Optimized Projection for Sparse Representation Based Classification
Tongji University（同济大学）；Hefei Institute of Intelligent Machines, Chinese Academy of Sciences（中国科学院合肥智能机械研究所）；University of Science and Technology of China（中国科学技术大学）
Dimensionality reduction (DR) methods have been commonly used as a principled way to understand the high-dimensional data such as facial images. In this paper, we propose a new supervised DR method called Optimized Projection for Sparse Representation based Classification (OP-SRC), which is based on the recent face recognition method, Sparse Representation based Classification (SRC). SRC seeks a sparse linear combination on all the training data for a given query image, and make the decision by the minimal reconstruction residual. OP-SRC is designed on the decision rule of SRC, it aims to reduce the within-class reconstruction residual and simultaneously increase the between-class reconstruction residual on the training data. The projections are optimized and match well with the mechanism of SRC. Therefore, SRC performs well in the OP-SRC transformed space. The feasibility and effectiveness of the proposed method is verified on the Yale, ORL and UMIST databases with promising results.
University of Maryland（马里兰大学）；Rutgers University（罗格斯大学）
It is proven that encoding images and videos through Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, can lead to increased classification performance. Taking into account manifold geometry is typically done via embedding the manifolds in tangent spaces, or Reproducing Kernel Hilbert Spaces (RKHS). Recently, it was shown that embedding such manifolds into a Random Projection Spaces (RPS), rather than RKHS or tangent space, leads to higher classification and clustering performance. However, based on structure and dimensionality of the r…
Embeddings provide compact representations of signals in order to perform efficient inference in a wide variety of tasks. In particular, random projections are common tools to construct Euclidean distance-preserving embeddings, while hashing techniques are extensively used to embed set-similarity metrics, such as the Jaccard coefficient. In this letter, we theoretically prove that a class of random projections based on sparse matrices, called SparseHash, can preserve the Jaccard coefficient between the supports of sparse signals, which can be used to estimate set similarities. Moreover, beside…
Henan University（河南大学）；Zhejiang Cancer Hospital（浙江省肿瘤医院）
Sparse representation classification achieves good results by addressing recognition problem with sufficient training samples per subject. However, SRC performs not very well for small sample data. In this paper, an inverse-projection group sparse representation model is presented for breast tumor classification, which is based on constructing low-rank variation dictionary. The proposed low-rank variation dictionary tackles tumor recognition problem from the viewpoint of detecting and using variations in gene expression profiles of normal and patients, rather than directly using these samples.…
Compressed sensing (CS) is a sampling theory that allows reconstruction of sparse (or compressible) signals from an incomplete number of measurements, using of a sensing mechanism implemented by an appropriate projection matrix. The CS theory is based on random Gaussian projection matrices, which satisfy recovery guarantees with high probability; however, sparse ternary {0, -1, +1} projections are more suitable for hardware implementation. In this paper, we present a deep learning approach to obtain very sparse ternary projections for compressed sensing. Our deep learning architecture jointly …
Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希-亚历山大大学）；Fraunhofer Development Center X-Ray Technology EZRT（弗劳恩霍夫X射线技术发展中心（EZRT））；Johns Hopkins University（约翰斯·霍普金斯大学）
We present a method for selecting valuable projections in computed tomography (CT) scans to enhance image reconstruction and diagnosis. The approach integrates two important factors, projection-based detectability and data completeness, into a single feed-forward neural network. The network evaluates the value of projections, processes them through a differentiable ranking function and makes the final selection using a straight-through estimator. Data completeness is ensured through the label provided during training. The approach eliminates the need for heuristically enforcing data completene…
Filtered back projection (FBP) is a classical method for image reconstruction from sinogram CT data. FBP is computationally efficient but produces lower quality reconstructions than more sophisticated iterative methods, particularly when the number of views is lower than the number required by the Nyquist rate. In this paper, we use a deep convolutional neural network (CNN) to produce high-quality reconstructions directly from sinogram data. A primary novelty of our approach is that we first back project each view separately to form a stack of back projections and then feed this stack as input…
PPCAR-Net: Projection-Refined Parametric 3D Coronary Artery Reconstruction from Sparse X-ray Angiographic Views
Bioinformatics Institute, Agency for Science, Technology and Research (A*STAR)（生物信息学研究所，科技研究局（A*STAR））；College of Computing and Data Science, Nanyang Technological University（南洋理工大学计算与数据科学学院）；National Heart Centre Singapore（新加坡国家心脏中心）
University of Texas, Austin（德克萨斯大学奥斯汀分校）；University of California, Berkeley（加州大学伯克利分校）
Motivated by an emerging theory of robust low-rank matrix representation, in this paper, we introduce a novel solution for online rigid-body motion registration. The goal is to develop algorithmic techniques that enable a robust, real-time motion registration solution suitable for low-cost, portable 3-D camera devices. Assuming 3-D image features are tracked via a standard tracker, the algorithm first utilizes Robust PCA to initialize a low-rank shape representation of the rigid body. Robust PCA finds the global optimal solution of the initialization, while its complexity is comparable to sing…
Iterative Diffusion-Refined Neural Attenuation Fields for Multi-Source Stationary CT Reconstruction: NAF Meets Diffusion Model
School of Information Engineering, Nanchang University（南昌大学信息工程学院）；School of Mathematics and Computer Sciences, Nanchang University（南昌大学数学与计算机科学学院）；School of Biomedical Engineering, Sun Yat-sen University（中山大学生物医学工程学院）；Laboratory of Image Science and Technology, School of Computer Science and Engineering, and the Key Laboratory of New Generation Artificial Intelligence Technology and Its Interdisciplinary Applications, Ministry of Education, Southeast University（东南大学计算机科学与工程学院图像科学与技术实验室，以及教育部新一代人工智能技术及其交叉应用重点实验室）
As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is mainly exploited for the task of classification, this paper is developed to study the construction of random matrix from the viewpoint of feature selection, rather than of traditional distance preservation. This yields a somewhat surprising theoretical result, that is, the sparse random matrix with exactly one nonzero element per column, can present better featu…
Geometric Constraints Enable Self-Supervised Sinogram Inpainting in Sparse-View Tomography
Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希-亚历山大大学）；Fraunhofer Institute for Ceramic Technologies and Systems IKTS（弗劳恩霍夫陶瓷技术与系统研究所（IKTS））；Fraunhofer Development Center X-Ray Technology EZRT（弗劳恩霍夫X射线技术开发中心（EZRT））
Sparse-view CT reconstruction is important in a wide range of applications due to limitations on cost, acquisition time, or dosage. However, traditional direct reconstruction methods such as filtered back-projection (FBP) lead to low-quality reconstructions in the sub-Nyquist regime. In contrast, deep neural networks (DNNs) can produce high-quality reconstructions from sparse and noisy data, e.g. through post-processing of FBP reconstructions, as can model-based iterative reconstruction (MBIR), albeit at a higher computational cost. In this paper, we introduce a direct-reconstruction DNN metho…
University of Utah（犹他大学）；Trimble（天宝公司）；Instituto Superior Técnico, University of Lisboa（里斯本大学高等理工学院）
We propose a novel technique to register sparse 3D scans in the absence of texture. While existing methods such as KinectFusion or Iterative Closest Points (ICP) heavily rely on dense point clouds, this task is particularly challenging under sparse conditions without RGB data. Sparse texture-less data does not come with high-quality boundary signal, and this prohibits the use of correspondences from corners, junctions, or boundary lines. Moreover, in the case of sparse data, it is incorrect to assume that the same point will be captured in two consecutive scans. We take a different approach an…
Nanchang University（南昌大学）；Gannan Normal University（赣南师范大学）
The radiation dose in computed tomography (CT) examinations is harmful for patients but can be significantly reduced by intuitively decreasing the number of projection views. Reducing projection views usually leads to severe aliasing artifacts in reconstructed images. Previous deep learning (DL) techniques with sparse-view data require sparse-view/full-view CT image pairs to train the network with supervised manners. When the number of projection view changes, the DL network should be retrained with updated sparse-view/full-view CT image pairs. To relieve this limitation, we present a fully un…
Learning dictionaries suitable for sparse coding instead of using engineered bases has proven effective in a variety of image processing tasks. This paper studies the optimization of dictionaries on image data where the representation is enforced to be explicitly sparse with respect to a smooth, normalized sparseness measure. This involves the computation of Euclidean projections onto level sets of the sparseness measure. While previous algorithms for this optimization problem had at least quasi-linear time complexity, here the first algorithm with linear time complexity and constant space com…
3DGR-CAR: Coronary artery reconstruction from ultra-sparse 2D X-ray views with a 3D Gaussians representation
School of Biomedical Engineering, Division of Life Sciences and Medicine, University of Science and Technology of China (USTC)（中国科学技术大学生命科学与医学部生物医学工程学院）；Center for Medical Imaging, Robotics, Analytic Computing & Learning (MIRACLE), Suzhou Institute for Advance Research, USTC（中国科学技术大学苏州研究院医学影像、机器人、分析计算与学习中心）
Dimension reduction and data quantization are two important methods for reducing data complexity. In the paper, we study the methodology of first reducing data dimension by random projection and then quantizing the projections to ternary or binary codes, which has been widely applied in classification. Usually, the quantization will seriously degrade the accuracy of classification due to high quantization errors. Interestingly, however, we observe that the quantization could provide comparable and often superior accuracy, as the data to be quantized are sparse features generated with common fi…
driveU（driveU公司）；Institute of Measurement, Control and Microtechnology（测量、控制与微技术研究所）；Ulm University（乌尔姆大学）；Institute of Neural Information Processing（神经信息处理研究所）
Sparseness is a useful regularizer for learning in a wide range of applications, in particular in neural networks. This paper proposes a model targeted at classification tasks, where sparse activity and sparse connectivity are used to enhance classification capabilities. The tool for achieving this is a sparseness-enforcing projection operator which finds the closest vector with a pre-defined sparseness for any given vector. In the theoretical part of this paper, a comprehensive theory for such a projection is developed. In conclusion, it is shown that the projection is differentiable almost e…
University of Macau（澳门大学）；Zhejiang Normal University（浙江师范大学）
This paper addresses the color image completion problem in accordance with low-rank quatenrion matrix optimization that is characterized by sparse regularization in a transformed domain. This research was inspired by an appreciation of the fact that different signal types, including audio formats and images, possess structures that are inherently sparse in respect of their respective bases. Since color images can be processed as a whole in the quaternion domain, we depicted the sparsity of the color image in the quaternion discrete cosine transform (QDCT) domain. In addition, the representatio…
MVMS-RCN: A Dual-Domain Unfolding CT Reconstruction with Multi-sparse-view and Multi-scale Refinement-correction
Xiangtan University（湘潭大学）；Zhejiang Normal University（浙江师范大学）；The University of Liverpool（利物浦大学）；University of Strathclyde（斯特拉斯克莱德大学）；Hunan National Applied Mathematics Center（湖南国家应用数学中心）
In this paper, the Primal-Dual UNet for sparse view CT reconstruction is modified to be applicable to cone beam projections and perform reconstructions of entire volumes instead of slices. Experiments show that the PSNR of the proposed method is increased by 10dB compared to the direct FDK reconstruction and almost 3dB compared to the modified original Primal-Dual Network when using only 23 projections. The presented network is not optimized wrt. memory consumption or hyperparameters but merely serves as a proof of concept and is limited to low resolution projections and volumes.
Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）
Deep convolutional neural networks (CNNs) show strong promise for analyzing scientific data in many domains including particle imaging detectors such as a liquid argon time projection chamber (LArTPC). Yet the high sparsity of LArTPC data challenges traditional CNNs which were designed for dense data such as photographs. A naive application of CNNs on LArTPC data results in inefficient computations and a poor scalability to large LArTPC detectors such as the Short Baseline Neutrino Program and Deep Underground Neutrino Experiment. Recently Submanifold Sparse Convolutional Networks (SSCNs) have…
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）
X-ray computed tomography (CT) using sparse projection views is a recent approach to reduce the radiation dose. However, due to the insufficient projection views, an analytic reconstruction approach using the filtered back projection (FBP) produces severe streaking artifacts. Recently, deep learning approaches using large receptive field neural networks such as U-Net have demonstrated impressive performance for sparse- view CT reconstruction. However, theoretical justification is still lacking. Inspired by the recent theory of deep convolutional framelets, the main goal of this paper is, there…
Manifold learning has been successfully applied to a variety of medical imaging problems. Its use in real-time applications requires fast projection onto the low-dimensional space. To this end, out-of-sample extensions are applied by constructing an interpolation function that maps from the input space to the low-dimensional manifold. Commonly used approaches such as the Nyström extension and kernel ridge regression require using all training points. We propose an interpolation function that only depends on a small subset of the input training data. Consequently, in the testing phase each new …
