Sparsity-based methods have a long history in the field of signal processing and have been successfully applied to various image reconstruction problems. The involved sparsifying transformations or dictionaries are typically either pre-trained using a model which reflects the assumed properties of the signals or adaptively learned during the reconstruction - yielding so-called blind Compressed Sensing approaches. However, by doing so, the transforms are never explicitly trained in conjunction with the physical model which generates the signals. In addition, properly choosing the involved regularization parameters remains a challenging task. Another recently emerged training-paradigm for regularization methods is to use iterative neural networks (INNs) - also known as unrolled networks - which contain the physical model. In this work, we construct an INN which can be used as a supervised and physics-informed online convolutional dictionary learning algorithm. We evaluated the proposed approach by applying it to a realistic large-scale dynamic MR reconstruction problem and compared it to several other recently published works. We show that the proposed INN improves over two conventional model-agnostic training methods and yields competitive results also compared to a deep INN. Further, it does not require to choose the regularization parameters and - in contrast to deep INNs - each network component is entirely interpretable.
Convolutional sparse representations are a form of sparse representation with a dictionary that has a structure that is equivalent to convolution with a set of linear filters. While effective algorithms have recently been developed for the convolutional sparse coding problem, the corresponding dictionary learning problem is substantially more challenging. Furthermore, although a number of different approaches have been proposed, the absence of thorough comparisons between them makes it difficult to determine which of them represents the current state of the art. The present work both addresses…
Convolutional sparse representations are a form of sparse representation with a structured, translation invariant dictionary. Most convolutional dictionary learning algorithms to date operate in batch mode, requiring simultaneous access to all training images during the learning process, which results in very high memory usage and severely limits the training data that can be used. Very recently, however, a number of authors have considered the design of online convolutional dictionary learning algorithms that offer far better scaling of memory and computational cost with training set size tha…
School of Computer Science and Technology, Soochow University（苏州大学计算机科学与技术学院）
Both the Dictionary Learning (DL) and Convolutional Neural Networks (CNN) are powerful image representation learning systems based on different mechanisms and principles, however whether we can seamlessly integrate them to improve the per-formance is noteworthy exploring. To address this issue, we propose a novel generalized end-to-end representation learning architecture, dubbed Convolutional Dictionary Pair Learning Network (CDPL-Net) in this paper, which integrates the learning schemes of the CNN and dictionary pair learning into a unified framework. Generally, the architecture of CDPL-Net …
There has been a growing interest in the use of data-driven regularizers to solve inverse problems associated with computational imaging systems. The convolutional sparse representation model has recently gained attention, driven by the development of fast algorithms for solving the dictionary learning and sparse coding problems for sufficiently large images and data sets. Nevertheless, this model has seen very limited application to tomographic reconstruction problems. In this paper, we present a model-based tomographic reconstruction algorithm using a learnt convolutional dictionary as a reg…
Deep learning based methods hold state-of-the-art results in image denoising, but remain difficult to interpret due to their construction from poorly understood building blocks such as batch-normalization, residual learning, and feature domain processing. Unrolled optimization networks propose an interpretable alternative to constructing deep neural networks by deriving their architecture from classical iterative optimization methods, without use of tricks from the standard deep learning tool-box. So far, such methods have demonstrated performance close to that of state-of-the-art models while…
We present a new algorithm for estimating the Point Spread Function (PSF) in wide-field astronomical images with extreme source crowding. Robust and accurate PSF estimation in crowded astronomical images dramatically improves the fidelity of astrometric and photometric measurements extracted from wide-field sky monitoring imagery. Our radically new approach utilizes convolutional sparse representations to model the continuous functions involved in the image formation. This approach avoids the need to detect and precisely localize individual point sources that is shared by existing methods. In …
University of Basel（巴塞尔大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
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 rel…
Magnetic Resonance Fingerprinting (MRF) methods typically rely on dictionary matching to map the temporal MRF signals to quantitative tissue parameters. These methods suffer from heavy storage and computation requirements as the dictionary size grows. To address these issues, we proposed an end to end fully convolutional neural network for MRF reconstruction (MRF-FCNN), which firstly employ linear dimensionality reduction and then use neural network to project the data into the tissue parameters manifold space. Experiments on the MAGIC data demonstrate the effectiveness of the method.
University of Trento（特伦托大学）；Peking University（北京大学）；Shenzhen Lingxi Artificial Intelligence Co., Ltd（深圳灵犀人工智能有限公司）
We present a new Deep Dictionary Learning and Coding Network (DDLCN) for image recognition tasks with limited data. The proposed DDLCN has most of the standard deep learning layers (e.g., input/output, pooling, fully connected, etc.), but the fundamental convolutional layers are replaced by our proposed compound dictionary learning and coding layers. The dictionary learning learns an over-complete dictionary for input training data. At the deep coding layer, a locality constraint is added to guarantee that the activated dictionary bases are close to each other. Then the activated dictionary at…
Tencent Jarvis Lab（腾讯天衍实验室）；Xi’an Jiaotong University（西安交通大学）；Peng Cheng Laboratory（鹏城实验室）；Macau University of Science and Technology（澳门科技大学）
As a common weather, rain streaks adversely degrade the image quality. Hence, removing rains from an image has become an important issue in the field. To handle such an ill-posed single image deraining task, in this paper, we specifically build a novel deep architecture, called rain convolutional dictionary network (RCDNet), which embeds the intrinsic priors of rain streaks and has clear interpretability. In specific, we first establish a RCD model for representing rain streaks and utilize the proximal gradient descent technique to design an iterative algorithm only containing simple operators…
Learning spatially adaptive sparsity level maps for arbitrary convolutional dictionaries
Physikalisch-Technische Bundesanstalt (PTB), Braunschweig and Berlin, Germany（物理技术联邦机构（PTB），柏林和不莱梅，德国）；School of Mathematical Sciences, Queen Mary University of London, UK（伦敦女王学院数学科学学院，英国）
Indraprastha Institute of Information Technology, Delhi（因德拉普拉斯信息技术学院（德里））
This work proposes a new framework for deep learning that has been particularly tailored for hyperspectral image classification. We learn multiple levels of dictionaries in a robust fashion. The last layer is discriminative that learns a linear classifier. The training proceeds greedily, at a time a single level of dictionary is learnt and the coefficients used to train the next level. The coefficients from the final level are used for classification. Robustness is incorporated by minimizing the absolute deviations instead of the more popular Euclidean norm. The inbuilt robustness helps combat…
Sparse representation using over-complete dictionaries have shown to produce good quality results in various image processing tasks. Dictionary learning algorithms have made it possible to engineer data adaptive dictionaries which have promising applications in image compression and image enhancement. The most common sparse dictionary learning algorithms use the techniques of matching pursuit and K-SVD iteratively for sparse coding and dictionary learning respectively. While this technique produces good results, it requires a large number of iterations to converge to an optimal solution. In th…
Physikalisch-Technische Bundesanstalt（德国联邦物理技术研究院）；Charité - Universitätsmedizin Berlin（柏林夏里特医学院）；King’s College London（伦敦国王学院）；Technical University of Berlin（柏林工业大学）；University of Innsbruck（因斯布鲁克大学）
The concept of sparsity has been extensively applied for regularization in image reconstruction. Typically, sparsifying transforms are either pre-trained on ground-truth images or adaptively trained during the reconstruction. Thereby, learning algorithms are designed to minimize some target function which encodes the desired properties of the transform. However, this procedure ignores the subsequently employed reconstruction algorithm as well as the physical model which is responsible for the image formation process. Iterative neural networks - which contain the physical model - can overcome t…
This paper examines a combined supervised-unsupervised framework involving dictionary-based blind learning and deep supervised learning for MR image reconstruction from under-sampled k-space data. A major focus of the work is to investigate the possible synergy of learned features in traditional shallow reconstruction using adaptive sparsity-based priors and deep prior-based reconstruction. Specifically, we propose a framework that uses an unrolled network to refine a blind dictionary learning-based reconstruction. We compare the proposed method with strictly supervised deep learning-based rec…
School of Electronic and Electrical Engineering, Sungkyunkwan University（成均馆大学电子与电气工程学院）
This paper addresses an ill-posed problem of recovering a color image from its compressively sensed measurement data. Differently from the typical 1D vector-based approach of the state-of-the-art methods, we exploit the nonlocal similarities inherently existing in images by treating each patch of a color image as a 3D tensor consisting of not only horizontal and vertical but also spectral dimensions. A group of nonlocal similar patches form a 4D tensor for which a nonlocal higher order dictionary is learned via higher order singular value decomposition. The multiple sub-dictionaries contained …
Modern digital cameras and smartphones mostly rely on image signal processing (ISP) pipelines to produce realistic colored RGB images. However, compared to DSLR cameras, low-quality images are usually obtained in many portable mobile devices with compact camera sensors due to their physical limitations. The low-quality images have multiple degradations i.e., sub-pixel shift due to camera motion, mosaick patterns due to camera color filter array, low-resolution due to smaller camera sensors, and the rest information are corrupted by the noise. Such degradations limit the performance of current …
Deep convolutional neural networks (CNNs) have recently achieved great success for single image super-resolution (SISR) task due to their powerful feature representation capabilities. The most recent deep learning based SISR methods focus on designing deeper / wider models to learn the non-linear mapping between low-resolution (LR) inputs and high-resolution (HR) outputs. These existing SR methods do not take into account the image observation (physical) model and thus require a large number of network's trainable parameters with a great volume of training data. To address these issues, we pro…
A deep dictionary network-based foundation model for ultra-low-dose CT denoising
Yanshan University（燕山大学）；Capital Medical University（首都医科大学）；Beijing Friendship Hospital（北京友谊医院）；Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）；Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局）
Image fusion is a significant problem in many fields including digital photography, computational imaging and remote sensing, to name but a few. Recently, deep learning has emerged as an important tool for image fusion. This paper presents three deep convolutional sparse coding (CSC) networks for three kinds of image fusion tasks (i.e., infrared and visible image fusion, multi-exposure image fusion, and multi-modal image fusion). The CSC model and the iterative shrinkage and thresholding algorithm are generalized into dictionary convolution units. As a result, all hyper-parameters are learned …
Stanford University（斯坦福大学）；Hokkaido University（北海道大学）；Global Institution for Collaborative Research and Education (GI-CoRE)（全球合作研究与教育机构（GI-CoRE））
This paper presents a dictionary learning-based method with region-specific image patches to maximize the utility of the powerful sparse data processing technique for CT image reconstruction. Considering heterogeneous distributions of image features and noise in CT, region-specific customization of dictionaries is utilized in iterative reconstruction. Thoracic CT images are partitioned into several regions according to their structural and noise characteristics. Dictionaries specific to each region are then learned from the segmented thoracic CT images and applied to subsequent image reconstru…
In the machine learning era, sparsity continues to attract significant interest due to the benefits it provides to learning models. Algorithms aiming to optimise the \(\ell_0\)- and \(\ell_1\)-norm are the common choices to achieve sparsity. In this work, an alternative algorithm is proposed, which is derived based on the assumption of a Cauchy distribution characterising the coefficients in sparse domains. The Cauchy distribution is known to be able to capture heavy-tails in the data, which are linked to sparse processes. We begin by deriving the Cauchy proximal operator and subsequently prop…
