Convolutional Dictionary Learning Research Articles

Deep M2CDL: Deep Multi-Scale Multi-Modal Convolutional Dictionary Learning Network.

For multi-modal image processing, network interpretability is essential due to the complicated dependency across modalities. Recently, a promising research direction for interpretable network is to incorporate dictionary learning into deep learning through unfolding strategy. However, the existing multi-modal dictionary learning models are both single-layer and single-scale, which restricts the representation ability. In this paper, we first introduce a multi-scale multi-modal convolutional dictionary learning ( M2CDL) model, which is performed in a multi-layer strategy, to associate different image modalities in a coarse-to-fine manner. Then, we propose a unified framework namely Deep M2CDL derived from the M2CDL model for both multi-modal image restoration (MIR) and multi-modal image fusion (MIF) tasks. The network architecture of Deep M2CDL fully matches the optimization steps of the M2CDL model, which makes each network module with good interpretability. Different from handcrafted priors, both the dictionary and sparse feature priors are learned through the network. The performance of the proposed Deep M2CDL is evaluated on a wide variety of MIR and MIF tasks, which shows the superiority of it over many state-of-the-art methods both quantitatively and qualitatively. In addition, we also visualize the multi-modal sparse features and dictionary filters learned from the network, which demonstrates the good interpretability of the Deep M2CDL network.

Deep Convolutional Dictionary Learning Denoising Method Based on Distributed Image Patches

To address susceptibility to noise interference in Micro-LED displays, a deep convolutional dictionary learning denoising method based on distributed image patches is proposed in this paper. In the preprocessing stage, the entire image is partitioned into locally consistent image patches, and a dictionary is learned based on the non-local self-similar sparse representation of distributed image patches. Subsequently, a convolutional dictionary learning method is employed for global self-similarity matching. Local constraints and global constraints are combined for effective denoising, and the final denoising optimization algorithm is obtained based on the confidence-weighted fusion technique. The experimental results demonstrate that compared with traditional denoising methods, the proposed denoising method effectively restores fine-edge details and contour information in images. Moreover, it exhibits superior performance in terms of PSNR and SSIM. Particularly noteworthy is its performance on the grayscale dataset Set12. When evaluated with Gaussian noise σ=50, it outperforms DCDicL by 3.87 dB in the PSNR and 0.0012 in SSIM.

Automatic calculation of step size and inertia parameter for convolutional dictionary learning

The convergent methods available for convolutional dictionary learning (CDL) are the proximal gradient method (PGM) and the inertial proximal gradient method (IPGM). However, it is not trivial and heuristic for IPGM to set the step size and inertia parameter, and IPGM produces local minima and oscillating solutions. To address these issues, in this paper, we introduce a dry friction, which has an oscillation-alleviating property. Specifically, the proposed IPGM with dry friction (IPGM-DF) generates the composite proximal mappings, whose construction and optimization solver are two challenges. An auxiliary function is designed to construct the composite proximal mappings, whose optimization problem is solved by the alternating direction method of multipliers. Fortunately, IPGM-DF obtains the formulas of the step size and inertia parameter. The finite convergence of IPGM-DF is proved. Experimental results of image reconstruction, separation, and fusion demonstrate the superiority of IPGM-DF over IPGM and the state-of-the-art methods. For image reconstruction, the objective function value of IPGM-DF is reduced by about 38.708% than that of IPGM. Throughout alleviating oscillations, IPGM-DF obtains a much lower value of the objective function than IPGM, which indicates that IPGM-DF jumps out of the local minima of IPGM. In addition, the average PSNR of IPGM-DF is about 3.5 dB larger than that of IPGM and the state-of-the-art methods. The code is available.

Deep convolutional dictionary learning network for sparse view CT reconstruction with a group sparse prior

Purpose Numerous techniques based on deep learning have been utilized in sparse view computed tomography (CT) imaging. Nevertheless, the majority of techniques are instinctively constructed utilizing state-of-the-art opaque convolutional neural networks (CNNs) and lack interpretability. Moreover, CNNs tend to focus on local receptive fields and neglect nonlocal self-similarity prior information. Obtaining diagnostically valuable images from sparsely sampled projections is a challenging and ill-posed task.Method To address this issue, we propose a unique and understandable model named DCDL-GS for sparse view CT imaging. This model relies on a network comprised of convolutional dictionary learning and a nonlocal group sparse prior. To enhance the quality of image reconstruction, we utilize a neural network in conjunction with a statistical iterative reconstruction framework and perform a set number of iterations. Inspired by group sparsity priors, we adopt a novel group thresholding operation to improve the feature representation and constraint ability and obtain a theoretical interpretation. Furthermore, our DCDL-GS model incorporates filtered backprojection (FBP) reconstruction, fast sliding window nonlocal self-similarity operations, and a lightweight and interpretable convolutional dictionary learning network to enhance the applicability of the model.Results The efficiency of our proposed DCDL-GS model in preserving edges and recovering features is demonstrated by the visual results obtained on the LDCT-P and UIH datasets. Compared to the results of the most advanced techniques, the quantitative results are enhanced, with increases of 0.6-0.8 dB for the peak signal-to-noise ratio (PSNR), 0.005-0.01 for the structural similarity index measure (SSIM), and 1-1.3 for the regulated Fréchet inception distance (rFID) on the test dataset. The quantitative results also show the effectiveness of our proposed deep convolution iterative reconstruction module and nonlocal group sparse prior.Conclusion In this paper, we create a consolidated and enhanced mathematical model by integrating projection data and prior knowledge of images into a deep iterative model. The model is more practical and interpretable than existing approaches. The results from the experiment show that the proposed model performs well in comparison to the others.

Multi-layer convolutional dictionary learning network for signal denoising and its application to explainable rolling bearing fault diagnosis

As a vital mechanical sub-component, the health monitoring of rolling bearings is important. Vibration signal analysis is a commonly used approach for fault diagnosis of bearings. Nevertheless, the collected vibration signals cannot avoid interference from noises which has a negative influence on fault diagnosis. Thus, denoising needs to be utilized as an essential step of vibration signal processing. Traditional denoising methods need expert knowledge to select hyperparameters. And data-driven methods based on deep learning lack interpretability and a clear justification for the design of architecture in a “black-box” deep neural network. An approach to systematically design neural networks is by unrolling algorithms, such as learned iterative soft-thresholding (LISTA). In this paper, the multi-layer convolutional LISTA (ML-CLISTA) algorithm is derived by embedding a designed multi-layer sparse coder to the convolutional extension of LISTA. Then the multi-layer convolutional dictionary learning (ML-CDL) network for mechanical vibration signal denoising is proposed by unrolling ML-CLISTA. By combining ML-CDL network with a classifier, the proposed denoising method is applied to the explainable rolling bearing fault diagnosis. The experiments on two bearing datasets show the superiority of the ML-CDL network over other typical denoising methods.

Adaptive convolutional dictionary learning for denoising seismocardiogram to enhance the classification performance of aortic stenosis

Background:Aortic stenosis (AS) is the most prevalent type of valvular heart disease (VHD), traditionally diagnosed using echocardiogram or phonocardiogram. Seismocardiogram (SCG), an emerging wearable cardiac monitoring modality, is proved to be feasible in non-invasive and cost-effective AS diagnosis. However, SCG waveforms acquired from patients with heart diseases are typically weak, making them more susceptible to noise contamination. While most related researches focus on motion artifacts, sensor noise and quantization noise have been mostly overlooked. These noises pose additional challenges for extracting features from the SCG, especially impeding accurate AS classification. Method:To address this challenge, we present a convolutional dictionary learning-based method. Based on sparse modeling of SCG, the proposed method generates a personalized adaptive-size dictionary from noisy measurements. The dictionary is used for sparse coding of the noisy SCG into a transform domain. Reconstruction from the domain removes the noise while preserving the individual waveform pattern of SCG. Results:Using two self-collected SCG datasets, we established optimal dictionary learning parameters and validated the denoising performance. Subsequently, the proposed method denoised SCG from 50 subjects (25 AS and 25 non-AS). Leave-one-subject-out cross-validation (LOOCV) was applied to 5 machine learning classifiers. Among the classifiers, a bi-layer neural network achieved a moderate accuracy of 90.2%, with an improvement of 13.8% from the denoising. Conclusions:The proposed sparsity-based denoising technique effectively removes stochastic sensor noise and quantization noise from SCG, consequently improving AS classification performance. This approach shows promise for overcoming instrumentation constraints of SCG-based diagnosis.

Enhancement based convolutional dictionary network with adaptive window for low-dose CT denoising.

Recently, one promising approach to suppress noise/artifacts in low-dose CT (LDCT) images is the CNN-based approach, which learns the mapping function from LDCT to normal-dose CT (NDCT). However, most CNN-based methods are purely data-driven, thus lacking sufficient interpretability and often losing details. To solve this problem, we propose a deep convolutional dictionary learning method for LDCT denoising, in which a novel convolutional dictionary learning model with adaptive window (CDL-AW) is designed, and a corresponding enhancement-based convolutional dictionary learning network (called ECDAW-Net) is constructed to unfold the CDL-AW model iteratively using the proximal gradient descent technique. In detail, the adaptive window-constrained convolutional dictionary atom is proposed to alleviate spectrum leakage caused by data truncation during convolution. Furthermore, in the ECDAW-Net, a multi-scale edge extraction module that consists of LoG and Sobel convolution layers is proposed in the unfolding iteration, to supplement lost textures and details. Additionally, to further improve the detail retention ability, the ECDAW-Net is trained by the compound loss function of the pixel-level MSE loss and the proposed patch-level loss, which can assist to retain richer structural information. Applying ECDAW-Net to the Mayo dataset, we obtained the highest peak signal-to-noise ratio (33.94) and sub-optimal structural similarity (0.92). Compared with some state-of-art methods, the interpretable ECDAW-Net performs well in suppressing noise/artifacts and preserving textures of tissue.

Multi-modal deep convolutional dictionary learning for image denoising

Leveraging the capabilities of traditional dictionary learning (DicL) and drawing upon the success of deep neural networks (DNNs), the recently proposed framework of deep convolutional dictionary learning (DCDicL) has exhibited remarkable behaviours in image denoising. Note that, the application of the DCDicL method is confined to single modality scenarios, whereas the images in practice often originate from diverse modalities. In this paper, to broaden the application scope of the DCDicL method, we design a multi-modal version of it, dubbed MMDCDicL. Specifically, within the mathematical model of MMDCDicL, we adopt an analytical approach to tackle the sub-problem linked to the guidance modality, harnessing its inherent reliability. Meanwhile, like in DCDicL, we utilize a network-based learning approach for the noisy modality to extract trustworthy information from the data. Based on the solution, we establish an interpretable network structure for MMDCDicL. Additionally, wherein, we design a multi-kernel channel attention block (MKCAB) in the structure to efficiently integrate the information from diverse modalities. Experimental results suggest that MMDCDicL can reconstruct higher-quality outcomes both quantitatively and perceptually. Code is available at http://www.diplab.net/lunwen/mmdcdicl.htm.

Convolutional dictionary learning based on filter bank theory : Convolutional network construction using structural constraints

Convolutional dictionary learning based on filter bank theory : Convolutional network construction using structural constraints

Deep Dynamic Memory Augmented Attentional Dictionary Learning for Image Denoising

Motivated by the advance of deep learning methods, deep unfolding methods such as deep convolutional dictionary learning have achieved great success in image denoising tasks. The main advantages are inheriting both the merits of deep learning (strong learning capacity) and traditional machine learning (powerful interpretable capacity). We observe that the update of dictionaries and coefficients is highly correlated with the previous iterative stage information for deep unfolding-based methods. However, most existing deep convolutional dictionary learning methods deal with each iteration step individually, ignoring the inner-memory within the stage and cross-memory across the stages. To alleviate these issues, we propose a dynamic inner-cross memory augmented attentional dictionary learning (M2ADL) network with attention guided residual connection module, which utilizes the previous important stage features such that better uncovering the inner-cross information. Specifically, the proposed inner-cross memory fully utilizes the previous stage’s hidden and last-layer information to learn the dictionary. In addition, we develop a dual attention-guided residual connection module to well exploit the deep feature learning ability to capture the spatial-spectral attention across the deep tensor-based features. Considerable experiments on both synthetic and real image datasets demonstrate the superiority of the proposed method over other state-of-the-art methods.

Iterative shrinkage-thresholding algorithm with inertia and dry friction for convolutional dictionary learning

The iterative shrinkage-thresholding algorithm (ISTA) is often used to address the convolutional dictionary learning problem. However, the ISTA algorithm is easy to fall into the local minimum, and some atoms in the convolution dictionary change little when updated. Therefore, in this paper, we propose an improved ISTA algorithm, iterative shrinkage-thresholding algorithm with inertia and dry friction (ISTA-IDF). An inertia is introduced to avoid falling into the local minimum but generating an oscillatory behavior since the values of the objective function is not monotonic decreasing, which can be alleviated by dry friction. From the perspective of dynamics, ISTA can be seen as an iteration algorithm deduced by a forward-backward Euler discretization of a first-order dynamic system, and ISTA-IDF can be regarded as the forward-backward Euler discretization of a second-order heavy-ball system with dry friction (HBDF). So using the dynamics theory, we establish the linear and finite convergence property of ISTA-IDF. The experimental results on image reconstruction and denoising tasks demonstrate the superior performance of the proposed ISTA-IDF compared with ISTA and FISTA.

Improved deep convolutional dictionary learning with no noise parameter for low-dose CT image processing.

Low-Dose computed tomography (LDCT) reduces radiation damage to patients, however, the reconstructed images contain severe noise, which affects doctors' diagnosis of the disease. The convolutional dictionary learning has the advantage of the shift-invariant property. The deep convolutional dictionary learning algorithm (DCDicL) combines deep learning and convolutional dictionary learning, which has great suppression effects on Gaussian noise. However, applying DCDicL to LDCT images cannot get satisfactory results. To address this challenge, this study proposes and tests an improved deep convolutional dictionary learning algorithm for LDCT image processing and denoising. First, we use a modified DCDicL algorithm to improve the input network and make it do not need to input noise intensity parameter. Second, we use DenseNet121 to replace the shallow convolutional network to learn the prior on the convolutional dictionary, which can obtain more accurate convolutional dictionary. Last, in the loss function, we add MSSIM to enhance the detail retention ability of the model. The experimental results on the Mayo dataset show that the proposed model obtained an average value of 35.2975 dB in PSNR, which is 0.2954 -1.0573 dB higher than the mainstream LDCT algorithm, indicating the excellent denoising performance. The study demonstrates that the proposed new algorithm can effectively improve the quality of LDCT images acquired in the clinical practice.

DeepCDL-PR: Deep unfolded convolutional dictionary learning with weighted ℓ1-norm for phase retrieval

Phase retrieval (PR) aims to recover the image of interest from the recorded phaseless measurement. Traditional PR algorithms that use hand-crafted priors suffer from low-quality reconstructions at low signal to noise ratios (SNRs). Recent efforts overcome this limitation by using deep priors, but existing algorithms ignore structural priors. To remedy this issue, we propose a deep unfolded convolutional dictionary learning with the weighted ℓ1-norm, termed DeepCDL, for PR. By doing so, deep priors and structural priors can be utilized. Concretely, we exploit the weighted ℓ1-norm to formulate a convolutional dictionary learning (CDL)-based minimization problem, and then unfold the corresponding iterative algorithm into a deep network architecture. Moreover, we design a data-driven weight generator to generate crucial weights in the weighted ℓ1-norm from representation coefficients. For the PR task, we first utilize structural priors to formulate a PR minimization problem, and then propose an iterative algorithm to deal with the formulated problem. The proposed DeepCDL method is utilized to solve the convolutional dictionary learning subproblem with the weighted ℓ1-norm, and an inertial epigraph method employing the inertial technique is proposed to tackle the image updating subproblem. Furthermore, the proposed PR iterative algorithm is unfolded into a feed-forward network dubbed as DeepCDL-PR, where DeepCDL serves as a prior module and the unfolded inertial epigraph method acts as an image updating module. Experiments demonstrate that DeepCDL-PR can recover higher-quality images at various noise levels, compared with previous PR algorithms.

Born Iterative Method Based on Convolutional Dictionary Learning for Inverse Scattering Problems

In this letter, a Born iterative method based on convolutional dictionary learning is proposed to solve inverse scattering problems. The method is inspired by compressed sensing, which indicates that the contrast can be represented by nonzero expansion coefficients with respect to expansion bases. The inverse scattering problem is changed from solving the contrast to solving the nonzero expansion coefficients under the expansion bases. In our method, the bases are obtained by convolutional dictionary learning from a set of training data, which learn and characterize the intrinsic laws of the local contrast. The performance of the proposed method is verified using simulated data. We compare it with the Born iterative method and the contrast source inversion method, and the results show that the proposed method can get better results.

Image Denoising for Low-Dose CT via Convolutional Dictionary Learning and Neural Network

Removing noise and artifacts from low-dose computed tomography (LDCT) is a challenging task, and most existing image-based algorithms tend to blur the results. To improve the resolution of denoising results, we combine convolutional dictionary learning and convolutional neural network (CNN), and propose a transfer learning densely connected convolutional dictionary learning (TLD-CDL) framework. In detail, we first introduce the dense connections and multi-scale Inception structure to the network, and train the pre-model on the natural image dataset, then fit the model to the post-processing of LDCT images in the way of transfer learning. In addition, considering that a single pixel-level loss is difficult to achieve satisfactory results both in the index and visual perception, we use the compound loss function of L1 loss and SSIM loss to guide the training. The experimental result shows that TLD-CDL has a good balance between noise reduction and the preservation of details, and acquires inspiring effectiveness in terms of qualitative and quantitative perspective.

Parametric Convolutional Dictionary Learning and its Applications to Seismic Data Processing

Parametric Convolutional Dictionary Learning and its Applications to Seismic Data Processing

Using convolutional dictionary learning to detect task-related neuromagnetic transients and ageing trends in a large open-access dataset

Human neuromagnetic activity is characterised by a complex combination of transient bursts with varying spatial and temporal characteristics. The characteristics of these transient bursts change during task performance and normal ageing in ways that can inform about underlying cortical sources. Many methods have been proposed to detect transient bursts, with the most successful ones being those that employ multi-channel, data-driven approaches to minimize bias in the detection procedure. There has been little research, however, into the application of these data-driven methods to large datasets for group-level analyses. In the current work, we apply a data-driven convolutional dictionary learning (CDL) approach to detect neuromagnetic transient bursts in a large group of healthy participants from the Cam-CAN dataset. CDL was used to extract repeating spatiotemporal motifs in 538 participants between the ages of 18–88 during a sensorimotor task. Motifs were then clustered across participants based on similarity, and relevant task-related clusters were analysed for age-related trends in their spatiotemporal characteristics. Seven task-related motifs resembling known transient burst types were identified through this analysis, including beta, mu, and alpha type bursts. All burst types showed positive trends in their activation levels with age that could be explained by increasing burst rate with age. This work validated the data-driven CDL approach for transient burst detection on a large dataset and identified robust information about the complex characteristics of human brain signals and how they change with age.

Proximal gradient nonconvex optimization algorithm for the slice-based [formula omitted]-constrained convolutional dictionary learning

Convolutional dictionary learning (CDL) aims to learn a structured local convolutional dictionary and the sparse coefficient maps from the signals of various of interest, achieving better results than traditional patch-based dictionary learning in signal processing applications. Currently, most CDL methods are used to solve the ℓ1-constrained convex CDL problem using the patch-based, Fourier-based, or slice-based representation, which may lead to non-sparse coefficient maps, thus degrading the performance of applications. The slice-based representation via local processing has shown more beneficial than the Fourier-based representation for convex CDL problems. It can allow a different number of nonzeros for each spatial location of the signal according to the local complexity. However, it has not been used for the nonconvex CDL problem. In this paper, a slice-based ℓ0-constrained nonconvex CDL problem is proposed. It is the slice-based counterpart of the Fourier-based ℓ0-constrained nonconvex CDL problems and the nonconvex extension of the slice-based ℓ1-constrained convex CDL problems. A novel method named proximal gradient nonconvex optimization algorithm (PGNOA) is introduced. We prove that PGNOA can converge to a critical point. Extensive experiments are carried out on the benchmark data, and the results show that PGNOA is superior to the existing slice-based convex CDL methods and the Fourier-based nonconvex CDL methods in terms of the objective function value. The dictionaries learned from PGNOA are applied to image inpainting and image separation tasks. The experimental results demonstrate that PGNOA can perform better than other CDL methods.

A Model-Driven Deep Unfolding Method for JPEG Artifacts Removal.

Deep learning-based methods have achieved notable progress in removing blocking artifacts caused by lossy JPEG compression on images. However, most deep learning-based methods handle this task by designing black-box network architectures to directly learn the relationships between the compressed images and their clean versions. These network architectures are always lack of sufficient interpretability, which limits their further improvements in deblocking performance. To address this issue, in this article, we propose a model-driven deep unfolding method for JPEG artifacts removal, with interpretable network structures. First, we build a maximum posterior (MAP) model for deblocking using convolutional dictionary learning and design an iterative optimization algorithm using proximal operators. Second, we unfold this iterative algorithm into a learnable deep network structure, where each module corresponds to a specific operation of the iterative algorithm. In this way, our network inherits the benefits of both the powerful model ability of data-driven deep learning method and the interpretability of traditional model-driven method. By training the proposed network in an end-to-end manner, all learnable modules can be automatically explored to well characterize the representations of both JPEG artifacts and image content. Experiments on synthetic and real-world datasets show that our method is able to generate competitive or even better deblocking results, compared with state-of-the-art methods both quantitatively and qualitatively.

Convolutional analysis operator learning for multifocus image fusion

Sparse representation (SR), convolutional sparse representation (CSR) and convolutional dictionary learning (CDL) are synthetic-based priors that have proven to be successful in signal inverse problems (such as multifocus image fusion). Unlike “synthesis” formulas, “analysis” model assigns probabilities to signals through various forward measurements of signals. Analysis operator learning (AOL) is a classical analysis-based learning method. Convolutional analysis operator learning (CAOL) is convolutional form of AOL. CAOL uses unsupervised learning method to train autocoded convolutional neural network (CNN) to more accurately solve inverse problem. From the perspective of CAOL, this paper introduces learned convolutional regularizers into multifocus image fusion and proposes CAOL-based multifocus image fusion algorithm. In the CDL stage, convergent block proximal extrapolated gradient method with majorizer (BPEG-M) and adaptive momentum restarting scheme are used. In the sparse fusion stage, alternating direction method of multipliers (ADMM) approach with convolutional basis pursuit denoising (CBPDN) and l1 norm maximum strategy are employed for high-frequency and low-frequency component, respectively. 3 types of multifocus images (static gray images, gray images in sports and color images) are tested to verify performance of the proposed method. A comparison with representative methods demonstrates superiority of our method in terms of subjective observation and objective evaluation.