain the stability of these representations an error control multiresolution algorithm is introduced a prescribed accuracy in various norms is ensured by these strategies explicit error bounds are presented finally a nonlinear reconstruction is proposed and tested

nonlinear scale space filtering and multiresolution system we derive and demonstrate a nonlinear scale space filter and its application in generating a nonlinear multiresolution system for each datum in a signal a neighborhood of weighted data is used for clustering the cluster center becomes the filter output the filter is governed by a single scale parameter that dictates the spatial extent of nearby data used for clustering this together with the local characteristic of the signal determines the scale parameter in the output space which dictates the influences of these data on the output this filter is thus adaptive and data driven it provides a mechanism for a removing impulsive noise b improved smoothing of nonimpulsive noise and c preserving edges comparisons with gaussian scale space filtering and median filters are made using real images using the architecture of the laplacian pyramid and this nonlinear filter for interpolation we construct a nonlinear multiresolution system that has two features 1 edges are well preserved at low resolutions and 2 difference signals are small and spatially localized this filter implicitly presents a new mechanism for detecting discontinuities differing from techniques based on local gradients and line processes this work shows that scale space filtering nonlinear filtering and scale space clustering are closely related and provides a framework within which further image processing image coding and computer vision problems can be investigated

nonexpansive pyramid for image coding using a nonlinear filterbank a nonexpansive pyramidal decomposition is proposed for low complexity image coding the image is decomposed through a nonlinear filterbank into low and highpass signals and the recursion of the filterbank over the lowpass signal generates a pyramid resembling that of the octave wavelet transform the structure itself guarantees perfect reconstruction and we have chosen nonlinear filters for performance reasons the transformed samples are grouped into square blocks and used to replace the discrete cosine transform dct in the joint photographic expert group jpeg coder the proposed coder has some advantages over the dct based jpeg computation is greatly reduced image edges are better encoded blocking is eliminated and it allows lossless coding

convex multiresolution analysis a standard wavelet multiresolution analysis can be defined via a sequence of projectors onto a monotone sequence of closed vector subspaces possessing certain properties we propose a nonlinear extension of this framework in which the vector subspaces are replaced by convex subsets these sets are chosen so as to provide a recursive monotone approximation scheme that allows for various signal and image features to be investigated several classes of convex multiresolution analyses are discussed and numerical applications to signal and image processing problems are demonstrated

m band nonlinear subband decompositions with perfect reconstruction we investigate nonlinear multirate filterbanks with maximal decimation and perfect reconstruction definitions of the desired properties of such structures are given for general nonlinear filterbanks we then consider a triangular representation of linear filterbanks and see that it may be easily extended to the nonlinear case furthermore general nonlinear filterbanks are presented for which perfect reconstruction is either inherently guaranteed or ensured subject to an easily verified condition extensions to bidimensional filters are also discussed and an application for nonlinear multiresolution schemes to feature sieves is shown

time invariant orthonormal wavelet representations a simple construction of an orthonormal basis starting with a so called mother wavelet together with an efficient implementation gained the wavelet decomposition easy acceptance and generated a great research interest in its applications an orthonormal basis may not however always be a suitable representation of a signal particularly when time or space invariance is a required property the conventional way around this problem is to use a redundant decomposition we address the time invariance problem for orthonormal wavelet transforms and propose an extension to wavelet packet decompositions we show that it is possible to achieve time invariance and preserve the orthonormality we subsequently propose an efficient approach to obtain such a decomposition we demonstrate the importance of our method by considering some application examples in signal reconstruction and time delay estimation

design of signal adapted multidimensional lifting scheme for lossy coding this paper proposes a new method for the design of lifting filters to compute a multidimensional nonseparable wavelet transform our approach is stated in the general case and is illustrated for the 2 d separable and for the quincunx images results are shown for the jpeg2000 database and for satellite images acquired on a quincunx sampling grid the design of efficient quincunx filters is a difficult challenge which has already been addressed for specific cases our approach enables the design of less expensive filters adapted to the signal statistics to enhance the compression efficiency in a more general case it is based on a two step lifting scheme and joins the lifting theory with wiener s optimization the prediction step is designed in order to minimize the variance of the signal and the update step is designed in order to minimize a reconstruction error application for lossy compression shows the performances of the method

best wavelet packet bases in a rate distortion sense a fast rate distortion r d optimal scheme for coding adaptive trees whose individual nodes spawn descendents forming a disjoint and complete basis cover for the space spanned by their parent nodes is presented the scheme guarantees operation on the convex hull of the operational r d curve and uses a fast dynamic programing pruning algorithm to markedly reduce computational complexity applications for this coding technique include r coefman et al s yale univ 1990 generalized multiresolution wavelet packet decomposition iterative subband coders and quadtree structures applications to image processing involving wavelet packets as well as discrete cosine transform dct quadtrees are presented

the digital morphological sampling theorem morphological sampling reduces processing time and cost and yet produces results sufficiently close to the result of full processing a morphological sampling theorem is described which states 1 how a digital image must be morphologically filtered before sampling in order to preserve the relevant information after sampling 2 to what precision an appropriate morphologically filtered image can be reconstructed after sampling and 3 the relationship between morphologically operating before sampling and the more computationally efficient scheme of morphologically operating on the sampled image with a sampled structuring element the digital sampling theorem is developed first for the case of binary morphology and then it is extended to gray scale morphology through the use of the umbra homomorphism theorems

morphological pyramids with alternating sequential filters the aim of this paper is to find a relationship between alternating sequential filters asf and the morphological sampling theorem mst developed by haralick et al 1987 the motivation behind this approach is to take advantage of the computational efficiency offered by the mst to implement morphological operations first we show alternative proofs for opening and closing in the sampled and unsampled domain using the basis functions these proofs are important because they show that it possible to obtain any level of a morphological pyramid in one step rather than the traditional two step procedure this decomposition is then used to show the relationship of the open closing in the sampled and unsampled domain an upper and a lower bound for the above relationships are presented under certain circumstances an equivalence is shown for open closing between the sampled and the unsampled domain an extension to more complicated algorithms using a union of openings and an intersection of closings is also proposed using the hausdorff metric it is shown that a morphologically reconstructed image cannot have a better accuracy than twice the radius of the reconstruction structuring element binary and gray scale examples are presented

nonlinear multiresolution signal decomposition schemes ii morphological wavelets interest in multiresolution techniques for signal processing and analysis is increasing steadily an important instance of such a technique is the so called pyramid decomposition scheme this paper presents a general theory for constructing linear as well as nonlinear pyramid decomposition schemes for signal analysis and synthesis the proposed theory is based on the following ingredients 1 the pyramid consists of a finite or infinite number of levels such that the information content decreases toward higher levels and 2 each step toward a higher level is implemented by an information reducing analysis operator whereas each step toward a lower level is implemented by an information preserving synthesis operator one basic assumption is necessary synthesis followed by analysis yields the identity operator meaning that no information is lost by these two consecutive steps several examples of pyramid decomposition schemes are shown to be instances of the proposed theory a particular class of linear pyramids morphological skeleton decompositions the morphological haar pyramid median pyramids etc furthermore the paper makes a distinction between single scale and multiscale decomposition schemes i e schemes without or with sample reduction finally the proposed theory provides the foundation of a general approach to constructing nonlinear wavelet decomposition schemes and filter banks

lossless image compression based on optimal prediction adaptive lifting and conditional arithmetic coding the optimal predictors of a lifting scheme in the general n dimensional case are obtained and applied for the lossless compression of still images using first quincunx sampling and then simple row column sampling in each case the efficiency of the linear predictors is enhanced nonlinearly directional postprocessing is used in the quincunx case and adaptive length postprocessing in the row column case both methods are seen to perform well the resulting nonlinear interpolation schemes achieve extremely efficient image decorrelation we further investigate context modeling and adaptive arithmetic coding of wavelet coefficients in a lossless compression framework special attention is given to the modeling contexts and the adaptation of the arithmetic coder to the actual data experimental evaluation shows that the best of the resulting coders produces better results than other known algorithms for multiresolution based lossless image coding

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed