Mean Square Reconstruction Error Research Articles

Attention-based deep learning approach for CSI feedback under 5G TDL channel

In 5G communication systems, accurate channel state information (CSI) is indispensable for signal detection and regulation at the base station side. However, frequent CSI feedback from users leads to excessive system overhead. To tackle this challenge, this paper puts forward a novel deep learning framework - HCNet based on attention mechanism and autoencoder, aiming to efficiently compress and reconstruct the high-dimensional time-varying CSI matrices in an end-to-end approach. The proposed framework incorporates a self-attention module in the encoder to explicitly capture global dependencies within the CSI matrix. Meanwhile, the decoder adopts gated recurrent unit networks to fully exploit inter-feature correlations and redundancy. To evaluate the performance, simulations are conducted using datasets conforming to current 5G time-varying TDL channel models. Results demonstrate superior performance over existing deep learning based feedback networks. Specifically, the proposed framework can reduce the normalized mean square error of CSI reconstruction by 4 dB under various compression ratios which confirms the effectiveness of the attention-enhanced autoencoder structure for compressive CSI sensing and feedback in practical dynamic communication systems.

Deep learning based coherence holography reconstruction of 3D objects.

We propose a reconstruction method for coherence holography using deep neural networks. cGAN and U-NET models were developed to reconstruct 3D complex objects from recorded interferograms. Our proposed methods, dubbed deep coherence holography (DCH), predict the non-diffracted fields or the sub-objects included in the 3D object from the captured interferograms, yielding better reconstructed objects than the traditional analytical imaging methods in terms of accuracy, resolution, and time. The DCH needs one image per sub-object as opposed to N images for the traditional sin-fit algorithm, and hence the total reconstruction time is reduced by N×. Furthermore, with noisy interferograms the DCH amplitude mean square reconstruction error (MSE) is 5×104× and 104× and phase MSE is 102× and 3×103× better than Fourier fringe and sin-fit algorithms, respectively. The amplitude peak signal to noise ratio (PSNR) is 3× and 2× and phase PSNR is 5× and 3× better than Fourier fringe and sin-fit algorithms, respectively. The reconstruction resolution is the same as sin-fit but 2× better than the Fourier fringe analysis technique.

Early Gas Kick Warning Based on Temporal Autoencoder

The timing of the data is not taken into account by the majority of risk warnings today. However, identifying temporal fluctuations in data, which is a vital method for detecting risk, is neglected by the majority of intelligent gas kick warning models now in use. To accurately and early detect the gas kick risk, a temporal series gas kick detection method based on sequence-to-sequence depth autoencoder is proposed in this paper. A depth autoencoder model based on bidirectional long short-term memory (BiLSTM-AE) network is established to encode and compress input series, and decode and reconstruct the output series. Firstly, the BiLSTM-AE network is trained on normal drilling data based on unsupervised learning. Then, the model is tested by gas kick data, and the mean square error of reconstruction is calculated. The results show that the BiLSTM-AE model is more robust and generalized, and its accuracy is 95%. Experimental preliminary results show that this approach is capable of extracting bidirectional temporal information from risk sequence data, but long short-term memory (LSTM) and autoencoder models based on multilayer perceptron (MLP-AE) are unable to do so. By taking into account the temporal characteristics of the data, this study offers a strategy to integrate prior knowledge and significantly enhances the accuracy and stability of the model.

Single-Shot Three-Dimensional Measurement by Fringe Analysis Network

Fringe projection profilometry (FPP) has been broadly applied in three-dimensional (3D) measurements, but the existing multi-shot methods, which mostly utilize phase-shifting techniques, are heavily affected by the disturbance of vibration and cannot be used in dynamic scenes. In this work, a single-shot 3D measurement method using a deep neural network named the Fringe Analysis Network (FrANet) is proposed. The FrANet is composed of a phase retrieval subnetwork, phase unwrapping subnetwork, and refinement subnetwork. The combination of multiple subnetworks can help to recover long-range information that is missing for a single U-Net. A two-stage training strategy in which the FrANet network is pre-trained using fringe pattern reprojection and fine-tuned using ground truth phase maps is designed. Such a training strategy lowers the number of ground truth phase maps in the data set, saves time during data collection, and maintains the accuracy of supervised methods in real-world setups. Experimental studies were carried out on a setup FPP system. In the test set, the mean absolute error (MAE) of the refined absolute phase maps was 0.0114 rad, and the root mean square error (RMSE) of the 3D reconstruction results was 0.67 mm. The accuracy of the proposed method in dynamic scenes was evaluated by measuring moving standard spheres. The measurement of the sphere diameter maintained a high accuracy of 84 μm at a speed of 0.759 m/s. Two-stage training only requires 8800 fringe images in data acquisition, while supervised methods require 96,000 fringe images for the same number of iterations. Ablation studies verified the effectiveness of two training stages and three subnetworks. The proposed method achieved accurate single-shot 3D measurements comparable to those obtained using supervised methods and has a high data efficiency. This enables the accurate 3D shape measurement of moving or vibrating objects in industrial manufacturing and allows for further exploration of network architecture and training strategy with few training samples for single-shot 3D measurement.

Inference of interactions between players based on asynchronously updated evolutionary game data

The interactions between players of the prisoner’s dilemma game are inferred using observed game data. All participants play the game with their counterparts and gain corresponding rewards during each round of the game. The strategies of each player are updated asynchronously during the game. Two inference methods of the interactions between players are derived with naïve mean-field (nMF) approximation and maximum log-likelihood estimation (MLE), respectively. Two methods are tested numerically also for fully connected asymmetric Sherrington–Kirkpatrick models, varying the data length, asymmetric degree, payoff, and system noise (coupling strength). We find that the mean square error of reconstruction for the MLE method is inversely proportional to the data length and typically half (benefit from the extra information of update times) of that by nMF. Both methods are robust to the asymmetric degree but work better for large payoffs. Compared with MLE, nMF is more sensitive to the strength of couplings and prefers weak couplings.

Single-Cell Map of Childhood Acute Myeloid Leukaemia Using Variational Auto-Encoders

Acute myeloid leukaemia (AML) is a haematological cancer in the bone marrow, with accumulation and expansion of immature cells of the myeloid lineage. Standard treatment of childhood AML is chemotherapy, which does not achieve durable remission in many patients. Personalised medicine including immunotherapies against surface antigens can potentially target chemotherapy resistant cells and achieve long-term remission. Identifying AML blasts and suitable targets for AML therapy are hampered by the heterogeneity and complex clonal and phenotypic composition of the cancer, as well as its complex evolution as the disease progresses into relapse. Aberrant expression of surface antigens on AML blasts measured by flow cytometry is an established strategy to monitor measurable residual disease. Although the likelihood to find blasts is increased as more markers are included in a staining, manual interrogation of all possible combinations exceeding 10 markers becomes extremely difficult. We aim to identify malignant cells based on expression of 23 surface markers normally or aberrantly expressed during hematopoiesis using spectral flow cytometry and machine learning. The goal of this high-dimensional approach is to distinguish leukaemia cells from normal myeloid cells with high confidence, and to place the blasts along the normal myeloid developmental trajectory. We built a single-cell AML map from 20 paediatric AML patients enrolled in the Children's Oncology Group Phase III trial, AAML1031. All patients were treated with standard chemotherapy on Arm A and consented to provide tissue for research. Cryopreserved samples were obtained for three time-points: diagnosis, remission, and relapse. We assumed full remission samples to be healthy and used them to train variational auto-encoders with different hyper-parameters in a cross validated manner. These models subsequently learned to encode the expression of healthy cells in a reduced dimension and to reconstruct their expression from this latent space. We selected the top-10 models that best reconstruct the healthy cells and used it to encode and reconstruct cells from non-remission samples. Since the model works well for encoding and reconstructing healthy cells, we expect a good reconstruction of healthy cells in non-remission samples. For malignant cells we expect a poor reconstruction, as their expression pattern differs from healthy cells. Thus, we use the reconstruction error of cells from non-remission samples to classify them as healthy or malignant. We annotated some cells with clear aberrant expression as malignant and shuffled them with remission cells not used for model development. This resulted in multiple synthetic mixtures with known percentages of malignant cells (ranging from 10 to 90% blasts). Using these synthetic mixtures, we evaluated how well we can classify malignant cells based on their mean-squared reconstruction error. We can achieve an average area under the receiving operator curve of 0.9 over all synthetic mixtures (Fig. 1). The latent space of the variational auto-encoder captures the developmental trajectory of myeloid lineage bone marrow cells (Fig. 2), and we can use this to identify where among the developmental trajectory the leukaemia occurs. We aim to use the trajectory assignment to study the time evolution of the disease in terms of the distribution of malignant cells across the myeloid lineage as well as investigate differences between diagnosis and relapse. We expect that this work will reveal patterns of evolution from diagnosis to relapse that will inform the development of novel strategies to predict and prevent relapse. Figure 1View largeDownload PPTFigure 1View largeDownload PPT Close modal

Improved storage capacity for health care center using ant lion- ramp secret sharing scheme for data deduplication in cloud computing

The Cloud-based storage is able to store more information in gigabyte size in all formats such as text, image or video and it can access at any time with their login credentials. In such a system, reducing the duplication of data and increasing security is an important factor for efficient storage. In this work, the file level de-duplication process is applied on the Magnetic Resonance Imaging (MRI) brain image by reducing the shares of the image to retrieve an original image from the cloud. To reduce the storage problem in this an optimization-based RSSS is used. The objective of this investigation is to decrease the storage blow-up problem in Cloud storage and reduce the duplicate files in the Cloud storage of the health care centre. The proposed model comprises of two subsets: In the first set, the input image is divided into a number of shares using RSSS scheme. In the second set, the minimum share is determined by using the optimization process and it is encrypted and it is stored in the Cloud. Initially, the image is divided into number of shares for reconstructing using the ramp secret sharing scheme.Without these shares, the original image cannot be recovered. But storing all the shares result in high storage capacity. It is overcome with the help of Ant Lion optimization (ALO) to determine the minimum number of shares required for recovering the image. The ALO works to minimizing the Mean Square Error (MSE) of the image reconstruction to find the minimum shares. Then, the minimum shares are encrypted and converted into hash keys. Those hash keys are stored in the Cloud storage. The proposed ALO-RSSS is achieved its objective by reducing the shares to 2 as compared to the traditional method as well as the PSNR is 27% improved.

Open-circuit voltage curve reconstruction for degrading lithium-ion batteries utilizing discrete curve fragments from an online dataset

A complete open-circuit voltage (OCV) curve plotted against the state of charge (SOC) for degrading batteries, as a core indicator for battery state estimation and health diagnostics, is very important for whole-life management of battery. Unfortunately, such a curve is almost impossible to obtain in online battery management systems. Due to the uncontrollable OCV sample opportunities, only a series of isolated curve fragments consisting of scarce and discrete OCV-SOC points can be collected. Due to the unavoidable SOC estimation error, the relative position between fragments is uncertain. In order to reconstruct a complete OCV-SOC curve utilizing these isolated OCV curve fragments, an online and training-free curve reconstruction method is developed in this paper. Using this method, all isolated fragments from an online dataset are adaptively rearranged and uniquely located based on the positional interlock between different fragments, and fragments with abnormal state of health (SOH) or measurement errors are screened out. The test results demonstrated that the reconstruction method has a good stability, rapidity, and accuracy. The root mean square error of the curve reconstruction is well controlled within 5 mV throughout the battery's entire lifetime.

Spectrum Analysis for Multiband Signals With Nonuniform Sub-Nyquist Sampling in the Fractional Fourier Domain

This paper explores fractional spectrum analysis for periodically and nonuniformly sampled signals with finite disjoint bands in the fractional Fourier domain. Considering that spectrum aliasing occurs in sub-Nyquist sampling in the fractional Fourier domain, we study the conditions for reconstructing the fractional spectrum and devise relevant reconstruction methods. To obtain these goals, we investigate discrete-time fractional Fourier transform of the sampled signal that enables disjoint fractional frequency sub-intervals separated by aliasing boundaries. In order to implement perfect fractional spectrum reconstruction with reduced computations, we minimize the average sampling rate required by nonuniform sampling by means of properly choosing a sampling period. The theoretical lower bound on the optimized average sampling rate is much smaller than the lowest sampling rate required by uniform sampling under the same condition. Moreover, we derive the upper and lower bounds on the mean square error of fractional spectrum reconstruction with incorrect fractional spectrum modeling that assumes the signal as bandlimited to a large fractional frequency interval. Based on the derivations, we then obtain the optimal reconstruction parameters for spectrum reconstruction. Simulation results verify the effectiveness of our proposed methods.

Adversarial Attack for SAR Target Recognition Based on UNet-Generative Adversarial Network

Some recent articles have revealed that synthetic aperture radar automatic target recognition (SAR-ATR) models based on deep learning are vulnerable to the attacks of adversarial examples and cause security problems. The adversarial attack can make a deep convolutional neural network (CNN)-based SAR-ATR system output the intended wrong label predictions by adding small adversarial perturbations to the SAR images. The existing optimization-based adversarial attack methods generate adversarial examples by minimizing the mean-squared reconstruction error, causing smooth target edge and blurry weak scattering centers in SAR images. In this paper, we build a UNet-generative adversarial network (GAN) to refine the generation of the SAR-ATR models’ adversarial examples. The UNet learns the separable features of the targets and generates the adversarial examples of SAR images. The GAN makes the generated adversarial examples approximate to real SAR images (with sharp target edge and explicit weak scattering centers) and improves the generation efficiency. We carry out abundant experiments using the proposed adversarial attack algorithm to fool the SAR-ATR models based on several advanced CNNs, which are trained on the measured SAR images of the ground vehicle targets. The quantitative and qualitative results demonstrate the high-quality adversarial example generation and excellent attack effectiveness and efficiency improvement.

Incomplete PET projection data reconstruction method and simulation experiment

In positron emission tomography (PET) imaging, the whole body reconstruction is not required if the region of interest (ROI) is only a part of the object. This paper researched a local image reconstruction algorithm based on the PI-lines, and proposed the derivative-backprojection-Hilbert (DBH) algorithm which can use the incomplete PET projection data to achieve accurate reconstruction of ROI. We designed simulation experiments to evaluate the performance of the DBH algorithm with thorax model as the object of PET image reconstruction, and compared root mean square error (RMSE) of DBH reconstruction and RMSE of filtered backprojection (FBP) reconstruction from simulations data sets with and without noise. The result shows that DBH algorithm has advantages over traditional FBP algorithm, the RMSE decreases by 49.07% and 51.19% with the coincidence events number of 20 million and 40 million, respectively. Compared with traditional maximum-likelihood expectation-maximization (ML-EM), the local iteration algorithm which uses DBH reconstruction as the initial image produces a better reconstructed image at fewer iterations with the coincidence events number of 60 million. DBH algorithm is expected to be applied to fast two-dimensional local image reconstruction and optimize the local iterative reconstruction algorithm in clinical diagnosis.

Research on Sea Surface temperature Reconstruction from long-term MODIS data

Sea surface temperature (SST) is one of the important dynamic parameters to characterize the physical characteristics of seawater, and it is also an important basic auxiliary parameter for the quantitative observation of other ocean parameters. In view of the lack of remote sensing data mainly caused by cloud cover over the ocean, based on the long-term MODIS Aqua L3 8-day mean SST products from January 2003 to March 2015, the missing data in the East China Sea are reconstructed by Data Interpolating Empirical Orthogonal Function (DINEOF) method, and the reconstruction results are evaluated by error analysis before and after cross-validation data reconstruction. It shows that the image reconstructed by DINEOF method can reflect the temporal and spatial variation characteristics of sea surface temperature in the study area, and the root mean square error of reconstruction is 0.4272. DINEOF method can reconstruct large area missing data without any prior information and has high accuracy.

A Useful Sampling Representation for Mapping the Antenna Near-Field

A convenient sampling distribution and an optimal sampling interpolation algorithm are here presented for mapping the antenna near-field values on a planar surface. The mapping procedure is based on the theoretical background related to a non-redundant sampling representation of the electromagnetic field and uses an unconventional arrangement of the sampling points. Their position results from the standard plane-rectangular allocation by properly increasing the distance between near sampling points as their distance from the antenna grows. This permits to map the values in a given area by using the knowledge of a reduced number of samples and, therefore, the measurement time is conveniently shorted. Numerical simulations and antenna measurements in anechoic chamber have been executed to test the effectiveness of the mapping procedure, whose accuracy has been proved by means of maximum and mean-square reconstruction errors at given output points.

Reconstructing Sound Speed Profile From Remote Sensing Data: Nonlinear Inversion Based on Self-Organizing Map

By establishing a linear regression relationship between the projection coefficient of the empirical orthogonal function (EOF) of the sound speed profile (SSP) and remote sensing parameters of the sea surface, the single empirical orthogonal function regression (sEOF-r) method was used to reconstruct the underwater SSP from satellite remote sensing data. However, because the ocean is a complex dynamical system, the parameters of the surface and the subsurface did not conform to the linear regression model in strict sense. This paper proposes a self-organizing map (SOM)-based nonlinear inversion method that used satellite observations to obtain anomalies in data on the sea surface temperature and height, and combined them with the EOF coefficient from an Argo buoy to train and generate a map. The SSP was then reconstructed by obtaining the best matching neuron. The results of SSP reconstruction in the northern part of the South China Sea showed that the relationship between the parameters of the sea surface and the subsurface could be adequately expressed by the nonlinear neuronal topology. The SOM algorithm generated a smaller inversion error than linear inversion and had better robustness. It improved the average accuracy of reconstruction by 0.88 m/s and reduced the mean-squared reconstruction error to less than 1.19 m/s. It thus offered significant promise for acoustic applications.

Generative Adversarial Network for Desert Seismic Data Denoising

Seismic exploration is a kind of exploration method for oil and gas resources. However, the disturbance of numerous random noise will decrease the quality and signal-to-noise ratio (SNR) of real seismic records, which brings difficulties to the following works of processing and interpretation. The seismic records of desert region pose a particular problem because of the strong energy noise and the spectrum overlapping between effective signals and random noise. Recent research works demonstrate that a convolutional neural network (CNN) can increase the SNR of seismic records. The optimization of denoising methods based on CNN is principally driven by the loss functions that largely focus on minimizing the mean-squared reconstruction error between denoising records and theoretical pure records. The denoising results estimated by the CNN model are often lacking the perfection of the signal structure. Therefore, when processing seismic records with low SNR, the denoising results often have a lack of effective signal in some traces, which leads to the poor continuity of events. In order to solve this problem, we adopt the strategy of generative adversarial network (GAN) to construct a GAN for denoising. It is divided into two parts: the generator (the denoising network based on CNN) is used to remove noise, while the discriminator is used to guide the generator to restore the structure information of effective signals. The generator and discriminator enhance the performance of each other through adversarial training, and the generator after adversarial training can greatly recover events and suppress random noise in synthetic and real desert seismic data.

Enhancing ISAR Resolution by a Generative Adversarial Network

Recent studies have shown the superiority of neural networks on imaging equality and efficiency in inverse synthetic aperture radar (ISAR) resolution enhancement, but a central problem remains largely unsolved: all recent studies based on neural networks focused on minimizing the mean-squared reconstruction error (MSE), causing limited enhancing factors and inaccurate recovery of weak point scatters. In order to address this problem, a framework based on a generative adversarial network (GAN) using a combined loss composed of the absolute loss and the adversarial loss is proposed in this letter. The absolute loss ensures that reconstructed high-resolution ISAR images achieve higher enhancing factors and lower sidelobes. The adversarial loss pushes this framework to recover accurate amplitude and position of weak point scatters by a discriminator that is trained to differentiate reconstructed high-resolution ISAR images and real high-resolution ISAR images. Compared to some state-of-the-art methods, our GAN-based framework provides superior reconstruction with higher enhancing factors and more target details.

Online Data Dimensionality Reduction and Reconstruction Using Graph Filtering

Graphs have become a popular toolbox for capturing similarity relationships among data vectors in a variety of networks. Diffusion processes are used to model the data using the graph topology. A novel approach is put forth that exploits data similarity and diffusion models, in a graph, to improve upon the reconstruction mean-square error (MSE) performance of principal component analysis. The tasks of data dimensionality reduction and reconstruction are formulated as graph matrix filtering operations, that are utilized in a dimensionality reduction framework optimal in the MSE sense. The novel formulation is seeking MSE-optimal filter matrices that minimize the reconstruction MSE of all the graph data. Block coordinate descent techniques are employed in the graph spectral domain MSE cost to recursively determine the MSE-optimal dimensionality reducing and reconstruction filters. Online implementations are put forth to work with continuous streams of graph data, while almost sure convergence to a stationary point of the ensemble reconstruction MSE cost is established. Analysis of the reconstruction MSE reveals that the lowest MSE achieved by the novel approach is not larger than the standard PCA MSE, while there is a bound for the filter orders after which no more MSE reduction occurs. Extensive numerical tests using synthetic data, as well as real image datasets demonstrate the advantage of the novel graph-based framework over standard PCA and related methods.

Low-Complexity Vector Quantized Compressed Sensing via Deep Neural Networks

Sparse signals, encountered in many wireless and signal acquisition applications, can be acquired via compressed sensing (CS) to reduce computations and transmissions, crucial for resource-limited devices, e.g., wireless sensors. Since the information signals are often continuous-valued, digital communication of compressive measurements requires quantization. In such a quantized compressed sensing (QCS) context, we address remote acquisition of a sparse source through vector quantized noisy compressive measurements. We propose a deep encoder-decoder architecture, consisting of an encoder deep neural network (DNN), a quantizer, and a decoder DNN, that realizes low-complexity vector quantization aiming at minimizing the mean-square error of the signal reconstruction for a given quantization rate. We devise a supervised learning method using stochastic gradient descent and backpropagation to train the system blocks. Strategies to overcome the vanishing gradient problem are proposed. Simulation results show that the proposed non-iterative DNN-based QCS method achieves higher rate-distortion performance with lower algorithm complexity as compared to standard QCS methods, conducive to delay-sensitive applications with large-scale signals.

Analysis of the Reconstruction of Sparse Signals in the DCT Domain Applied to Audio Signals

Sparse signals can be reconstructed from a reduced set of signal samples using compressive sensing (CS) methods. The discrete cosine transform (DCT) can provide highly concentrated representations of audio signals. This property implies the DCT as a good sparsity domain for the audio signals. In this paper, the DCT is studied within the context of sparse audio signal processing using the CS theory and methods. The DCT coefficients of a sparse signal, calculated with a reduced set of available samples, can be modeled as random variables. It has been shown that the statistical properties of these variables are closely related to the unique reconstruction conditions. The main result of this paper is in an exact formula for the mean-square reconstruction error in the case of approximately sparse and nonsparse noisy signals reconstructed under the sparsity assumption. Based on the presented analysis, a simple and computationally efficient reconstruction algorithm is proposed. The presented theoretical concepts and the efficiency of the reconstruction algorithm are verified numerically, including examples with synthetic and recorded audio signals with unavailable or corrupted samples. Random disturbances and disturbances simulating clicks or inpainting in audio signals are considered. Statistical verification is done on a dataset with experimental signals. Results are compared with some classical and recent methods used in similar signal and disturbance scenarios.

S184. Sparse representation and classification of neural spikes using supervised dictionary learning

Neural spike sorting is curial for neuroscience applications. For example, spike sorting allows designing of efficient human-computer interfaces. Therefore, many investigations, aiming for accurate computer-aided algorithms for spike detection and classification, have emerged. However, many of the available algorithms require human intervention during the classification step. This study proposes decomposition and classification of spike waveforms using dictionary learning. In sparse decomposition, each spike is represented as a unique sparse combination of the dictionary basis vectors. This can lead to interesting sorting performance. Spiking activity was detected using amplitude thresholding and a 2.5-ms window around the peak value. Under the assumption that each neuron has a consistent waveform, the dictionary atoms were learned using training samples. This learned dictionary was used to get a sparse code representation for the test samples. These codes can be used to reconstruct the original spikes and therefore it provides data compression capability. Classification of the neural spikes was done using the sparse coefficients alongside with the reconstruction error. To ensure high discrimination, the dictionary was learned such that the resultant atoms have correspondence to class labels. In other words, the dictionary is structured of sub-dictionaries each corresponds to a different spiking pattern. Subsequently, an optimization problem was solved to make sure that (i) the sub-dictionaries accurately represent the training data, and (ii) the coding coefficients are sparse and minimize the reconstruction error. A testing sample was classified by sparsely coding it over each sub-dictionary. The reconstruction error for each sub-dictionary is computed. An error function is defined for each class as the summation of the reconstruction error and the difference between the sparse code and that class average. The testing sample was assigned to the class that gave the minimum error. The algorithm was tested on four simulated data sets, each contains spiking activities from three different neurons. Approximately 10% of each class data was used to construct the dictionary. The reconstruction mean-squared error for all the training samples was 3.49. This confirms the reconstruction power and accuracy of the learned dictionary. We measured the accuracy of our algorithm at different noise levels. The classification accuracy of the proposed method is 97% ± 5%. This accuracy outperforms the existing state-of-the-art algorithms. A dictionary learning based spike sorting algorithm has been developed. The results suggest that dictionary-based representation enables us to use the sparse representation of signals without a severe loss of data; besides that, this sparse representation can be also used for classification. This could also enable estimation of missing data points or clipped signals. The reconstruction error can be used to efficiently sort spikes.