Forward stagewise regression with multilevel memristor for sparse coding

Sparse coding is a prevalent method for image inpainting and feature extraction,which can repair corrupted images or improve data processing efficiency,and has numerous applications in computer vision and signal processing.Recently,sev-eral memristor-based in-memory computing systems have been proposed to enhance the efficiency of sparse coding remark-ably.However,the variations and low precision of the devices will deteriorate the dictionary,causing inevitable degradation in the accuracy and reliability of the application.In this work,a digital-analog hybrid memristive sparse coding system is pro-posed utilizing a multilevel Pt/Al_(2)O_(3)/AlO_(x)/W memristor,which employs the forward stagewise regression algorithm:The approxi-mate cosine distance calculation is conducted in the analog part to speed up the computation,followed by high-precision coeffi-cient updates performed in the digital portion.We determine that four states of the aforementioned memristor are sufficient for the processing of natural images.Furthermore,through dynamic adjustment of the mapping ratio,the precision require-ment for the digit-to-analog converters can be reduced to 4 bits.Compared to the previous system,our system achieves higher image reconstruction quality of the 38 dB peak-signal-to-noise ratio.Moreover,in the context of image inpainting,images containing 50%missing pixels can be restored with a reconstruction error of 0.0424 root-mean-squared error.

Two-level Bregmanized method for image interpolation with graph regularized sparse coding

A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inner-level Bregmanized method devotes to dictionary updating and sparse represention of small overlapping image patches. The introduced constraint of graph regularized sparse coding can capture local image features effectively, and consequently enables accurate reconstruction from highly undersampled partial data. Furthermore, modified sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge within a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can effectively reconstruct images and it outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.

Structured Sparse Coding With the Group Log-regularizer for Key Frame Extraction

Key frame extraction based on sparse coding can reduce the redundancy of continuous frames and concisely express the entire video.However,how to develop a key frame extraction algorithm that can automatically extract a few frames with a low reconstruction error remains a challenge.In this paper,we propose a novel model of structured sparse-codingbased key frame extraction,wherein a nonconvex group log-regularizer is used with strong sparsity and a low reconstruction error.To automatically extract key frames,a decomposition scheme is designed to separate the sparse coefficient matrix by rows.The rows enforced by the nonconvex group log-regularizer become zero or nonzero,leading to the learning of the structured sparse coefficient matrix.To solve the nonconvex problems due to the log-regularizer,the difference of convex algorithm(DCA)is employed to decompose the log-regularizer into the difference of two convex functions related to the l1 norm,which can be directly obtained through the proximal operator.Therefore,an efficient structured sparse coding algorithm with the group log-regularizer for key frame extraction is developed,which can automatically extract a few frames directly from the video to represent the entire video with a low reconstruction error.Experimental results demonstrate that the proposed algorithm can extract more accurate key frames from most Sum Me videos compared to the stateof-the-art methods.Furthermore,the proposed algorithm can obtain a higher compression with a nearly 18% increase compared to sparse modeling representation selection(SMRS)and an 8% increase compared to SC-det on the VSUMM dataset.

Graph Regularized Sparse Coding Method for Highly Undersampled MRI Reconstruction

The imaging speed is a bottleneck for magnetic resonance imaging( MRI) since it appears. To alleviate this difficulty,a novel graph regularized sparse coding method for highly undersampled MRI reconstruction( GSCMRI) was proposed. The graph regularized sparse coding showed the potential in maintaining the geometrical information of the data. In this study, it was incorporated with two-level Bregman iterative procedure that updated the data term in outer-level and learned dictionary in innerlevel. Moreover,the graph regularized sparse coding and simple dictionary updating stages derived by the inner minimization made the proposed algorithm converge in few iterations, meanwhile achieving superior reconstruction performance. Extensive experimental results have demonstrated GSCMRI can consistently recover both real-valued MR images and complex-valued MR data efficiently,and outperform the current state-of-the-art approaches in terms of higher PSNR and lower HFEN values.

ISAR target recognition based on non-negative sparse coding

Aiming at technical difficulties in feature extraction for the inverse synthetic aperture radar （ISAR） target recognition, this paper imports the concept of visual perception and presents a novel method, which is based on the combination of non-negative sparse coding （NNSC） and linear discrimination optimization, to recognize targets in ISAR images. This method implements NNSC on the matrix constituted by the intensities of pixels in ISAR images for training, to obtain non-negative sparse bases which characterize sparse distribution of strong scattering centers. Then this paper chooses sparse bases via optimization criteria and calculates the corresponding non-negative sparse codes of both training and test images as the feature vectors, which are input into k neighbors classifier to realize recognition finally. The feasibility and robustness of the proposed method are proved by comparing with the template matching, principle component analysis （PCA） and non-negative matrix factorization （NMF） via simulations.

Two-Level Bregman Method for MRI Reconstruction with Graph Regularized Sparse Coding

In this paper, a two-level Bregman method is presented with graph regularized sparse coding for highly undersampled magnetic resonance image reconstruction. The graph regularized sparse coding is incorporated with the two-level Bregman iterative procedure which enforces the sampled data constraints in the outer level and updates dictionary and sparse representation in the inner level. Graph regularized sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge with a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can consistently reconstruct both simulated MR images and real MR data efficiently, and outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.

Uniquely Decomposable Constellation Group-Based Sparse Vector Coding for Short Packet Communications

Sparse vector coding(SVC)is emerging as a potential technology for short packet communications.To further improve the block error rate(BLER)performance,a uniquely decomposable constellation group-based SVC(UDCG-SVC)is proposed in this article.Additionally,in order to achieve an optimal BLER performance of UDCG-SVC,a problem to optimize the coding gain of UDCG-based superimposed constellation is formulated.Given the energy of rotation constellations in UDCG,this problem is solved by converting it into finding the maximized minimum Euclidean distance of the superimposed constellation.Simulation results demonstrate the validness of our derivation.We also find that the proposed UDCGSVC has better BLER performance compared to other SVC schemes,especially under the high order modulation scenarios.

Impulse feature extraction method for machinery fault detection using fusion sparse coding and online dictionary learning

Impulse components in vibration signals are important fault features of complex machines. Sparse coding （SC） algorithm has been introduced as an impulse feature extraction method, but it could not guarantee a satisfactory performance in processing vibration signals with heavy background noises. In this paper, a method based on fusion sparse coding （FSC） and online dictionary learning is proposed to extract impulses efficiently. Firstly, fusion scheme of different sparse coding algorithms is presented to ensure higher reconstruction accuracy. Then, an improved online dictionary learning method using FSC scheme is established to obtain redundant dictionary and it can capture specific features of training samples and reconstruct the sparse approximation of vibration signals. Simulation shows that this method has a good performance in solving sparse coefficients and training redundant dictionary compared with other methods. Lastly, the proposed method is further applied to processing aircraft engine rotor vibration signals. Compared with other feature extraction approaches, our method can extract impulse features accurately and efficiently from heavy noisy vibration signal, which has significant supports for machinery fault detection and diagnosis.

Structured sparsity assisted online convolution sparse coding and its application on weak signature detection

Due to the strong background noise and the acquisition system noise,the useful characteristics are often difficult to be detected.To solve this problem,sparse coding captures a concise representation of the high-level features in the signal using the underlying structure of the signal.Recently,an Online Convolutional Sparse Coding(OCSC)denoising algorithm has been proposed.However,it does not consider the structural characteristics of the signal,the sparsity of each iteration is not enough.Therefore,a threshold shrinkage algorithm considering neighborhood sparsity is proposed,and a training strategy from loose to tight is developed to further improve the denoising performance of the algorithm,called Variable Threshold Neighborhood Online Convolution Sparse Coding(VTNOCSC).By embedding the structural sparse threshold shrinkage operator into the process of solving the sparse coefficient and gradually approaching the optimal noise separation point in the training,the signal denoising performance of the algorithm is greatly improved.VTNOCSC is used to process the actual bearing fault signal,the noise interference is successfully reduced and the interest features are more evident.Compared with other existing methods,VTNOCSC has better denoising performance.

Weak Correlation Dictionary Construction Method for Sparse Coding

For sparse coding, the weaker the correlation of dictionary atoms is, the better the representation capacity of dictionary will be. A weak correlation dictionary construction method for sparse coding has been proposed in this paper. Firstly, a new dictionary atom initialization is proposed in which data samples with weak correlation are selected as the initial dictionary atoms in order to effectively reduce the correlation among them.Then, in the process of dictionary learning, the correlation between atoms has been measured by correlation coefficient, and strong correlation atoms have been eliminated and replaced by weak correlation atoms in order to improve the representation capacity of the dictionary. An image classification scheme has been achieved by applying the weak correlation dictionary construction method proposed in this paper. Experimental results show that, the proposed method averagely improves image classification accuracy by more than 2%, compared to sparse coding spatial pyramid matching(Sc SPM) and other existing methods for image classification on the datasets of Caltech-101, Scene-15, etc.

Image Denoising via Improved Simultaneous Sparse Coding with Laplacian Scale Mixture

Image denoising is a well-studied problem closely related to sparse coding. Noticing that the Laplacian distribution has a strong sparseness, we use Laplacian scale mixture to model sparse coefficients. With the observation that prior information of an image is relevant to the estimation of sparse coefficients, we introduce the prior information into maximum a posteriori（MAP） estimation of sparse coefficients by an appropriate estimate of the probability density function. Extending to structured sparsity, a nonlocal image denoising model： Improved Simultaneous Sparse Coding with Laplacian Scale Mixture（ISSC-LSM） is proposed. The centering preprocessing, which admits biased-mean of sparse coefficients and saves expensive computation, is done firstly. By alternating minimization and learning an orthogonal PCA dictionary, an efficient algorithm with closed-form solutions is proposed. When applied to noise removal, our proposed ISSC-LSM can capture structured image features, and the adoption of image prior information leads to highly competitive denoising performance. Experimental results show that the proposed method often provides higher subjective and objective qualities than other competing approaches. Our method is most suitable for processing images with abundant self-repeating patterns by effectively suppressing undesirable artifacts while maintaining the textures and edges.

Speech enhancement with a GSC-like structure employing sparse coding

Speech communication is often influenced by various types of interfering signals. To improve the quality of the desired signal, a generalized sidelobe canceller(GSC), which uses a reference signal to estimate the interfering signal, is attracting attention of researchers. However, the interference suppression of GSC is limited since a little residual desired signal leaks into the reference signal. To overcome this problem, we use sparse coding to suppress the residual desired signal while preserving the reference signal. Sparse coding with the learned dictionary is usually used to reconstruct the desired signal. As the training samples of a desired signal for dictionary learning are not observable in the real environment, the reconstructed desired signal may contain a lot of residual interfering signal. In contrast,the training samples of the interfering signal during the absence of the desired signal for interferer dictionary learning can be achieved through voice activity detection(VAD). Since the reference signal of an interfering signal is coherent to the interferer dictionary, it can be well restructured by sparse coding, while the residual desired signal will be removed. The performance of GSC will be improved since the estimate of the interfering signal with the proposed reference signal is more accurate than ever. Simulation and experiments on a real acoustic environment show that our proposed method is effective in suppressing interfering signals.

Refined Sparse Representation Based Similar Category Image Retrieval

Given one specific image,it would be quite significant if humanity could simply retrieve all those pictures that fall into a similar category of images.However,traditional methods are inclined to achieve high-quality retrieval by utilizing adequate learning instances,ignoring the extraction of the image’s essential information which leads to difficulty in the retrieval of similar category images just using one reference image.Aiming to solve this problem above,we proposed in this paper one refined sparse representation based similar category image retrieval model.On the one hand,saliency detection and multi-level decomposition could contribute to taking salient and spatial information into consideration more fully in the future.On the other hand,the cross mutual sparse coding model aims to extract the image’s essential feature to the maximumextent possible.At last,we set up a database concluding a large number of multi-source images.Adequate groups of comparative experiments show that our method could contribute to retrieving similar category images effectively.Moreover,adequate groups of ablation experiments show that nearly all procedures play their roles,respectively.

PERFORMANCE OF SIMPLE-ENCODING IRREGULAR LDPC CODES BASED ON SPARSE GENERATOR MATRIX

A new method for the construction of the high performance systematic irregular low-density paritycheck （LDPC） codes based on the sparse generator matrix （G-LDPC） is introduced. The code can greatly reduce the encoding complexity while maintaining the same decoding complexity as traditional regular LDPC （H-LDPC） codes defined by the sparse parity check matrix. Simulation results show that the performance of the proposed irregular LDPC codes can offer significant gains over traditional LDPC codes in low SNRs with a few decoding iterations over an additive white Gaussian noise （AWGN） channel.

Jointly-check iterative decoding algorithm for quantum sparse graph codes

For quantum sparse graph codes with stabilizer formalism, the unavoidable girth-four cycles in their Tanner graphs greatly degrade the iterative decoding performance with standard belief-propagation （BP） algorithm. In this paper, we present a jointly-check iterative algorithm suitable for decoding quantum sparse graph codes efficiently. Numerical simulations show that this modified method outperforms standard BP algorithm with an obvious performance improvement.

Sparse Rev-Shift Coded Modulation with Novel Overhead Bound

To provide reliability in distributed systems,combination property(CP)is desired,where k original packets are encoded into n≥k packets and arbitrary k are sufficient to reconstruct all the original packets.Shift-and-add(SA)encoding combined with zigzag decoding(ZD)obtains the CP-ZD,which is promising to reap low computational complexity in the encoding/decoding process of these systems.As densely coded modulation is difficult to achieve CP-ZD,research attentions are paid to sparse coded modulation.The drawback of existing sparse CP-ZD coded modulation lies in high overhead,especially in widely deployed setting m<k,where m≜n−k.For this scenario,namely,m<k,a sparse reverseorder shift(Rev-Shift)CP-ZD coded modulation is designed.The proof that Rev-Shift possesses CP-ZD is provided.A lower bound for the overhead,as far as we know is the first for sparse CP-ZD coded modulation,is derived.The bound is found tight in certain scenarios,which shows the code optimality.Extensive numerical studies show that compared to existing sparse CP-ZD coded modulation,the overhead of Rev-Shift reduces significantly,and the derived lower bound is tight when k or m approaches 0.

Human interaction recognition based on sparse representation of feature covariance matrices

A new method for interaction recognition based on sparse representation of feature covariance matrices was presented.Firstly,the dense trajectories(DT)extracted from the video were clustered into different groups to eliminate the irrelevant trajectories,which could greatly reduce the noise influence on feature extraction.Then,the trajectory tunnels were characterized by means of feature covariance matrices.In this way,the discriminative descriptors could be extracted,which was also an effective solution to the problem that the description of the feature second-order statistics is insufficient.After that,an over-complete dictionary was learned with the descriptors and all the descriptors were encoded using sparse coding(SC).Classification was achieved using multiple instance learning(MIL),which was more suitable for complex environments.The proposed method was tested and evaluated on the WEB Interaction dataset and the UT interaction dataset.The experimental results demonstrated the superior efficiency.

LOW-DIMENSIONAL STRUCTURES:SP ARSE CODING FOR NEURONAL ACTIVITY

Neuronal ensemble activity codes working memory.In this work,we developed a neuronal ensemble sparse coding method,which can effectively reduce the dimension of the neuronal activity and express neural coding.Multichannel spike trains were recorded in rat prefrontal cortex during a work memory task in Y-maze.As discretesignals,spikes were transferred into cont inuous signals by estinating entropy.Then the normalized continuous signals were decomposed via non-negative sparse met hod.The non-negative components were extracted to reconstruct a low-dimensional ensemble,while none of the feature components were missed.The results showed that,for well-trained rats,neuronal ensemble activities in the prefrontal cortex changed dynamically during the.working memory task.And the neuronal ensemble is more explicit via using non-negative sparse coding.Our results indicate that the neuronal ensemblesparse coding method can effectively reduce the dimnension of neuronal activity and it is a useful tool to express neural coding.

Human Mouth-State Recognition Based on Image Warping and Sparse Representation Combined with Homotopy

It is often necessary to recognize human mouth-states for detecting the number of audio sources and improving the speech recognition capability of an intelligent robot auditory system. A human mouth-state recognition method based on image warping and sparse representation( SR) combined with homotopy is proposed.Using properly warped training mouth-state images as atoms of the overcomplete dictionary overcomes the impact of the diversity of the mouths' scales,shapes and positions so that further improvement of the robustness can be achieved and the requirement for a large number of training samples can be relieved. The homotopy method is employed to compute the expansion coefficients effectively,i. e.,for sparse coding. The orthogonal matching pursuit( OMP) is also tested and compared with the homototy method. Experimental results and comparisons with the state-of-the-art methods have proved the effectiveness of the proposed approach.

Polar Coded Iterative Multiuser Detection for Sparse Code Multiple Access System

Polar coded sparse code multiple access(SCMA) system is conceived in this paper. A simple but new iterative multiuser detection framework is proposed, which consists of a message passing algorithm(MPA) based multiuser detector and a soft-input soft-output(SISO) successive cancellation(SC) polar decoder. In particular, the SISO polar decoding process is realized by a specifically designed soft re-encoder, which is concatenated to the original SC decoder. This soft re-encoder is capable of reconstructing the soft information of the entire polar codeword based on previously detected log-likelihood ratios(LLRs) of information bits. Benefiting from the soft re-encoding algorithm, the resultant iterative detection strategy is able to obtain a salient coding gain. Our simulation results demonstrate that significant improvement in error performance is achieved by the proposed polar-coded SCMA in additive white Gaussian noise(AWGN) channels, where the performance of the conventional SISO belief propagation(BP) polar decoder aided SCMA, the turbo coded SCMA and the low-density parity-check(LDPC) coded SCMA are employed as benchmarks.