Visible and Infrared Image Fusion Based on Convolutional Sparse Coding with Gradient Regularization

Hyperspectral images (HSIs) play a crucial role in remote sensing but are often degraded by complex noise patterns. Ensuring the physical property of the denoised HSIs is vital for robust HSI denoising, giving the rise of deep unfolding-based methods. However, these methods map the optimization of a physical model to a learnable network with a predefined depth, which lacks convergence guarantees. In contrast, Deep Equilibrium (DEQ) models treat the hidden layers of deep networks as the solution to a fixed-point problem and models them as infinite-depth networks, naturally consistent with the optimization. Under the framework of DEQ, we propose a Deep Equilibrium Convolutional Sparse Coding (DECSC) framework that unifies local spatial-spectral correlations, nonlocal spatial self-similarities, and global spatial consistency for robust HSI denoising. Within the convolutional sparse coding (CSC) framework, we enforce shared 2D convolutional sparse representation to ensure global spatial consistency across bands, while unshared 3D convolutional sparse representation captures local spatial-spectral details. To further exploit nonlocal self-similarities, a transformer block is embedded after the 2D CSC. Additionally, a detail enhancement module is integrated with the 3D CSC to promote image detail preservation. We formulate the proximal gradient descent of the CSC model as a fixed-point problem and transform the iterative updates into a learnable network architecture within the framework of DEQ. Experimental results demonstrate that our DECSC method achieves superior denoising performance compared to state-of-the-art methods.

With the development of cross-modal image fusion in multi-sensor systems, current fusion technologies have made significant progress in feature extraction, facilitating more effective image analysis. However, insufficient fusion information may degrade the correlation between the source and fused images, often resulting in the omission of critical features from the original modalities. Therefore, in order to preserve as much information as possible, especially for the complete extraction of effective feature information in source images, this paper proposes a new cross-modal image fusion method based on low-rank representation and convolutional sparse learning named LRCFuse. Firstly, the learned low-rank representation (LLRR) blocks are employed to perform dimensionality reduction on the source images while simultaneously extracting their low-rank and sparse feature components. Nevertheless, considering that the low-rank representation has insufficient modeling ability for different modal images, we introduce common feature preservation module (CFPM) blocks based on convolutional sparse coding. By leveraging the CFPM module, LRCFuse recovers common features from both source images to mitigate the loss caused by the imperfect assumptions of low-rank representation. Based on this, a multi-level optimization strategy incorporating pixel loss, shallow-level loss, mid-level loss, deep-level loss, and sobel loss is proposed to hierarchically learn and refine diverse image features. Quantitative and qualitative evaluations are conducted across various datasets, revealing that LRCFuse can effectively detect targets infrared salient targets, preserve additional details in visible images, and achieve better fusion results for subsequent downstream tasks.

Improved multi-focus image fusion using online convolutional sparse coding based on sample-dependent dictionary

Deep learning has shown great potential for curvilinear structure (e.g., retinal blood vessels and neurites) segmentation as demonstrated by a recent auto-context regression architecture based on filter banks learned by convolutional sparse coding. However, learning such filter banks is very time-consuming, thus limiting the amount of filters employed and the adaptation to other data sets (i.e., slow re-training). We address this limitation by proposing a novel acceleration strategy to speed-up convolutional sparse coding filter learning for curvilinear structure segmentation. Our approach is based on a novel initialisation strategy (warm start), and therefore it is different from recent methods improving the optimisation itself. Our warm-start strategy is based on carefully designed hand-crafted filters (SCIRD-TS), modelling appearance properties of curvilinear structures which are then refined by convolutional sparse coding. Experiments on four diverse data sets, including retinal blood vessels and neurites, suggest that the proposed method reduces significantly the time taken to learn convolutional filter banks (i.e., up to -82%) compared to conventional initialisation strategies. Remarkably, this speed-up does not worsen performance; in fact, filters learned with the proposed strategy often achieve a much lower reconstruction error and match or exceed the segmentation performance of random and DCT-based initialisation, when used as input to a random forest classifier.

We have developed convolutional sparse coding (CSC) to attenuate noise in seismic data. CSC gives a data-driven set of basis functions whose coefficients form a sparse distribution. The noise attenuation method by CSC can be divided into the training and denoising phases. Seismic data with a relatively high signal-to-noise ratio are chosen for training to get the learned basis functions. Then, we use all (or a subset) of the basis functions to attenuate the random or coherent noise in the seismic data. Numerical experiments on synthetic data show that CSC can learn a set of shifted invariant filters, which can reduce the redundancy of learned filters in the traditional sparse-coding denoising method. CSC achieves good denoising performance when training with the noisy data and better performance when training on a similar but noiseless data set. The numerical results from the field data test indicate that CSC can effectively suppress seismic noise in complex field data. By excluding filters with coherent noise features, our method can further attenuate coherent noise and separate ground roll.

Convolution sparse coding (CSC) has attracted much attention recently due to its advantages in image reconstruction and enhancement. However, the coding process suffers from perturbations caused by variations of input samples, as the consistence of features from similar input samples are not well addressed in the existing literature. In this paper, we will tackle this feature consistence problem from a set of samples via a proposed manifold constrained convolutional sparse coding (MCSC) method. The core idea of MCSC is to use the intrinsic manifold (Laplacian) structure of the input data to regularize the traditional CSC such that the consistence between features extracted from input samples can be well preserved. To implement the proposed MCSC method efficiently, the alternating direction method of multipliers (ADMM) approach is employed, which can consistently integrate the underlying Laplacian constraints during the optimization process. With this regularized data structure constraint, the MCSC can achieve a much better solution which is robust to the variance of the input samples against overcomplete filters. We demonstrate the capacity of MCSC by providing the state-of-the-art results when applied it to the task of reconstructing light fields. Finally, we show that the proposed MCSC is a generic approach as it also achieves better results than the state-of-the-art approaches based on convolutional sparse coding in other image reconstruction tasks, such as face reconstruction, digit reconstruction, and image restoration.

Convolutional sparse coding (CSC) is a useful tool in many image and audio applications. Maximizing the performance of CSC requires that the dictionary used to store the features of signals can be learned from real data. The so-called convolutional dictionary learning (CDL) problem is formulated within a nonconvex, nonsmooth optimization framework. Most existing CDL solvers alternately update the coefficients and dictionary in an iterative manner. However, these approaches are prone to running redundant iterations, and their convergence properties are difficult to analyze. Moreover, most of those methods approximate the original nonconvex sparse inducing function using a convex regularizer to promote computational efficiency. This approach to approximation may result in nonsparse representations and, thereby, hinder the performance of the applications. In this paper, we deal with the nonconvex, nonsmooth constraints of the original CDL directly using the modified forward-backward splitting approach, in which the coefficients and dictionary are simultaneously updated in each iteration. We also propose a novel parameter adaption scheme to increase the speed of the algorithm used to obtain a usable dictionary and in so doing prove convergence. We also show that the proposed approach is applicable to parallel processing to reduce the computing time required by the algorithm to achieve convergence. The experimental results demonstrate that our method requires less time than the existing methods to achieve the convergence point while using a smaller final functional value. We also applied the dictionaries learned using the proposed and existing methods to an application involving signal separation. The dictionary learned using the proposed approach provides performance superior to that of comparable methods.

Convolutional sparse coding (CSC) plays an essential role in many computer vision applications ranging from image compression to deep learning. In this work, we spot the light on a new application where CSC can effectively serve, namely line drawing analysis. The process of drawing a line drawing can be approximated as the sparse spatial localization of a number of typical basic strokes, which in turn can be cast as a non-standard CSC model that considers the line drawing formation process from parametric curves. These curves are learned to optimize the fit between the model and a specific set of line drawings. Parametric representation of sketches is vital in enabling automatic sketch analysis, synthesis and manipulation. A couple of sketch manipulation examples are demonstrated in this work. Consequently, our novel method is expected to provide a reliable and automatic method for parametric sketch description. Through experiments, we empirically validate the convergence of our method to a feasible solution.

Multi-modality image fusion applied to improve image quality has drawn great attention from researchers in recent years. However, noise is actually generated in images captured by different types of imaging sensors, which can seriously affect the performance of multi-modality image fusion. As the fundamental method of noisy image fusion, source images are denoised first, and then the denoised images are fused. However, image denoising can decrease the sharpness of source images to affect the fusion performance. Additionally, denoising and fusion are processed in separate processing modes, which causes an increase in computation cost. To fuse noisy multi-modality image pairs accurately and efficiently, a multi-modality image simultaneous fusion and denoising method is proposed. In the proposed method, noisy source images are decomposed into cartoon and texture components. Cartoon-texture decomposition not only decomposes source images into detail and structure components for different image fusion schemes, but also isolates image noise from texture components. A Gaussian scale mixture (GSM) based sparse representation model is presented for the denoising and fusion of texture components. A spatial domain fusion rule is applied to cartoon components. The comparative experimental results confirm the proposed simultaneous image denoising and fusion method is superior to the state-of-the-art methods in terms of visual and quantitative evaluations.

Convolutional sparse coding-based deep random vector functional link network for distress classification of road structures

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.

Depth information can benefit various computer vision tasks on both images and videos. However, depth maps may suffer from invalid values in many pixels, and also large holes. To improve such data, we propose a joint self-supervised and reference-guided learning approach for depth inpainting. For the self-supervised learning strategy, we introduce an improved spatial convolutional sparse coding module in which total variation regularization is employed to enhance the structural information while preserving edge information. This module alternately learns a convolutional dictionary and sparse coding from a corrupted depth map. Then, both the learned convolutional dictionary and sparse coding are convolved to yield an initial depth map, which is effectively smoothed using local contextual information. The reference-guided learning part is inspired by the fact that adjacent pixels with close colors in the RGB image tend to have similar depth values. We thus construct a hierarchical joint bilateral filter module using the corresponding color image to fill in large holes. In summary, our approach integrates a convolutional sparse coding module to preserve local contextual information and a hierarchical joint bilateral filter module for filling using specific adjacent information. Experimental results show that the proposed approach works well for both invalid value restoration and large hole inpainting.

Most of the previous sparse coding (SC) based super resolution (SR) methods partition the image into overlapped patches, and process each patch separately. These methods, however, ignore the consistency of pixels in overlapped patches, which is a strong constraint for image reconstruction. In this paper, we propose a convolutional sparse coding (CSC) based SR (CSC-SR) method to address the consistency issue. Our CSC-SR involves three groups of parameters to be learned: (i) a set of filters to decompose the low resolution (LR) image into LR sparse feature maps, (ii) a mapping function to predict the high resolution (HR) feature maps from the LR ones, and (iii) a set of filters to reconstruct the HR images from the predicted HR feature maps via simple convolution operations. By working directly on the whole image, the proposed CSC-SR algorithm does not need to divide the image into overlapped patches, and can exploit the image global correlation to produce more robust reconstruction of image local structures. Experimental results clearly validate the advantages of CSC over patch based SC in SR application. Compared with state-of-the-art SR methods, the proposed CSC-SR method achieves highly competitive PSNR results, while demonstrating better edge and texture preservation performance.

We propose a system for visual scene analysis and recognition based on encoding the sparse, latent feature-representation of an image into a high-dimensional vector that is subsequently factorized to parse scene content. The sparse feature representation is learned from image statistics via convolutional sparse coding, while scene parsing is performed by a resonator network [1]. The integration of sparse coding with the resonator network increases the capacity of distributed representations and reduces collisions in the combinatorial search space during factorization. We find that for this problem the resonator network is capable of fast and accurate vector factorization, and we develop a confidence-based metric that assists in tracking the convergence of the resonator network.

Hyperspectral image fusion is a key technique of hyperspectral data processing. In recent years, many fusion methods have been proposed, but there is little work concerning evaluation of the performances of different image fusion methods. In this paper, a method called quantitative correlation analysis (QCA) is proposed, which provides a quantitative measure of the information transferred by an image fusion technique into the output image. Using the proposed method, the performances of different image fusion methods can be compared and analyzed directly based on the images of before and after performing the fusion. The correlation information entropy, based on the developed QCA, is also proposed and testified by numerical simulations. Typical hyperspectral data are applied to the proposed method. The results show that the method is effective, and its conclusions agree with the classification results in applications.