We propose a novel motion estimation compensation (ME MC) method for wavelet-based (in-band) motion compensated temporal filtering (MCTF), with application to low-bitrate video coding. Unlike the conventional in-band MCTF algorithms, which require redundancy to overcome the shift-variance problem of critically sampled (complete) discrete wavelet transforms (DWT), we perform ME MC steps directly on DWT coefficients by avoiding the need of shift-invariance. We omit upsampling, the inverse-DWT (IDWT), and the calculation of redundant DWT coefficients, while achieving arbitrary subpixel accuracy without interpolation, and high video quality even at very low-bitrates, by deriving the exact relationships between DWT subbands of input image sequences. Experimental results demonstrate the accuracy of the proposed method, confirming that our model for ME MC effectively improves video coding quality.
Although the methods cited above have good performance, they suffer from drifting and operational mismatch problems @cite_134 . Therefore, performing spatial transform before temporal decomposition was introduced to overcome these drawbacks. However, since complete DWT is shift variant, in order to achieve in-band ME MC (i.e. directly in the wavelet domain), several methods were proposed to tackle this problem by redundancy. Van der Auwera @cite_130 used a bottom-up prediction algorithm for a bottom-up overcomplete discrete wavelet transform (ODWT). Park and Kim @cite_94 proposed a low-band-shift method by constructing the wavelet tree by shifting low-band subband in each level for horizontal, vertical, and diagonal directions for one pixel and performing downsampling. Andreopoulos @cite_6 defined a complete to overcomplete discrete wavelet transform (CODWT), which avoids inverse DWT generally used to obtain ODWT. More recently, Liu and Ngan @cite_8 use partial distortion search and anisotropic double cross search algorithms with the MCTF method in @cite_6 for a fast motion estimation. Amiot @cite_114 perform MCTF for denoising, using dual-tree complex wavelet (DT-CW) coefficients.
@cite_8 @cite_6 @cite_130 @cite_134 @cite_114 @cite_94
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A new in-band motion compensation algorithm for wavelet-based video coding is proposed: the bottom-up prediction algorithm (BUP). This algorithm overcomes the periodic shift-invariance of the discrete wavelet transform (DWT) and is formalised into prediction rules using filtering operations. The combination of all prediction rules of the BUP algorithm defines a new transform: the bottom-up overcomplete DWT or BUP ODWT, which is shift-invariant. The envisaged application for the BUP algorithm is spatially scalable wavelet video coding. Motion estimation and compensation in wavelet domain have received much attention recently. To overcome the inefficiency of motion estimation in critically sampled wavelet domain, the low-band-shift (LBS) method and the complete-to-overcomplete discrete wavelet transform (CODWT) method are proposed for motion estimation in shift-invariant wavelet domain. However, a major disadvantage of these methods is the computational complexity. Although the CODWT method has reduced the computational complexity by skipping the inverse wavelet transform and making the direct link between the critically sampled subbands and the shift-invariant subbands, the full search algorithm (FSA) increases it. In this paper, we proposed two fast multiresolution motion estimation algorithms in shift-invariant wavelet domain: one is the wavelet matching error characteristic based partial distortion search (WMEC-PDS) algorithm, which improves computational efficiency of conventional partial distortion search algorithms while keeping the same estimate accuracy as the FSA; another is the anisotropic double cross search (ADCS) algorithm using multiresolution-spatio-temporal context, which provides a significantly computational load reduction while only introducing negligible distortion compared with the FSA. Due to the multiresolution nature, both the proposed approaches can be applied to wavelet-based scalable video coding. Experimental results show the superiority of the proposed fast motion estimation algorithms against other fast algorithms in terms of speed-up and quality. A new transform is proposed that derives the overcomplete discrete wavelet transform (ODWT) subbands from the critically sampled DWT subbands (complete representation). This complete-to-overcomplete DWT (CODWT) has certain advantages in comparison to the conventional approach that performs the inverse DWT to reconstruct the input signal, followed by the a spl grave -trous or the lowband shift algorithm. Specifically, the computation of the input signal is not required. As a result, the minimum number of downsampling operations is performed and the use of upsampling is avoided. The proposed CODWT computes the ODWT subbands by using a set of prediction-filter matrices and filtering-and-downsampling operators applied to the DWT. This formulation demonstrates a clear separation between the single-rate and multirate components of the transform. This can be especially significant when the CODWT is used in resource-constrained environments, such as resolution-scalable image and video codecs. To illustrate the applicability of the proposed transform in these emerging applications, a new scheme for the transform-calculation is proposed, and existing coding techniques that benefit from its usage are surveyed. The analysis of the proposed CODWT in terms of arithmetic complexity and delay reveals significant gains as compared with the conventional approach. The discrete wavelet transform (DWT) has several advantages of multiresolution analysis and subband decomposition, which has been successfully used in image processing. However, the shift-variant property is intrinsic due to the decimation process of the wavelet transform, and it makes the wavelet-domain motion estimation and compensation inefficient. To overcome the shift-variant property, a low-band-shift method is proposed and a motion estimation and compensation method in the wavelet-domain is presented. The proposed method has a superior performance to the conventional motion estimation methods in terms of the mean absolute difference (MAD) as well as the subjective quality. The proposed method can be a model method for the motion estimation in wavelet-domain just like the full-search block matching in the spatial domain. This paper introduces an expectation-maximization (EM) algorithm for image restoration (deconvolution) based on a penalized likelihood formulated in the wavelet domain. Regularization is achieved by promoting a reconstruction with low-complexity, expressed in the wavelet coefficients, taking advantage of the well known sparsity of wavelet representations. Previous works have investigated wavelet-based restoration but, except for certain special cases, the resulting criteria are solved approximately or require demanding optimization methods. The EM algorithm herein proposed combines the efficient image representation offered by the discrete wavelet transform (DWT) with the diagonalization of the convolution operator obtained in the Fourier domain. Thus, it is a general-purpose approach to wavelet-based image restoration with computational complexity comparable to that of standard wavelet denoising schemes or of frequency domain deconvolution methods. The algorithm alternates between an E-step based on the fast Fourier transform (FFT) and a DWT-based M-step, resulting in an efficient iterative process requiring O(NlogN) operations per iteration. The convergence behavior of the algorithm is investigated, and it is shown that under mild conditions the algorithm converges to a globally optimal restoration. Moreover, our new approach performs competitively with, in some cases better than, the best existing methods in benchmark tests. Abstract This paper describes a form of discrete wavelet transform, which generates complex coefficients by using a dual tree of wavelet filters to obtain their real and imaginary parts. This introduces limited redundancy (2m:1 for m-dimensional signals) and allows the transform to provide approximate shift invariance and directionally selective filters (properties lacking in the traditional wavelet transform) while preserving the usual properties of perfect reconstruction and computational efficiency with good well-balanced frequency responses. Here we analyze why the new transform can be designed to be shift invariant and describe how to estimate the accuracy of this approximation and design suitable filters to achieve this. We discuss two different variants of the new transform, based on odd even and quarter-sample shift (Q-shift) filters, respectively. We then describe briefly how the dual tree may be extended for images and other multi-dimensional signals, and finally summarize a range of applications of the transform that take advantage of its unique properties. Deconvolution of a noisy signal in a periodic band-limited wavelet basis exhibits visual artifacts in the neighbourhood of discontinuities. This phenomenon is similar to that appearing in denoising with compactly-supported wavelet transforms and can be reduced by "cycle spinning" as in Coifman and Donoho [3]. In this paper we present an algorithm which "cycle-spins" a periodic band-limited wavelet estimator over all circulant shifts in O(n(log(n))2) steps. Our approach is based on a mathematical idea and takes full advantage of the Fast Fourier Transform. A particular feature of our algorithm is to bounce from the Fourier domain (where deconvolution is performed) to the wavelet domain (where denoising is performed). For both smooth and boxcar convolutions observed in white noise, we illustrate the visual and numerical performances of our algorithm in an extensive simulation study of the estimator recently proposed by Johnstone, Kerkyacharian, Picard, and Raimondo [8]. All figures presented here are reproducible using the software package. Time series stored as feature vectors can be indexed by multidimensional index trees like R-Trees for fast retrieval. Due to the dimensionality curse problem, transformations are applied to time series to reduce the number of dimensions of the feature vectors. Different transformations like Discrete Fourier Transform (DFT) Discrete Wavelet Transform (DWT), Karhunen-Loeve (KL) transform or Singular Value Decomposition (SVD) can be applied. While the use of DFT and K-L transform or SVD have been studied on the literature, to our knowledge, there is no in-depth study on the application of DWT. In this paper we propose to use Haar Wavelet Transform for time series indexing. The major contributions are: (1) we show that Euclidean distance is preserved in the Haar transformed domain and no false dismissal will occur, (2) we show that Haar transform can outperform DFT through experiments, (3) a new similarity model is suggested to accommodate vertical shift of time series, and (4) a two-phase method is proposed for efficient n-nearest neighbor query in time series databases. We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the graph analogue of the Fourier domain, namely the spectral decomposition of the discrete graph Laplacian L. Given a wavelet generating kernel g and a scale parameter t, we define the scaled wavelet operator Ttg = g(tL). The spectral graph wavelets are then formed by localizing this operator by applying it to an indicator function. Subject to an admissibility condition on g, this procedure defines an invertible transform. We explore the localization properties of the wavelets in the limit of fine scales. Additionally, we present a fast Chebyshev polynomial approximation algorithm for computing the transform that avoids the need for diagonalizing L. We highlight potential applications of the transform through examples of wavelets on graphs corresponding to a variety of different problem domains. We consider a wavelet neural network approach for electricity load prediction. The wavelet transform is used to decompose the load into different frequency components that are predicted separately using neural networks. We firstly propose a new approach for signal extension which minimizes the border distortion when decomposing the data, outperforming three standard methods. We also compare the performance of the standard wavelet transform, which is shift variant, with a non-decimated transform, which is shift invariant. Our results show that the use of shift invariant transform considerably improves the prediction accuracy. In addition to wavelet neural network, we also present the results of wavelet linear regression, wavelet model trees and a number of baselines. Our evaluation uses two years of Australian electricity data. Images are often corrupted as a result of various factors that can occur during acquisition and transmission processes. Image denoising is aimed at removing or reducing noise, so that a good-quality image can be obtained for various applications. The paper presents a neural network based denoising method implemented in the wavelet transform domain. A noisy image is first wavelet transformed into four subbands, then a trained layered neural network is applied to each subband to generate noise-removed wavelet coefficients from their noisy ones. The denoised image is thereafter obtained through the inverse transform on the noise-removed wavelet coefficients. Simulation results demonstrate that this method is very efficient in removing noise. Compared with other methods performed in the wavelet domain, it requires no a priori knowledge about the noise and needs only one level of signal decomposition to obtain very good denoising results. Recent advances have seen a surge of deep learning approaches for image super-resolution. Invariably, a network, e.g. a deep convolutional neural network (CNN) or auto-encoder is trained to learn the relationship between low and high-resolution image patches. Recognizing that a wavelet transform provides a "coarse" as well as "detail" separation of image content, we design a deep CNN to predict the "missing details" of wavelet coefficients of the low-resolution images to obtain the Super-Resolution (SR) results, which we name Deep Wavelet Super-Resolution (DWSR). Out network is trained in the wavelet domain with four input and output channels respectively. The input comprises of 4 sub-bands of the low-resolution wavelet coefficients and outputs are residuals (missing details) of 4 sub-bands of high-resolution wavelet coefficients. Wavelet coefficients and wavelet residuals are used as input and outputs of our network to further enhance the sparsity of activation maps. A key benefit of such a design is that it greatly reduces the training burden of learning the network that reconstructs low frequency details. The output prediction is added to the input to form the final SR wavelet coefficients. Then the inverse 2d discrete wavelet transformation is applied to transform the predicted details and generate the SR results. We show that DWSR is computationally simpler and yet produces competitive and often better results than state-of-the-art alternatives. Abstract Orthonormal wavelet analysis (OWA) is a special form of wavelet analysis, especially suitable for analyzing spatial structures, such as atmospheric fields. For this purpose, OWA is much more efficient and accurate than the nonorthogonal wavelet transform (WT), which was introduced to the meteorological community recently and which is more suitable for time series analysis. Whereas the continuous WT is strictly correct only for infinite domains, OWA is derived from periodizing and discretizing the infinite-domain case and so is correct for periodic boundary conditions. Unlike Fourier spectra, OWA is not shift invariant. Nor is it equivariant like the WT; that is, the OWA output does not shift as its input shifts. Two remedies are to combine all possible shifts, known as the overcomplete, nonorthogonal shift equivariant WT, or else to use a “best shift,” known as best shift wavelet analysis. Although shift invariant and orthonormal w.r.t. arbitrary inputs, the latter’s optimization generally depend... Multimodal medical image fusion is an important task for the retrieval of complementary information from medical images. Shift sensitivity, lack of phase information and poor directionality of real valued wavelet transforms motivated us to use complex wavelet transform for fusion. We have used Daubechies complex wavelet transform (DCxWT) for image fusion which is approximately shift invariant and provides phase information. In the present work, we have proposed a new multimodal medical image fusion using DCxWT at multiple levels which is based on multiresolution principle. The proposed method fuses the complex wavelet coefficients of source images using maximum selection rule. Experiments have been performed over three different sets of multimodal medical images. The proposed fusion method is visually and quantitatively compared with wavelet domain (Dual tree complex wavelet transform (DTCWT), Lifting wavelet transform (LWT), Multiwavelet transform (MWT), Stationary wavelet transform (SWT)) and spatial domain (Principal component analysis (PCA), linear and sharp) image fusion methods. The proposed method is further compared with Contourlet transform (CT) and Nonsubsampled contourlet transform (NSCT) based image fusion methods. For comparison of the proposed method, we have used five fusion metrics, namely entropy, edge strength, standard deviation, fusion factor and fusion symmetry. Comparison results prove that performance of the proposed fusion method is better than any of the above existing fusion methods. Robustness of the proposed method is tested against Gaussian, salt & pepper and speckle noise and the plots of fusion metrics for different noise cases established the superiority of the proposed fusion method. The JPEG2000 standard uses the 2D Discrete Wavelet Transform (2D DWT), while the JPEG standard uses the 2D Discrete Cosine Transform (DCT). However, the 2D DWT has higher computational requirements than the 2D DCT and consumes a significant part of the total JPEG2000 encoding time. One way to improve the performance of the 2D DWT is using parallel techniques on an SIMD-enhanced architecture. In this paper, we apply data-level parallelism technique to exploit available parallelism of the 2D DWT. We focus on the two algorithms to traverse an image to implement the 2D Discrete Wavelet Transform (DWT), namely Row-Column Wavelet Transform (RCWT) and Line-Based Wavelet Transform (LBWT). Our experimental results show that the SIMD implementation of the LBWT algorithm is more complicated than the SIMD implementation of the RCWT algorithm, while the former algorithm is 1.60 times faster than the latter algorithm for an image of size 4096 × 4096. This article is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This decomposition corresponds to a factorization of the polyphase matrix of the wavelet or subband filters into elementary matrices. That such a factorization is possible is well-known to algebraists (and expressed by the formula SL(n; R(Z, z-I)) = E(n; R(z, z-l))); it is also used in linear systems theory in the electrical engineering community. We present here a self-contained derivation, building the decomposition from basic principles such as the Euclidean algorithm, with a focus on applying it to wavelet filtering. This factorization provides an alternative for the lattice factorization, with the advantage that it can also be used in the biorthogonal, i.e., non-unitary case. Like the lattice factorization, the decomposition presented here asymptotically reduces the computational complexity of the transform by a factor two. It has other applications, such as the possibility of defining a wavelet-like transform that maps integers to integers. A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 . In a document network such as a citation network of scientific documents, web-logs, etc., the content produced by authors exhibits their interest in certain topics. In addition some authors influence other authors' interests. In this work, we propose to model the influence of cited authors along with the interests of citing authors. Moreover, we hypothesize that apart from the citations present in documents, the context surrounding the citation mention provides extra topical information about the cited authors. However, associating terms in the context to the cited authors remains an open problem. We propose novel document generation schemes that incorporate the context while simultaneously modeling the interests of citing authors and influence of the cited authors. Our experiments show significant improvements over baseline models for various evaluation criteria such as link prediction between document and cited author, and quantitatively explaining unseen text. Abstract In this paper, we introduce a new (constructive) characterization of tight wavelet frames on non-flat domains in both continuum setting, i.e. on manifolds, and discrete setting, i.e. on graphs; we discuss how fast tight wavelet frame transforms can be computed and how they can be effectively used to process graph data. We start with defining the quasi-affine systems on a given manifold M . The quasi-affine system is formed by generalized dilations and shifts of a finite collection of wavelet functions Ψ : = ψ j : 1 ≤ j ≤ r ⊂ L 2 ( R ) . We further require that ψ j is generated by some refinable function ϕ with mask a j . We present the condition needed for the masks a j : 0 ≤ j ≤ r , as well as regularity conditions needed for ϕ and ψ j , so that the associated quasi-affine system generated by Ψ is a tight frame for L 2 ( M ) . The condition needed for the masks is a simple set of algebraic equations which are not only easy to verify for a given set of masks a j , but also make the construction of a j entirely painless. Then, we discuss how the transition from the continuum (manifolds) to the discrete setting (graphs) can be naturally done. In order for the proposed discrete tight wavelet frame transforms to be useful in applications, we show how the transforms can be computed efficiently and accurately by proposing the fast tight wavelet frame transforms for graph data (WFTG). Finally, we consider two specific applications of the proposed WFTG: graph data denoising and semi-supervised clustering. Utilizing the sparse representation provided by the WFTG, we propose l 1 -norm based optimization models on graphs for denoising and semi-supervised clustering. On one hand, our numerical results show significant advantage of the WFTG over the spectral graph wavelet transform (SGWT) by [1] for both applications. On the other hand, numerical experiments on two real data sets show that the proposed semi-supervised clustering model using the WFTG is overall competitive with the state-of-the-art methods developed in the literature of high-dimensional data classification, and is superior to some of these methods.