Convolutional Sparse Coding Model Research Articles

Deep unfolding for multi-measurement vector convolutional sparse coding to denoise unobtrusive electrocardiography signals

The use of wearable technology for monitoring a person’s health status is becoming increasingly more popular. Unfortunately, this technology typically suffers from low-quality measurement data, making the acquisition of, for instance, the heart rate based on electrocardiography data from non-adhesive sensors challenging. Such sensors are prone to motion artifacts and hence the electrocardiogram (ECG) measurements require signal processing to enhance their quality and enable detection of the heart rate. Over the last years, considerable progress has been made in the use of deep neural networks for many signal processing challenges. Yet, for healthcare applications their success is limited because the required large datasets to train these networks are typically not available. In this paper we propose a method to embed prior knowledge about the measurement data and problem statement in the network architecture to make it more data efficient. Our proposed method aims to enhance the quality of ECG signals by describing ECG signals from the perspective of a multi-measurement vector convolutional sparse coding model and use a deep unfolded neural network architecture to learn the model parameters. The sparse coding problem was solved using the Alternation Direction Method of Multipliers. Our method was evaluated by denoising ECG signals, that were corrupted by adding noise to clean ECG signals, and subsequently detecting the heart beats from the denoised data and compare these to the heartbeats and derived heartrate variability features detected in the clean ECG signals. This evaluation demonstrated an improved in the signal-to-noise ratio (SNR) improvement ranging from 17 to 27 dB and an improvement in heart rate detection (i.e. F1 score) ranging between 0 and 50%, where the range depends on the SNR of the input signals. The performance of the method was compared to that of a denoising encoder-decoder neural network and a wavelet-based denoising method, showing equivalent and better performance, respectively.

Damage localization with Lamb waves using dense convolutional sparse coding network

Composite materials are progressively employed in many safety-critical structural applications due to their superior properties. Structural health monitoring techniques based on Lamb waves have been utilized to assess the damages of composite structures. Recently, deep learning algorithms are adopted for damage detection and localization. Identifying valid damage-related features through neural networks is a crucial step in the analysis process. However, most implemented deep learning architectures are still lacking physical interpretability to some extent. In this paper, a dense convolutional sparse coding network (DCSCNet) is presented for Lamb wave-based damage localization in composite structures, providing a possibility to interpret current networks. In DCSCNet, narrowband Hanning windowed toneburst signals are utilized as kernels of the first convolutional layer to learn more meaningful features. Dense connection is theoretically demonstrated in the scope of DCSCNet, which gathers multiple feature maps directly to develop the potential of the network through feature reuse. The multi-layer iterative soft thresholding algorithm with the dense connection is then employed for solving the multi-layer convolutional sparse coding model. Moreover, effective Squeeze-Excitation is introduced as the channel attention module to boost the representational capability of the network. The experimental results demonstrate the high-performance and interpretable characteristics of the proposed DCSCNet, verifying its feasibility and effectiveness in Lamb wave-based damage localization of composite structures.

Deep High-Order Tensor Convolutional Sparse Coding for Hyperspectral Image Classification

Most hyperspectral image (HSI) data exist in the form of tensor; the tensor representation preserves the potential spatial–spectral structure information compared with the vector representation, which can help improve the classification performance of HSI. In this article, a deep high-order tensor convolutional sparse coding (CSC) model is proposed, which can be used to train deep high-order filters. Based on the deep high-order tensor CSC model, a deep feature extraction network (DHTCSCNet) is constructed, which is used for feature extraction of HSIs. By combining the spectral–spatial feature and the features extracted by the proposed DHTCSCNet at each layer, a combined feature that incorporates shallow, deep, spectral, and spatial features can be obtained. Then, the graph-based learning (GSL) methods are used to classify the combined feature. Experimental results show that the DHTCSCNet can obtain better classification performance compared with other HSI classification methods.

Revisiting Convolutional Sparse Coding for Image Denoising: From a Multi-Scale Perspective

Recently, convolutional sparse coding (CSC) has shown great success in many image processing tasks, such as image super-resolution and image separation. However, it performs poorly in image denoising task. In this letter, we provide a new insight for CSC denoising by revisiting the CSC from a multi-scale perspective. We propose a multi-scale CSC model for image denoising. By unrolling the multi-scale solution into a learnable network, we obtain an interpretable lightweight multiscale network, namely MCSCNet. Experimental results show that the proposed MCSCNet significantly advances the denoising performance, with an average PSNR improvement of 0.32 dB over the state-of-the-art (SOTA) CSC based method. In addition, our MCSCNet is on par with many SOTA deep learning based methods, with less network parameters and lower FLOPs. The ablation study also validates the effectiveness of the multi-scale CSC mechanism.

Denoising convolutional neural network inspired via multi-layer convolutional sparse coding

Sparse prior to image denoising is a classical research field with a long history in computer vision. We propose an end-to-end supervised neural network, named DnMLCSC-net, which is inspired via multi-layer convolutional sparse coding model embedded with symbiotic analysis–synthesis priors for natural image denoising. Unfolding a multi-layer, learned iterative soft thresholding algorithm (ML-LISTA) and developing into a convolutional recurrent neural network, all parameters in the model are updated adaptively to minimize mixed loss via gradient descent using backpropagation. In addition, a combined ReLU function is taken as the activation function. Inconsistent dilated convolution and batch normalization were empirically introduced into the encoding layers corresponding to the first iteration of ML-LISTA. Experimental results show that our network achieves a competitive denoising effect in comparison with several state-of-the-art denoising methods.

Two Layer Tensor Form Convolutional Sparse Coding for Stereo Matching

Stereo matching is an important research topic in the field of computer vision. It recovers depth information from a pair of color images. Unfortunately, converting multi-dimensional (more than two-dimensional) data into two-dimensional data, such formulations ignore the spatial structure of multi-dimensional images/data. Tensors can be used to describe high-dimensional data structure, which can retain the hidden structure of data, but cannot obtain the deep features that helps to improve the performance of the algorithm. Therefore, it is very important to establish a deep tensor model. In this paper, we propose a two layer tensor form convolutional sparse coding model, which can automatically learn the deep convolutional kernel. Based on the learned two layer convolutional kernels, a two-layer dictionary learning model is established. Then, a new weighted matching cost method is constructed, which combines shallow and deep features. The experimental results on the Middlebury benchmark v2 and Middlebury benchmark v3 show that the proposed two layer tensor convolutional sparse coding is effective for stereo matching.

Convergence of Slice-Based Block Coordinate Descent Algorithm for Convolutional Sparse Coding

Convolutional sparse coding (CSC) models are becoming increasingly popular in the signal and image processing communities in recent years. Several research studies have addressed the basis pursuit (BP) problem of the CSC model, including the recently proposed local block coordinate descent (LoBCoD) algorithm. This algorithm adopts slice-based local processing ideas and splits the global sparse vector into local vector needles that are locally computed in the original domain to obtain the encoding. However, a convergence theorem for the LoBCoD algorithm has not been given previously. This paper presents a convergence theorem for the LoBCoD algorithm which proves that the LoBCoD algorithm will converge to its global optimum at a rate of O1/k. A slice-based multilayer local block coordinate descent (ML-LoBCoD) algorithm is proposed which is motivated by the multilayer basis pursuit (ML-BP) problem and the LoBCoD algorithm. We prove that the ML-LoBCoD algorithm is guaranteed to converge to the optimal solution at a rate O1/k. Preliminary numerical experiments demonstrate the better performance of the proposed ML-LoBCoD algorithm compared to the LoBCoD algorithm for the BP problem, and the loss function value is also lower for ML-LoBCoD than LoBCoD.

Retinex Based Image Enhancement via General Dictionary Convolutional Sparse Coding

Retinex theory represents the human visual system by showing the relative reflectance of an object under various illumination conditions. A feature of this human visual system is color constancy, and the Retinex theory is designed in consideration of this feature. The Retinex algorithms have been popularly used to effectively decompose the illumination and reflectance of an object. The main aim of this paper is to study image enhancement using convolution sparse coding and sparse representations of the reflectance component in the Retinex model over a learned dictionary. To realize this, we use the convolutional sparse coding model to represent the reflectance component in detail. In addition, we propose that the reflectance component can be reconstructed using a trained general dictionary by using convolutional sparse coding from a large dataset. We use singular value decomposition in limited memory to construct a best reflectance dictionary. This allows the reflectance component to provide improved visual quality over conventional methods, as shown in the experimental results. Consequently, we can reduce the difference in perception between humans and machines through the proposed Retinex-based image enhancement.

Variations on the Convolutional Sparse Coding Model

Over the past decade, the celebrated sparse representation model has achieved impressive results in various signal and image processing tasks. A convolutional version of this model, termed convolutional sparse coding (CSC), has been recently reintroduced and extensively studied. CSC brings a natural remedy to the limitation of typical sparse enforcing approaches of handling global and high-dimensional signals by local, patch-based, processing. While the classic field of sparse representations has been able to cater for the diverse challenges of different signal processing tasks by considering a wide range of problem formulations, almost all available algorithms that deploy the CSC model consider the same $\ell _1 - \ell _2$ problem form. As we argue in this paper, this CSC pursuit formulation is also too restrictive as it fails to explicitly exploit some local characteristics of the signal. This work expands the range of formulations for the CSC model by proposing two convex alternatives that merge global norms with local penalties and constraints. The main contribution of this work is the derivation of efficient and provably converging algorithms to solve these new sparse coding formulations.

Generalized Convolutional Sparse Coding with Unknown Noise.

Convolutional sparse coding (CSC) can learn representative shift-invariant patterns from multiple kinds of data. However, existing CSC methods can only model noises from Gaussian distribution, which is restrictive and unrealistic. In this paper, we propose a generalized CSC model capable of dealing with complicated unknown noise. The noise is now modeled by Gaussian mixture model, which can approximate any continuous probability density function. We use the expectation-maximization algorithm to solve the problem and design an efficient method for the weighted CSC problem in maximization step. The crux is to speed up the convolution in the frequency domain while keeping the other computations involving weight matrix in the spatial domain. Besides, we simultaneously update the dictionary and codes by nonconvex accelerated proximal gradient algorithm without bringing in extra alternating loops. The resultant method, called generalized convolutional sparse coding (GCSC), obtains the same space complexity and a smaller running time compared with existing CSC methods. Extensive experiments on synthetic and real-world noisy data sets validate that GCSC can model noise effectively and obtain high-quality filters and representations.

Image super-resolution algorithm's research using convolutional sparse coding model

According to image super-resolution reconstruction for convolutional sparse coding model, a novel super-resolution reconstruction algorithm named four-channel convolutional sparse coding model has proposed via improving convolutional sparse coding method. In the proposed method, the testing image was put in four-channel via rotating image ninety degrees in four times. Then, the high-frequent part and low-frequent part were reconstructed by means of convolutional sparse coding method and cubic interpolation method respectively. Finally, the reconstructed high-resolution image has obtained via the process of weighting on four images. The proposed method not only overcomes the problem of consistency for the overlapping patches, but also improves the detail contour for the reconstructed image and enhances its stability. The experimental results have shown that the proposed method has better PSNR, SSIM, and noise immunity than some classical super-resolution reconstruction methods.

Image super-resolution algorithm's research using convolutional sparse coding model

According to image super-resolution reconstruction for convolutional sparse coding model, a novel super-resolution reconstruction algorithm named four-channel convolutional sparse coding model has proposed via improving convolutional sparse coding method. In the proposed method, the testing image was put in four-channel via rotating image ninety degrees in four times. Then, the high-frequent part and low-frequent part were reconstructed by means of convolutional sparse coding method and cubic interpolation method respectively. Finally, the reconstructed high-resolution image has obtained via the process of weighting on four images. The proposed method not only overcomes the problem of consistency for the overlapping patches, but also improves the detail contour for the reconstructed image and enhances its stability. The experimental results have shown that the proposed method has better PSNR, SSIM, and noise immunity than some classical super-resolution reconstruction methods.

Convolutional Sparse Coding Using Wavelets for Single Image Super-Resolution

In this paper, we propose the convolutional sparse coding based model in the wavelet domain for the task of single image super-resolution (SISR). The conventional sparse coding based approaches work on overlapping image patches and use the dictionary atoms to sparse code an image patch. Further, at the final stage, an overlap-add mechanism is used to get the final high-resolution image estimate. However, these algorithms fail to take into account the consistency present in the overlapping patches which limits their performance. We propose the use of wavelet integrated convolutional sparse coding approach where instead of dictionary atoms we utilize the convolution summations between the learned filters and their mappings for sparse representation based SISR. The use of wavelets is proposed owing to their unique directional and compact features. A pair of filters are learned along with a mapping function for each wavelet sub-band to exploit the consistency among patches. The proposed wavelet integrated convolutional sparse coding model helps capture useful contextual information. The proposed model is evaluated on publicly available datasets for different scale-up parameters. To show the efficacy of the proposed model we compare it with recent state-of-the-art algorithms. The visual results along with the quantitative ones indicate that the proposed model performs well for the tasks of super-resolution.

Convolutional Sparse Autoencoders for Image Classification.

Convolutional sparse coding (CSC) can model local connections between image content and reduce the code redundancy when compared with patch-based sparse coding. However, CSC needs a complicated optimization procedure to infer the codes (i.e., feature maps). In this brief, we proposed a convolutional sparse auto-encoder (CSAE), which leverages the structure of the convolutional AE and incorporates the max-pooling to heuristically sparsify the feature maps for feature learning. Together with competition over feature channels, this simple sparsifying strategy makes the stochastic gradient descent algorithm work efficiently for the CSAE training; thus, no complicated optimization procedure is involved. We employed the features learned in the CSAE to initialize convolutional neural networks for classification and achieved competitive results on benchmark data sets. In addition, by building connections between the CSAE and CSC, we proposed a strategy to construct local descriptors from the CSAE for classification. Experiments on Caltech-101 and Caltech-256 clearly demonstrated the effectiveness of the proposed method and verified the CSAE as a CSC model has the ability to explore connections between neighboring image content for classification tasks.