Fourier ptychography (FP) is a new computational imaging technique with the advantage of being able to provide super-resolution imaging. FP has a very complex degradation process. Merging with Fourier transforms and pupil aperture scanning causes difficulty in reconstructing high-resolution images by the commonly used deep neural network methods, e.g., based on convolutional neural networks (CNNs). In this paper, we propose a new optimization algorithm for FP, which is carefully designed so that it only constrains concise operations. Then, we unfold the proposed algorithm to design a new neural network, MDFP-Net, specifically for the FP task. MDFP-Net is consistent with a few stages, which well corresponds to the iterations of the proposed optimization algorithm for FP. This not only makes MDFP-Net more intuitively interpretable, but also makes MDFP-Net much more suitable for FP tasks than commonly used CNNs. Moreover, we have built a long-distance reflection FP measurement system and tested our neural network in real experiments. Simulation and real experimental results show that the proposed network can provide better reconstruction results than either traditional algorithms or other deep learning methods. Code is available at https://github.com/BP113/MDFPNET.

Skewed histogram shifting (SHS) is an efficient scheme in reversible data hiding (RDH) research. By employing a pair of symmetric predictors which averages part of sorted pixels around the to-be-predicted pixel, two skewed histograms are generated. With the embedding and shifting directions toward the short tail of the two histograms, SHS reduces many invalid modifications. However, the design of the symmetric predictors pair is strictly constrained, which seriously degrades the performance on both embedding capacity and distortion of this SHS scheme. In this work, we propose a generalized SHS model to remove the weight and symmetry constraints. With the help of differential evolution algorithm, the optimized parameters are obtained in a short period of time, avoiding wasting time using exhaustive search. What is more, adaptive pairwise mapping and embedding bin selection are also realized by adding parameters into the evolutionary process, which greatly improve the embedding performance without increasing too much computational complexity. Experiments demonstrate the superiority of our method by comparing it with state-of-the-art RDH schemes.

Local Binary Pattern (LBP) based framework only uses a scalar threshold to binarize all magnitude vectors inPdifferent directions around each center pixel of a texture image. Hence, the original LBP-based framework, in fact, can not precisely extract different magnitude features inPdifferent directions around each center pixel. Furthermore, the value of magnitude vectors can have dramatic changes from coarse areas to flat areas in the same texture image. Therefore, using a scalar threshold calculated from whole texture image can not precisely binarize all magnitude vectors in coarse areas and flat areas simultaneously. To overcome these two drawbacks, we propose a novel adaptively binarizing magnitude vector (ABMV) method. Firstly, we adaptively calculate the average vector threshold$\boldsymbol{\vec{t}_{P}}$withPdifferent directional values of all magnitude vectors to replace the scalar thresholdtto binarize the magnitude vectors. The proposed ABMV method can more precisely extract the different magnitude features inPdifferent directions around each center pixel. Secondly, we divide the original texture image into smaller sub-images and adaptively extract their average vector threshold from each sub-image separately. Because the correlation of the pixels in the same sub-image is stronger than that in a whole texture image, the ABMV method can more precisely extract different magnitude features from either coarse areas or flat areas. Finally, we introduce the proposed ABMV method into LBP-based framework. Extensive experiments are conducted on five representative texture databases: Outex, UIUC, CUReT, XU_HR and ALOT database. After introducing the ABMV method into CLBP, CLBC, BRINT and CJLBP, the classification accuracy and the robustness to noise of these methods can be significantly improved.

The convolutional model, which describes the relation among poststack seismic data, wavelet, and reflectivity, is the foundation of seismic deconvolution (SD). However, this model is only an approximation of the seismic wave equation, and it may not work in complex cases especially when the medium is anelastic, heterogeneous, and anisotropic. In this article, we propose a generalized convolutional model for poststack seismic data. A deep-learning-based data correction term is added to characterize the data ingredients that cannot be characterized by the convolutional model. The data correction term of the new model is realized using the long-short term memory (LSTM)-based deep learning architecture, of which parameters are learned based on the dataset from several well logs. Based on the new model, we propose an SD method and investigate its performance in building reflectivity models using complex numerical examples. The results verified that the new model can accurately characterize complex seismic data, which cannot be characterized by a convolutional model. In addition, the proposed SD method has significant advantages over traditional methods in building high-fidelity reflectivity models in complex cases.

In this letter, we propose a new global optimization method for nonlinear seismic inversion problems. The proposed method is a development of the existing method MMDE-Net by introducing a learnable strategy for choosing problem-dependent basis vectors and regularization parameters that are considered to be fixed in MMDE-Net. We name the proposed method as the optimized MMDE-Net (OMMDE-Net) and investigate its performance in seismic inversion through both synthetic and field data examples. The experimental results demonstrate that OMMDE-Net has advantages over MMDE-Net in effectiveness and efficiency.

Seismic inversion problems often involve strong nonlinear relationships between model and data so that their misfit functions usually have many local minima. Global optimization methods are well known to be able to find the global minimum without requiring an accurate initial model. However, when the dimensionality of model space becomes large, global optimization methods will converge slow, which seriously hinders their applications in large-dimensional seismic inversion problems. In this article, we propose a new method for large-dimensional seismic inversion based on global optimization and a machine learning technique called autoencoder. Benefiting from the dimensionality reduction characteristics of autoencoder, the proposed method converts the original large-dimensional seismic inversion problem into a low-dimensional one that can be effectively and efficiently solved by global optimization. We apply the proposed method to seismic impedance inversion problems to test its performance. We use a trace-by-trace inversion strategy, and regularization is used to guarantee the lateral continuity of the inverted model. Well-log data with accurate velocity and density are the prerequisite of the inversion strategy to work effectively. Numerical results of both synthetic and field data examples clearly demonstrate that the proposed method can converge faster and yield better inversion results compared with common methods.

Pixel-value-ordering (PVO) is a widely used reversible data hiding (RDH) framework which aims to achieve the high quality of stego-image under low capacity. In this letter, we propose a general location-based adaptive complexity for PVO. Different from the block-based complexity in the previous PVO-based methods, our proposed method adaptively selects context pixels from the perspective of the relative locations of predicted pixel and prediction pixel. Consequently, different number of high correlation context pixels can be adaptively selected and the context pixels can break the limitation of the current block. Moreover, instead of sharing the same block complexity by two predicted pixels in the current block, each predicted pixel can be utilized independently according to its own corresponding complexity. Our proposed adaptive complexity can combine with any PVO-based methods and the experimental results show that our proposed method achieves a significant improvement in prediction accuracy and embedding performance.

In this article, we propose a convolutional neural network with mapping layers (MCNN) for hyperspectral image (HSI) classification. The proposed mapping layers map the input patch into a low-dimensional subspace by multilinear algebra. We use our mapping layers to reduce the spectral and spatial redundancies and maintain most energy of the input. The feature extracted by our mapping layers can also reduce the number of following convolutional layers for feature extraction. Our MCNN architecture avoids the declining accuracy with increasing layers phenomenon of deep learning models for HSI classification and also saves the training time for its effective mapping layers. Furthermore, we impose the 3-D convolutional kernel on the convolutional layer to extract the spectral-spatial features for HSI. We tested our MCNN on three data sets of Indian Pines, University of Pavia, and Salinas, and we achieved the classification accuracy of 98.3%, 99.5%, and 99.3%, respectively. Experimental results demonstrate that the proposed MCNN can significantly improve classification accuracy and save much time consumption.

The k -nearest neighbor (KNN) rule is a successful technique in pattern classification due to its simplicity and effectiveness. As a supervised classifier, KNN classification performance usually suffers from low-quality samples in the training data set. Thus, training data set cleaning (TDC) methods are needed for enhancing the classification accuracy by cleaning out noisy, or even wrong, samples in the original training data set. In this paper, we propose a classification ability ranking (CAR)-based TDC method to improve the performance of a KNN classifier, namely CAR-based TDC method. The proposed classification ability function ranks a training sample in terms of its contribution to correctly classify other training samples as a KNN through the leave-one-out (LV1) strategy in the cleaning stage. The training sample that likely misclassifies the other samples during the KNN classifications according to the LV1 strategy is considered to have lower classification ability and will be cleaned out from the original training data set. Extensive experiments, based on ten real-world data sets, show that the proposed CAR-based TDC method can significantly reduce the classification error rates of KNN-based classifiers, while reducing computational complexity thanks to a smaller cleaned training data set.

Target detection of hyperspectral image (HSI) is a research hotspot in the field of remote sensing. It is of particular importance in many domains, especially in military application. Unsupervised target detection is usually more difficult because there is no prior information about target. Traditional algorithms exploit spectral information, only. This study introduces the idea of saliency detection from the visual technique into HSI processing domain and proposes a novel approach named spectral saliency target detection (SSD). It establishes a novel salient model, which utilises both spatial saliency and spectral saliency. In the framework of SSD, it combines the model with spectral matching algorithm to make it perform well even in situations where the target is concealed and small. A HSI set comprised of eight different scenes with complex background is setup to evaluate the performance of the proposed algorithm. The final visible detection results demonstrate that the SSD algorithm outperforms the others. The receiver operation characteristic (ROC) curve and area under the ROC curve are applied to evaluate the results. The proposed algorithm shows superior and stable performance.

Full-waveform inversion (FWI) attempts to find optimal models of subsurface by using full information of the observed data. One difficulty in conventional FWI is that the misfit function has many local minima because of cycle skipping. Envelope inversion (EI), which uses the envelope operator (EO)-based misfit function, has been proven to be effective in mitigating cycle skipping and recovering long-wavelength velocity model. However, EI ignores the fact that the information within different frequency bands plays different roles in inversion. In this paper, a frequency controllable EO, which can control the frequency components being used to construct envelope, is proposed. We propose a new misfit function and a multiscale FWI method. Using synthetic experiments based on the Marmousi model, we demonstrate that the proposed method is better than EI in mitigating cycle skipping and in building an accurate initial model for conventional FWI to significantly improve its final result. In addition, this method can tolerate a wide range of noise levels. Its effectiveness has also been successfully demonstrated using a field data set.

Seismic inversion problems are well-known to be nonlinear and their misfit functions often involve many local minima. Global optimization methods are capable of converging to the global minimum of a misfit function, thus, they are promising in seismic inversion. As a global optimization method, multimutation differential evolution (MMDE) has been proven to be effective in solving high-dimensional seismic inversion problems. However, it is challenging to choose the optimal parameters for MMDE to achieve the best performance in seismic inversion. In this paper, we propose a new deep network based on MMDE and name it as MMDE-Net, which enables us to learn the optimal parameters by using a network training procedure rather than empirically choosing them. Benefiting from the learned parameters, MMDE-Net has advantages over MMDE in applications. Numerical examples based on synthetic and field data set clearly indicate that MMDE-Net can provide faster convergence speed and better inversion result than conventional methods in seismic inversion.

In the re-evaluated paper, Xie et al. proposed a new fast search algorithm for vector quantization encoding, which optimized the priority checking order of variance and norm inequality in order to speed up the encoding procedure. CPU time of different encoding algorithms is given to support their algorithm. However, first, some of the experimental data in the re-evaluated paper are unreasonable and unrepeatable. And second, as an improved algorithm of equal-average equal-variance equal-norm nearest neighbor fast search algorithm, the re-evaluated algorithm in fact cannot achieve a better performance than the existing improved equal-average equal-variance nearest neighbor fast search algorithm. In this paper, these two problems are analyzed, re-evaluated, and discussed in detail.

Block‐matching motion estimation (BME) can efficiently reduce the temporal redundancy between the successive video sequences in video compression coding system. In this study, a fast BME algorithm using multilevel distortion search in Walsh–Hadamard domain is proposed to reduce the computational burden and speed up coding process. First, the proposed algorithm divides the block into several sub‐blocks. Then, the Walsh–Hadamard transform is applied to these sub‐blocks. Finally, the proposed algorithm calculates the partial block matching distortion by utilising a novel back diagonal search scheme which can quickly reject unnecessary candidate block in a multilevel manner. Experimental results show that the proposed algorithm effectively reduces the number of operations in block distortion calculation meanwhile maintains the best motion estimation matching quality. Compared with the full search, the proposed algorithm can reduce 87.19% computational complexity without any degradation of the peak signal to noise ratio. In addition, compared with the partial distortion search algorithm, successive elimination algorithm, multilevel successive elimination algorithm and the transform‐domain successive elimination algorithm, the proposed algorithm can also save 68.27, 70.09, 37.81 and 37.44% computational complexity, respectively. Moreover, the proposed algorithm can also be easily incorporated into any block‐based template search motion estimation algorithm.

Local binary pattern (LBP) is sensitive to the noise and suffers from limited discriminative capability, and many LBP variants are reported in the recent literatures. Although a lot of significant progresses have been made, most LBP variants still have limitations of noise sensitivity, high dimensionality, and computational inefficiency. In view of this, we propose a new noise-robust local image descriptor named the diamond sampling structure-based local adaptive binary pattern (DLABP) in this letter, which aims at achieving both efficiency and simplicity at the same time. It mainly features three contributions: 1) an effective diamond sampling structure to decrease the feature dimensionality significantly by fixing the number of sampling neighbors to a constant of 8; 2) a simple and new “average method on the radial direction” to enhance the noise robustness; and 3) an effective adaptive quantization threshold strategy to restore the noise-corrupted nonuniform patterns back to possible uniform patterns. Extensive experiments are conducted on three benchmark texture databases of Outex, UIUC, and CUReT. Compared to state-of-the-art LBP-like methods, the proposed approach consistently demonstrates superior performances both in noise-free conditions and in the presence of high levels of noise, while it has a low complexity and a smaller feature dimension.

For relay terminals in wireless communication systems, the difference of the power consumed for relaying signals means unfairness, which may reduce the network lifetime when the system is energy‐constrained. Classic opportunistic relay selections always cause unequal power consumption among all relays. In this study, the authors propose a novel distributed relay selection strategy, named the fair opportunistic relay selection (FORS) strategy, for amplify‐and‐forward (AF) opportunistic cooperative systems. The FORS strategy is designed based on physical‐layer fairness that means all available relays cumulatively consume equal power. They use a set of weight coefficients to adjust the channel fading coefficients effectively and then change the selection probabilities for all relays on the basis of proportional fair scheduling. Considering that the ‘optimal’ relay can be selected proactively in quasi‐static Rayleigh fading channels based on local channel state information, the overhead of the proposed scheme is small. Then, they analyse the performance of the FORS strategy and provide an exact analytical expression for the outage probability ( P out ) and the average symbol error probability. Numerical simulation results validate their analysis. The results show that the FORS strategy approximately achieves the upper bound of physical‐layer fairness in the AF relaying system.

Seismic inversion problems often involve nonlinear relationships between data and model and usually have many local minima. Linearized inversion methods have been widely used to solve such problems. However, these kinds of methods often strongly depend on the initial model and are easily trapped in a local minimum. Global optimization methods, on the other hand, do not require a very good initial model and can approach a global minimum. However, global optimization methods are exhaustive search techniques that can be very time consuming. When the model dimension or the search space becomes large, these methods can be very slow to converge. In this paper, we propose a new global optimization algorithm by incorporating a new multimutation scheme into a differential evolution algorithm. Because mutation operation with the new multimutation scheme can generate better mutant vectors, the new global optimization algorithm has a very good ability of exploring the search space and can converge very fast. We apply the proposed algorithm to both synthetic and field data to test its performance. The results have clearly indicated that the new global optimization algorithm provides faster convergence and yields better results compared with the conventional global optimization methods in seismic inversion.

The regularized kernel method for the ranking problem has attracted increasing attentions in machine learning. The previous regularized ranking algorithms are usually based on reproducing kernel Hilbert spaces with a single kernel. In this paper, we go beyond this framework by investigating the generalization performance of the regularized ranking with multiscale kernels. A novel ranking algorithm with multiscale kernels is proposed and its representer theorem is proved. We establish the upper bound of the generalization error in terms of the complexity of hypothesis spaces. It shows that the multiscale ranking algorithm can achieve satisfactory learning rates under mild conditions. Experiments demonstrate the effectiveness of the proposed method for drug discovery and recommendation tasks.

Side match vector quantisation (SMVQ) technique has been widely used in a lot of image compression and data hiding applications. It can effectively decrease the bit rate (BR) but the encoding visual quality of the image using SMVQ is generally poor because the correlation among neighbouring image blocks is still low. In this study, the authors propose a new enhanced SMVQ (ESMVQ) by introducing the concept of complementary state codebook (CSC) to improve the visual quality of SMVQ. Encoding input vectors by using CSC, ESMVQ can achieve almost the same encoding visual quality as using the conventional vector quantisation. As a result, the encoding visual quality of image can be significantly improved by exploiting the power of CSC. Experimental results show that the improvement of proposed ESMVQ method over SMVQ is up to 4.677 dB at a similar BR for image Lena when the main codebook size is 1024.

The codebook design which determines the quality of the encoded images is an important problem in the vector quantisation technique. The Linde–Buzo–Gray (LBG) technique is a widely used algorithm in the codebook design. However, LBG algorithm is very sensitive to the initial codebook and tends to trap to the local minimum. In this study, a high‐quality initial codebook design method is proposed. The proposed method utilises both the mean characteristic value and variance characteristic value of training vectors to divide the training vectors into groups. Then codewords are selected from each group to generate an initial codebook. The experimental results demonstrate that the authors proposed method has a better performance in the initial codebook than that of the related methods.

Steganography based on vector quantisation (VQ)‐compressed indices is widely used in information hiding. In this study, the authors propose a new reversible information hiding method for VQ indices using an on‐line generated locally adaptive complete coding list. The complete coding list guarantees that all VQ indices can embed one or two secret bits which efficiently increase the embedding capacity. Additionally, they propose a mixed coding method with an index position threshold by exploring the biased‐distribution of locally complete coding indices in order to reduce the bit rate. Experimental results demonstrated that the authors proposed method has a better performance in embedding capacity, bit rate and the embedding‐efficiency compared with the four information hiding methods.

In this paper, a new high-performance reversible data hiding method for vector quantization (VQ) indices is proposed. The codebook is firstly sorted using the unidirectional static distance-order technique to improve the correlation among the neighboring indices. The two-dimensional structure of image and the high correlation among the neighboring blocks are used to update the self-organized list L in the improved locally adaptive coding scheme (ILAS). Then a new embedding rule according to the complexity of the region at which the current block locates and the position of current block index in the list L is proposed to obtain a better embedding capacity. The experimental results demonstrate that our proposed method has a better performance in terms of compression rate, embedding capacity and embedding rate compared with the related data hiding methods.

In this letter, a new adaptive differential evolution (DE) for high-dimensional waveform inversion is proposed. In conventional DE algorithms, individuals are treated as a whole and share the same fitness function and parameters. However, conventional DE algorithms have ignored the huge difference among the subcomponents in an individual and are not effective for high-dimensional problems. Therefore, for high-dimensional problems, we expand the unit of crossover rate from the whole individual to its subcomponents and propose a new adaption algorithm by adjusting the crossover rate of each subcomponent. In our algorithm, both kinds of crossover rate, including individual crossover rate and subcomponent crossover rate, play important roles in crossover operation. Based on local fitness function, the subcomponent crossover rate is adaptively obtained to improve the efficiency of crossover operation. On the other hand, the individual crossover rate is used to prevent the population diversity from decreasing in crossover operation. We embed the adaption algorithm into cooperative coevolutionary DE (CCDE) and propose a new adaptive DE by adjusting the subcomponent crossover rate named CRsADE. We have conducted experiments on waveform inversion to test the performance of the proposed algorithm. The results show that CRsADE performs better than CCDE significantly both on convergence speed and accuracy. In order to estimate the validity of CRsADE, we have also applied it to real seismic data.

Local binary pattern (LBP) is a simple and effective descriptor for texture classification. However, it has two main disadvantages: (1) different structural patterns sometimes have the same binary code and (2) it is sensitive to noise. In order to overcome these disadvantages, we propose a new local descriptor named local vector quantization pattern (LVQP). In LVQP, different kinds of texture images are chosen to train a local pattern codebook, where each different structural pattern is described by a unique codeword index. Contrarily to the original LBP and its many variants, LVQP does not quantize each neighborhood pixel separately to 0/1, but aims at quantizing the whole difference vector between the central pixel and its neighborhood pixels. Since LVQP deals with the structural pattern as a whole, it has a high discriminability and is less sensitive to noise. Our experimental results, achieved by using four representative texture databases of Outex, UIUC, CUReT, and Brodatz, show that the proposed LVQP method can improve classification accuracy significantly and is more robust to noise.

In this letter, a new differential evolution (DE) algorithm is proposed and applied to waveform inversion. The traditional evolution strategy of this algorithm is not efficient because it treats the individuals in a population equally and evolves all of them in each generation. In order to overcome this shortcoming, we propose a new population evolution strategy (PES) to decrease the population size based on the differences among individuals during an evolution process. We embed the new strategy into the cooperative coevolutionary DE (CCDE) and obtain a new highly efficient DE (HEDE). We apply this new algorithm to waveform inversion experiments of both synthetic and real seismic data to test its performance and demonstrate its validity. The results have clearly shown that, under the same inversion precision, the HEDE can reduce the runtime by about 50% compared with the CCDE.

In this letter, we consider a density-level detection (DLD) problem by a coefficient-based classification framework with [Formula: see text]-regularizer and data-dependent hypothesis spaces. Although the data-dependent characteristic of the algorithm provides flexibility and adaptivity for DLD, it leads to difficulty in generalization error analysis. To overcome this difficulty, an error decomposition is introduced from an established classification framework. On the basis of this decomposition, the estimate of the learning rate is obtained by using Rademacher average and stepping-stone techniques. In particular, the estimate is independent of the capacity assumption used in the previous literature.

Encoding speed is one of the key issues in vector quantization (VQ). In order to effectively reduce computational complexity, before actually computing the expensive real Euclidean distance in VQ, it is possible to estimate the Euclidean distance first by using the statistical features of sum and variance of a k-D vector. The IEENNS method has been proposed to reject most unlikely candidate codewords for the input vector. Furthermore, by partitioning a k-D vector in half to construct its two (k/2)-D subvectors and then apply IEENNS method again to each of the two subvectors separately, SIEENNS method has been reported as well. The SIEENNS method is the most essential subvector-based search method for VQ but it failed to deal with the two subvectors at the same time, which degrades the search performance obviously. This paper aims at generalizing and enhancing state-of-the-art SIEENNS method by means of simultaneously instead of separately using the two subvectors so as to reject more unlikely candidate codewords for the input vector. Mathematical analysis and experimental results confirmed that the proposed method in this paper can significantly improve the search efficiency to 68.3%~82.2% compared to the SIEENNS method.

Vector quantization (VQ) is a popular image compression method and the encoding speed of VQ is very important to its practical applications. In a conventional encoding process of VQ, because a lot of k-dimensional (k-D) Euclidean distances must be computed so as to find out the best-match for each input vector, VQ is computationally very expensive. In order to avoid immediately computing the real Euclidean distance for a candidate codeword, IEENNS method has been proposed to reject the unlikely codeword by using the famous scalar features of the sum and the variance of a k-D vector. Furthermore, in order to improve the precision of Euclidean distance estimation so as to enhance the rejection capability, by dividing a k-D vector in half to generate two (k/2)-D subvectors and then apply IEENNS method again to each of the subvectors, a complete-version C-SIEENNS method and a simplified-version S-SIEENNS method have been reported recently as well. Apparently, how to construct the two (k/2)-D subvectors is the core problem in a subvector-based method for achieving a higher encoding performance. However, the previous works just fixedly construct their two subvectors by using the first half original vector of [1 /spl sim/ k/2] dimensions and the second half original vector of [k/2+1 /spl sim/ k] dimensions for simplicity. It is clear there is no guarantee that this kind of subvector construction way is optimal. Instead, this paper proposes a criterion to construct two better subvectors by letting the difference between the two partial sums approach the maximum based on adaptively analyzing the property of each codeword offline. Experimental results confirmed that by simply replacing the fixed subvectors with the adaptively constructed subvectors in S-SIEENNS method, it can further improve the search efficiency by 19.9% /spl sim/ 36.8%.

VQ is a famous signal compression method. The encoding speed of VQ is a key problem for its practical application. In principle, the high dimension of a vector makes it very expensive computationally to find the best-matched template in a codebook for an input vector by Euclidean distance. As a result, many fast search methods have been developed in previous works based on statistical features (i.e. mean, variance or L/sub 2/ norm) or multi-resolution representation (i.e. various pyramid data structures) of a vector to deal with this computational complexity problem. Therefore, how to use them optimally in terms of a small memory requirement and a little computational overhead becomes very important. This paper proposes to combine both the 2-PM sum pyramid and (n/spl times/n)-PM variance pyramid of a vector to construct a new mixed pyramid data structure, which only requires (k+1) memories for a k-dimensional vector. Experimental results confirmed that the encoding efficiency by using this mixed pyramid outperforms the previous works significantly.

In a framework of vector quantization (VQ), the encoding speed is a key issue for its practical applications. To speed up the VQ encoding process, Walsh transform is introduced in the previous work to map vectors in a k-dimensional (k-D) spatial domain into k-D Walsh domain in order to exploit the energy-compaction property of an orthogonal transform. However, there still exist a serious problem in that previous work because it just simply used the most common sequency-ordered Walsh transform kernel, which is actually not very high efficient for fast VQ encoding. In order to solve the kernel order problem in VQ encoding this paper proposes an optimal order for Walsh transform kernel based on the energy distribution of a particular codebook at each dimension in a k-D Walsh domain, which requires that the dimension with a larger energy distribution be put forward to be as a lower dimension. Experimental results confirmed that the proposed method could reduce the computational cost to 85.9% /spl sim/ 53.1% compared to the previous work so as to enhance its performance obviously.

The encoding process of image vector quantization (VQ) is very heavy due to it performing a lot of k-dimensional Euclidean distance computations. In order to speed up VQ encoding, it is most important to avoid unnecessary exact Euclidean distance computations as many as possible by using features of a vector to estimate how large it is first so as to reject most of unlikely codewords. The mean, the variance, L2 norm and partial sum of a vector have been proposed as effective features in previous works for fast VQ encoding. Recently, in the previous work [6], three features of the mean, the variance and L2 norm are used together to derive an EEENNS search method, which is very search efficient but still has obvious computational redundancy. This paper aims at modifying the results of EEENNS method further by introducing another feature of partial sum to replace L2 norm feature so as to reduce more search space. Mathematical analysis and experimental results confirmed that the proposed method is more search efficient compared to [6].

The L/sub 2/-norm pyramid has already been investigated as a promising data structure for the fast search of vector quantization (VQ) encoding in the previous work. Because the distortion at the top level is always tested first when using such a conventional L/sub 2/-norm pyramid, the top level is most important. In order to enhance the capability of achieving a rejection decision at the top level, a modification is introduced into the conventional L/sub 2/-norm pyramid in this letter by using both the mean and the variance of a vector simultaneously to replace the L/sub 2/-norm of the vector for distortion computation at the top level. Two issues are made clear as 1) why this modification is beneficial to the distortion test is proved and 2) why only the top level of a conventional L/sub 2/-norm pyramid should be modified is interpreted as well. Experimental results confirmed that the performance of VQ encoding by using the modified L/sub 2/-norm pyramid can be improved obviously.

Vector quantization (VQ) is a famous signal compression method. In VQ encoding, a fast search method for finding the best-matched codeword (winner) is a key issue because it is the time bottleneck for practical applications. To speed up the VQ encoding process, some fast search methods that are based on the concept of multiresolutions by introducing a pyramid data structure have already been proposed in previous works. However, there still exist two serious problems in them. First, they need a lot of extra memories for storing all purposely constructed intermediate levels in a pyramid, which becomes an overhead of memory. Second, they completely discard the obtained Euclidean distance that has already been computed at an intermediate level whenever a rejection test fails at this level during a search process, which becomes an overhead of computation. In order to solve the overhead problems of both memory and computation as described above, this paper proposes a memory-efficient storing for vector and recursive computation for Euclidean distance level by level based on a 2-pixel-merging (2-PM) sum pyramid, which can thoroughly reuse the obtained value of Euclidean distance at any level to compute the next rejection test condition at a successive level. Mathematically, this method does not need any extra memories at all and can reduce the original computational burden that is needed in conventional nonrecursive computation to about half at each level. Experimental results confirm that the proposed method outperforms the previous works.

In a framework of vector quantization (VQ), the fast search method for finding the best-matched codeword (winner) is a key issue because it is the time bottleneck for practical applications. To speed up VQ encoding process, some fast search methods that are based on the concept of projection axes or Walsh transform have already been proposed in previous works (L. Guan and M. Kamel, Oct 1992)-(S. Baek and K. Sung 2001). However, there still exist two serious problems in them because they use both spatial domain and partial Walsh domain simultaneously. First, they need extra memories for storing projected values on selected projection axes or the first several elements in partial Walsh domain, which becomes an overhead of memory. Second, once all rejection tests fail finally, they completely discard the obtained distortion that has already been computed in partial Walsh domain and return to spatial domain to compute real Euclidean distance again from the very beginning, which is certainly a waste and becomes an overhead of computation. In order to solve the overhead problems of both memory and computation as described above, firstly a memory-efficient storing way for a vector is proposed by completely mapping a vector into Walsh domain but NOT using-the original spatial domain any more, which can avoid extra memory requirement Secondly, the discarded distortion in partial Walsh domain is reused so as to avoid any waste to the executed computation. In addition, a more efficient rejection test is suggested to reduce more search space. Experimental results confirmed that the proposed method outperforms the previous works obviously.

Within the framework of vector quantization (VQ), the fast search method is a key issue because it is the time bottleneck in the VQ encoding process. To speed up VQ some very effective fast search methods that are based on using statistical features (i.e. the mean, the variance and L/sub 2/ norm) of a k-dimensional vector have already been proposed. It is rather easy to obtain the mean of an input vector online. However. in order to obtain the variance of an input vector, it needs (2k-1) additions (/spl plusmn/), k multiplications (/spl times/) and once square root (sqrt) operation on-line. Similarly, to obtain the L/sub 2/ norm of an input vector, it also needs (k-l) additions (/spl plusmn/), k multiplications (/spl times/) and once square root (sqrt) operation on-line. Clearly, these operations are a rather heavy overhead in the search process. In addition, all computations in a search process must use real rather than integer value. For each codeword, three extra memories are necessary to store its features. To solve the overhead problem of computing the variance and L/sub 2/ norm of an input vector on-line and to make all computations in integer form possible, previous works proposed to use the sum and two partial sums only as features of a vector for reducing search space. But they need three extra memories as well for each codeword to store the features. In order to avoid this extra memory requirement this paper proposes a memory-efficient data structure for storing the sum, two partial sums and the original vector to further improve the previous works (Pan et al. (2002), (2003)). Meanwhile, a more efficient computation method for rejection tests is also developed. In addition, all computations can be realized in integer form. Experimental results confirmed that the proposed method outperforms the previous works.

Vector quantization (VQ) is a well-known signal compression method. In VQ, the search process to find the winner for an input vector either at the codebook generation stage or the VQ encoding stage is extremely time consuming. By using the law of cosines to estimate the Euclidean distance first, Mielikainen has developed a highly efficient full-search-equivalent algorithm. However, some computational redundancies still exist in it. In this letter, we introduce an additional new estimation for the Euclidean distance and then optimize the computing way given by Mielikainen. Mathematical analyses show that our proposed search method can improve Mielikainen's method. And experimental results of VQ encoding demonstrate that the proposed method is very search effective.

Vector quantization (VQ) is a famous asymmetric signal compression method. In VQ, the search process to find the winner for an input vector is extremely time consuming due to a lot of k-dimensional Euclidean distance computations. This property of VQ constrains its practical applications to some extent. In order to speed up the search process of VQ, a unified projection method is proposed in this letter to reject a candidate code vector by a lighter computational burden. This method is universal because it can unify several types of previous works through suitably selecting a projection axis. Furthermore, two criteria for how to select an optimal projection axis for a code vector are proven mathematically, which are most important because they demonstrate the direction for a potential improvement to the search efficiency of VQ. Experimental results of VQ encoding show that the proposed method is very search effective.

The encoding process of vector quantization (VQ) is very heavy and it constrains VQ's application a great deal. In order to speed up VQ encoding, it is most important to avoid unnecessary Euclidean distance computation (k-D) as much as possible by the difference check that uses simpler features (low dimensional) while winner searching is going on. Sum (1-D) and partial sums (2-D) are used together as the appropriate features in this paper because they are the first 2 simplest features. Then, sum difference and partial sum difference are computed as the estimations of Euclidean distance and they are connected to each other by the Cauchy-Schwarz inequality so as to reject a lot of codewords. For typical standard images with very different details (Lena, F-16, Pepper and Baboon), the final must-do Euclidean distance computation using the proposed method can be reduced to less than 10% as compared to full search (FS) meanwhile keeping the PSNR not degraded.