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 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. 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. 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. 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. 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. 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. 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. We propose joint spatial division and multiplexing (JSDM), an approach to multiuser MIMO downlink that exploits the structure of the correlation of the channel vectors in order to allow for a large number of antennas at the base station while requiring reduced-dimensional channel state information at the transmitter (CSIT). JSDM achieves significant savings both in the downlink training and in the CSIT uplink feedback, thus making the use of large antenna arrays at the base station potentially suitable also for frequency division duplexing (FDD) systems, for which uplink downlink channel reciprocity cannot be exploited. In the proposed scheme, the multiuser MIMO downlink precoder is obtained by concatenating a prebeamforming matrix, which depends only on the channel second-order statistics, with a classical multiuser precoder, based on the instantaneous knowledge of the resulting reduced dimensional “effective” channel matrix. We prove a simple condition under which JSDM incurs no loss of optimality with respect to the full CSIT case. For linear uniformly spaced arrays, we show that such condition is approached in the large number of antennas limit. For this case, we use Szego's asymptotic theory of Toeplitz matrices to show that a DFT-based prebeamforming matrix is near-optimal, requiring only coarse information about the users angles of arrival and angular spread. Finally, we extend these ideas to the case of a 2-D base station antenna array, with 3-D beamforming, including multiple beams in the elevation angle direction. We provide guidelines for the prebeamforming optimization and calculate the system spectral efficiency under proportional fairness and max-min fairness criteria, showing extremely attractive performance. Our numerical results are obtained via asymptotic random matrix theory, avoiding lengthy Monte Carlo simulations and providing accurate results for realistic (finite) number of antennas and users. 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. Abstract Visual tracking algorithms based on structured output support vector machine (SOSVM) have demonstrated excellent performance. However, sampling methods and optimization strategies of SOSVM undesirably increase the computational overloads, which hinder real-time application of these algorithms. Moreover, due to the lack of high-dimensional features and dense training samples, SOSVM-based algorithms are unstable to deal with various challenging scenarios, such as occlusions and scale variations. Recently, visual tracking algorithms based on discriminative correlation filters (DCF), especially the combination of DCF and features from deep convolutional neural networks (CNN), have been successfully applied to visual tracking, and attains surprisingly good performance on recent benchmarks. The success is mainly attributed to two aspects: the circular correlation properties of DCF and the powerful representation capabilities of CNN features. Nevertheless, compared with SOSVM, DCF-based algorithms are restricted to simple ridge regression which has a weaker discriminative ability. In this paper, a novel circular and structural operator tracker (CSOT) is proposed for high performance visual tracking, it not only possesses the powerful discriminative capability of SOSVM but also efficiently inherits the superior computational efficiency of DCF. Based on the proposed circular and structural operators, a set of primal confidence score maps can be obtained by circular correlating feature maps with their corresponding structural correlation filters. Furthermore, an implicit interpolation is applied to convert the multi-resolution feature maps to the continuous domain and make all primal confidence score maps have the same spatial resolution. Then, we exploit an efficient ensemble post-processor based on relative entropy, which can coalesce primal confidence score maps and create an optimal confidence score map for more accurate localization. The target is localized on the peak of the optimal confidence score map. Besides, we introduce a collaborative optimization strategy to update circular and structural operators by iteratively training structural correlation filters, which significantly reduces computational complexity and improves robustness. Experimental results demonstrate that our approach achieves state-of-the-art performance in mean AUC scores of 71.5 and 69.4 on the OTB2013 and OTB2015 benchmarks respectively, and obtains a third-best expected average overlap (EAO) score of 29.8 on the VOT2017 benchmark. 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. 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. Large CNNs have delivered impressive performance in various computer vision applications. But the storage and computation requirements make it problematic for deploying these models on mobile devices. Recently, tensor decompositions have been used for speeding up CNNs. In this paper, we further develop the tensor decomposition technique. We propose a new algorithm for computing the low-rank tensor decomposition for removing the redundancy in the convolution kernels. The algorithm finds the exact global optimizer of the decomposition and is more effective than iterative methods. Based on the decomposition, we further propose a new method for training low-rank constrained CNNs from scratch. Interestingly, while achieving a significant speedup, sometimes the low-rank constrained CNNs delivers significantly better performance than their non-constrained counterparts. On the CIFAR-10 dataset, the proposed low-rank NIN model achieves @math accuracy (without data augmentation), which also improves upon state-of-the-art result. We evaluated the proposed method on CIFAR-10 and ILSVRC12 datasets for a variety of modern CNNs, including AlexNet, NIN, VGG and GoogleNet with success. For example, the forward time of VGG-16 is reduced by half while the performance is still comparable. Empirical success suggests that low-rank tensor decompositions can be a very useful tool for speeding up large CNNs. 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. In this paper, a prototype wavelet-based neural-network classifier for recognizing power-quality disturbances is implemented and tested under various transient events. The discrete wavelet transform (DWT) technique is integrated with the probabilistic neural-network (PNN) model to construct the classifier. First, the multiresolution-analysis technique of DWT and the Parseval's theorem are employed to extract the energy distribution features of the distorted signal at different resolution levels. Then, the PNN classifies these extracted features to identify the disturbance type according to the transient duration and the energy features. Since the proposed methodology can reduce a great quantity of the distorted signal features without losing its original property, less memory space and computing time are required. Various transient events tested, such as momentary interruption, capacitor switching, voltage sag swell, harmonic distortion, and flicker show that the classifier can detect and classify different power disturbance types efficiently. Abstract: Large CNNs have delivered impressive performance in various computer vision applications. But the storage and computation requirements make it problematic for deploying these models on mobile devices. Recently, tensor decompositions have been used for speeding up CNNs. In this paper, we further develop the tensor decomposition technique. We propose a new algorithm for computing the low-rank tensor decomposition for removing the redundancy in the convolution kernels. The algorithm finds the exact global optimizer of the decomposition and is more effective than iterative methods. Based on the decomposition, we further propose a new method for training low-rank constrained CNNs from scratch. Interestingly, while achieving a significant speedup, sometimes the low-rank constrained CNNs delivers significantly better performance than their non-constrained counterparts. On the CIFAR-10 dataset, the proposed low-rank NIN model achieves @math accuracy (without data augmentation), which also improves upon state-of-the-art result. We evaluated the proposed method on CIFAR-10 and ILSVRC12 datasets for a variety of modern CNNs, including AlexNet, NIN, VGG and GoogleNet with success. For example, the forward time of VGG-16 is reduced by half while the performance is still comparable. Empirical success suggests that low-rank tensor decompositions can be a very useful tool for speeding up large CNNs. In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the past few decades. These methods produce excellent results, but can be challenging to deploy in practice due to factors including the high computational cost of the forward and adjoint operators and the difficulty of hyperparameter selection. The starting point of this paper is the observation that unrolled iterative methods have the form of a CNN (filtering followed by pointwise non-linearity) when the normal operator ( @math , where @math is the adjoint of the forward imaging operator, @math ) of the forward model is a convolution. Based on this observation, we propose using direct inversion followed by a CNN to solve normal-convolutional inverse problems. The direct inversion encapsulates the physical model of the system, but leads to artifacts when the problem is ill posed; the CNN combines multiresolution decomposition and residual learning in order to learn to remove these artifacts while preserving image structure. We demonstrate the performance of the proposed network in sparse-view reconstruction (down to 50 views) on parallel beam X-ray computed tomography in synthetic phantoms as well as in real experimental sinograms. The proposed network outperforms total variation-regularized iterative reconstruction for the more realistic phantoms and requires less than a second to reconstruct a @math image on the GPU. Statistical image reconstruction using penalized weighted least-squares (PWLS) criteria can improve image-quality in X-ray computed tomography (CT). However, the huge dynamic range of the statistical weights leads to a highly shift-variant inverse problem making it difficult to precondition and accelerate existing iterative algorithms that attack the statistical model directly. We propose to alleviate the problem by using a variable-splitting scheme that separates the shift-variant and ("nearly") invariant components of the statistical data model and also decouples the regularization term. This leads to an equivalent constrained problem that we tackle using the classical method-of-multipliers framework with alternating minimization. The specific form of our splitting yields an alternating direction method of multipliers (ADMM) algorithm with an inner-step involving a "nearly" shift-invariant linear system that is suitable for FFT-based preconditioning using cone-type filters. The proposed method can efficiently handle a variety of convex regularization criteria including smooth edge-preserving regularizers and non- smooth sparsity-promoting ones based on the l1-norm and total variation. Numerical experiments with synthetic and real in vivo human data illustrate that cone-filter preconditioners accelerate the proposed ADMM resulting in fast convergence of ADMM compared to conventional (nonlinear conjugate gradient, ordered subsets) and state-of-the-art (MFISTA, split-Bregman) algorithms that are applicable for CT. Piecewise smooth (PWS) images (e.g., depth maps or animation images) contain unique signal characteristics such as sharp object boundaries and slowly varying interior surfaces. Leveraging on recent advances in graph signal processing, in this paper, we propose to compress the PWS images using suitable graph Fourier transforms (GFTs) to minimize the total signal representation cost of each pixel block, considering both the sparsity of the signal’s transform coefficients and the compactness of transform description. Unlike fixed transforms, such as the discrete cosine transform, we can adapt GFT to a particular class of pixel blocks. In particular, we select one among a defined search space of GFTs to minimize total representation cost via our proposed algorithms, leveraging on graph optimization techniques, such as spectral clustering and minimum graph cuts. Furthermore, for practical implementation of GFT, we introduce two techniques to reduce computation complexity. First, at the encoder, we low-pass filter and downsample a high-resolution (HR) pixel block to obtain a low-resolution (LR) one, so that a LR-GFT can be employed. At the decoder, upsampling and interpolation are performed adaptively along HR boundaries coded using arithmetic edge coding, so that sharp object boundaries can be well preserved. Second, instead of computing GFT from a graph in real-time via eigen-decomposition, the most popular LR-GFTs are pre-computed and stored in a table for lookup during encoding and decoding. Using depth maps and computer-graphics images as examples of the PWS images, experimental results show that our proposed multiresolution-GFT scheme outperforms H.264 intra by 6.8 dB on average in peak signal-to-noise ratio at the same bit rate. Neural networks rely on convolutions to aggregate spatial information. However, spatial convolutions are expensive in terms of model size and computation, both of which grow quadratically with respect to kernel size. In this paper, we present a parameter-free, FLOP-free "shift" operation as an alternative to spatial convolutions. We fuse shifts and point-wise convolutions to construct end-to-end trainable shift-based modules, with a hyperparameter characterizing the tradeoff between accuracy and efficiency. To demonstrate the operation's efficacy, we replace ResNet's 3x3 convolutions with shift-based modules for improved CIFAR10 and CIFAR100 accuracy using 60 fewer parameters; we additionally demonstrate the operation's resilience to parameter reduction on ImageNet, outperforming ResNet family members. We finally show the shift operation's applicability across domains, achieving strong performance with fewer parameters on image classification, face verification and style transfer.