Convolutional Sparse Coding Method Research Articles

Efficient ADMM-Based Algorithms for Convolutional Sparse Coding

Convolutional sparse coding improves on the standard sparse approximation by incorporating a global shift-invariant model. The most efficient convolutional sparse coding methods are based on the alternating direction method of multipliers and the convolution theorem. The only major difference between these methods is how they approach a convolutional least-squares fitting subproblem. This letter presents a solution to this subproblem, which improves the efficiency of the state-of-the-art algorithms. We also use the same approach for developing an efficient convolutional dictionary learning method. Furthermore, we propose a novel algorithm for convolutional sparse coding with a constraint on the approximation error.

Learning Multiscale Convolutional Dictionaries for Image Reconstruction

Convolutional neural networks (CNNs) have been tremendously successful in solving imaging inverse problems. To understand their success, an effective strategy is to construct simpler and mathematically more tractable convolutional sparse coding (CSC) models that share essential ingredients with CNNs. Existing CSC methods, however, underperform leading CNNs in challenging inverse problems. We hypothesize that the performance gap may be attributed in part to how they process images at different spatial scales: While many CNNs use multiscale feature representations, existing CSC models mostly rely on single-scale dictionaries. To close the performance gap, we thus propose a multiscale convolutional dictionary structure. The proposed dictionary structure is derived from the U-Net, arguably the most versatile and widely used CNN for image-to-image learning problems. We show that incorporating the proposed multiscale dictionary in an otherwise standard CSC framework yields performance competitive with state-of-the-art CNNs across a range of challenging inverse problems including CT and MRI reconstruction. Our work thus demonstrates the effectiveness and scalability of the multiscale CSC approach in solving challenging inverse problems.

Interpretable convolutional sparse coding method of Lamb waves for damage identification and localization

Lamb wave-based damage identification and localization methods hold the potential for nondestructive evaluation and structural health monitoring. Dispersive and multimodal characteristics lead to complicated Lamb wave signals that are challenging to be analyzed. Deep learning architectures could identify damage-related features effectively. Convolutional neural network (CNN) is a promising architecture that has been widely applied in recent years. However, this data-driven approach still lacks a certain degree of physical interpretability and requires a large number of parameters. In this article, an interpretable Lamb wave convolutional sparse coding (LW-CSC) method is proposed for structural damage identification and localization. First, toneburst signals at different center frequencies are considered in the first convolutional layer. The network convolves the waveforms with a set of parametrized functions that implement band-pass filters, which performs more physical interpretability compared to conventional CNN model. Subsequently, the damage features are extracted according to the multi-layer iterative soft thresholding algorithm for multi-layer CSC model, which could realize a deeper network without adding parameters unlike CNN. Finally, Lamb wave-based damage localization is visualized using an imaging algorithm. The experimental results demonstrate that the proposed method not only enables improvement of the classification accuracy but also achieves structural damage localization accurately.

CSID: A Novel Multimodal Image Fusion Algorithm for Enhanced Clinical Diagnosis.

Technology-assisted clinical diagnosis has gained tremendous importance in modern day healthcare systems. To this end, multimodal medical image fusion has gained great attention from the research community. There are several fusion algorithms that merge Computed Tomography (CT) and Magnetic Resonance Images (MRI) to extract detailed information, which is used to enhance clinical diagnosis. However, these algorithms exhibit several limitations, such as blurred edges during decomposition, excessive information loss that gives rise to false structural artifacts, and high spatial distortion due to inadequate contrast. To resolve these issues, this paper proposes a novel algorithm, namely Convolutional Sparse Image Decomposition (CSID), that fuses CT and MR images. CSID uses contrast stretching and the spatial gradient method to identify edges in source images and employs cartoon-texture decomposition, which creates an overcomplete dictionary. Moreover, this work proposes a modified convolutional sparse coding method and employs improved decision maps and the fusion rule to obtain the final fused image. Simulation results using six datasets of multimodal images demonstrate that CSID achieves superior performance, in terms of visual quality and enriched information extraction, in comparison with eminent image fusion algorithms.

Single Satellite Imagery Superresolution Based on Hybrid Nonlocal Similarity Constrained Convolution Sparse Coding

The traditional superresolution methods based on image patches often ignore the consistency between the overlapped patches, causing block effects in produced images. The convolutional sparse coding based superresolution method uses the translation invariance of the convolution filter to directly encode the entire image, maintaining consistency and good performance. In this article, we propose a novel approach to single-image superresolution reconstruction based on hybrid nonlocal similarity constrained convolution sparse coding. We first decompose the input image into a smooth part and a texture part. The Bayesian nonparametric model can use more prior information of the original image, so we replace the previous bicubic interpolation with this method to better reconstruct the residual high-frequency information in the smooth part. When reconstructing the texture part, this article proposes a nonlocal similarity constrained convolutional sparse coding method, which transforms the reconstruction of the texture part to minimize the convolution sparse coding noise of the feature maps and classifies the image patches in the search space by using the correlation coefficients as the structural information, avoiding unnecessary weight calculation. Several methods were tested on satellite images extensively. Both visual inspection and quantitative analysis results demonstrate that our method outperforms other state-of-the-art methods and increases noise immunity effectively.

Convolutional Dictionary Learning With Grid Refinement

Given a continuous-time signal that can be modeled as the superposition of localized, time-shifted events from multiple sources, the goal of Convolutional Dictionary Learning (CDL) is to identify the location of the events--by Convolutional Sparse Coding (CSC)--and learn the template for each source--by Convolutional Dictionary Update (CDU). In practice, because we observe samples of the continuous-time signal on a uniformly-sampled grid in discrete time, classical CSC methods can only produce estimates of the times when the events occur on this grid, which degrades the performance of the CDU. We introduce a CDL framework that significantly reduces the errors arising from performing the estimation in discrete time. Specifically, we construct an expanded dictionary that comprises, not only discrete-time shifts of the templates, but also interpolated variants, obtained by bandlimited interpolation, that account for continuous-time shifts. For CSC, we develop a novel computationally efficient CSC algorithm, termed Convolutional Orthogonal Matching Pursuit with interpolated dictionary (COMP-INTERP). We benchmarked COMP-INTERP to Contiunuous Basis Pursuit (CBP), the state-of-the-art CSC algorithm for estimating off-the-grid events, and demonstrate, on simulated data, that 1) COMP-INTERP achieves a similar level of accuracy, and 2) is two orders of magnitude faster. For CDU, we derive a novel procedure to update the templates given sparse codes that can occur both on and off the discrete-time grid. We also show that 3) dictionary update with the overcomplete dictionary yields more accurate templates. Finally, we apply the algorithms to the spike sorting problem on electrophysiology recording and show their competitive performance.

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.

Single image super-resolution based on adaptive convolutional sparse coding and convolutional neural networks

The convolutional sparse coding-based super-resolution (CSC-SR) method has shown its good performance in single image super-resolution. It divides the low-resolution (LR) image into low-frequency part and the high-frequency part, and reconstructs their corresponding high-resolution (HR) image with bicubic interpolation and convolutional sparse coding (CSC) method, respectively. This paper is devoted to improve the performance of CSC-SR method. As convolutional neural network (CNN) can reveal the mapping relation between the LR image and the HR image for the low-frequency part better, we replace the bicubic interpolation with CNN to reconstruct the HR image for the low-frequency part. In addition, we propose an adaptive CSC method to reconstruct the HR image for the high-frequency part. We name our proposed super-resolution method as hybrid adaptive convolutional sparse coding-based super-resolution (HACSC-SR) method. Many comparison experiments illustrate that our proposed HACSC-SR method is superior to CSC-SR, CNN as well as several existing super-resolution methods.

Scalable Online Convolutional Sparse Coding.

Convolutional sparse coding (CSC) improves sparse coding by learning a shift-invariant dictionary from the data. However, most existing CSC algorithms operate in the batch mode and are computationally expensive. In this paper, we alleviate this problem by online learning. The key is a reformulation of the CSC objective so that convolution can be handled easily in the frequency domain, and much smaller history matrices are needed. To solve the resultant optimization problem, we use the alternating direction method of multipliers (ADMMs), and its subproblems have efficient closed-form solutions. Theoretical analysis shows that the learned dictionary converges to a stationary point of the optimization problem. Extensive experiments are performed on both the standard CSC benchmark data sets and much larger data sets such as the ImageNet. Results show that the proposed algorithm outperforms the state-of-the-art batch and online CSC methods. It is more scalable, has faster convergence, and better reconstruction performance.