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Dictionary learning for sparse representations has been successful in many reconstruction tasks. Simplicial learning is an adaptation of dictionary learning, where subspaces become clipped and acquire arbitrary offsets, taking the form of…

Machine Learning · Computer Science 2020-05-19 Yigit Oktar , Mehmet Turkan

There are two main approaches in compressed sensing: the geometric approach and the combinatorial approach. In this paper we introduce an information theoretic approach and use results from the theory of Huffman codes to construct a…

Information Theory · Computer Science 2009-06-26 Akram Aldroubi , Haichao Wang , Kourosh Zarringhalam

When dealing with clinical text classification on a small dataset recent studies have confirmed that a well-tuned multilayer perceptron outperforms other generative classifiers, including deep learning ones. To increase the performance of…

Machine Learning · Computer Science 2022-09-27 Thanh-Dung Le , Rita Noumeir , Jerome Rambaud , Guillaume Sans , Philippe Jouvet

A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is…

Computer Vision and Pattern Recognition · Computer Science 2010-10-22 Guoshen Yu , Guillermo Sapiro

This paper introduces a deep learning enabled generative sensing framework which integrates low-end sensors with computational intelligence to attain a high recognition accuracy on par with that attained with high-end sensors. The proposed…

Computer Vision and Pattern Recognition · Computer Science 2018-01-10 Lina Karam , Tejas Borkar , Yu Cao , Junseok Chae

Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…

Machine Learning · Computer Science 2015-10-26 Saiprasad Ravishankar , Yoram Bresler

Compressive sensing (CS) is a promising technology for realizing energy-efficient wireless sensors for long-term health monitoring. However, conventional model-driven CS frameworks suffer from limited compression ratio and reconstruction…

Machine Learning · Computer Science 2016-12-19 Kai Xu , Yixing Li , Fengbo Ren

This paper deals with the design of a sensing matrix along with a sparse recovery algorithm by utilizing the probability-based prior information for compressed sensing system. With the knowledge of the probability for each atom of the…

Machine Learning · Computer Science 2019-10-29 Q. Jiang , S. Li , Z. Zhu , H. Bai , X. He , R. C. de Lamare

Supervised deep learning requires a large amount of training samples with annotations (e.g. label class for classification task, pixel- or voxel-wised label map for segmentation tasks), which are expensive and time-consuming to obtain.…

Computer Vision and Pattern Recognition · Computer Science 2020-04-14 Yuanhan Mo , Shuo Wang , Chengliang Dai , Rui Zhou , Zhongzhao Teng , Wenjia Bai , Yike Guo

In compressed sensing, we wish to reconstruct a sparse signal $x$ from observed data $y$. In sparse coding, on the other hand, we wish to find a representation of an observed signal $y$ as a sparse linear combination, with coefficients $x$,…

Computer Vision and Pattern Recognition · Computer Science 2013-11-25 Will Landecker , Rick Chartrand , Simon DeDeo

Reducing acquisition time is a crucial challenge for many imaging techniques. Compressed Sensing (CS) theory offers an appealing framework to address this issue since it provides theoretical guarantees on the reconstruction of sparse…

Applications · Statistics 2014-07-17 Nicolas Chauffert , Philippe Ciuciu , Jonas Kahn , Pierre Weiss

An intriguing phenomenon in many instances of compressed sensing is that the reconstruction quality is governed not just by the overall sparsity of the signal, but also on its structure. This paper is about understanding this phenomenon,…

Functional Analysis · Mathematics 2014-03-28 Ben Adcock , Anders C. Hansen , Bogdan Roman

Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this correspondence, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via additive…

Information Theory · Computer Science 2010-10-04 Nam Yul Yu

Accelerated MRI protocols routinely involve a predefined sampling pattern that undersamples the k-space. Finding an optimal pattern can enhance the reconstruction quality, however this optimization is a challenging task. To address this…

Image and Video Processing · Electrical Eng. & Systems 2024-08-30 Cagan Alkan , Morteza Mardani , Congyu Liao , Zhitao Li , Shreyas S. Vasanawala , John M. Pauly

A novel framework of compressed sensing, namely statistical compressed sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution, and achieving accurate reconstruction on average, is…

Computer Vision and Pattern Recognition · Computer Science 2015-05-27 Guoshen Yu , Guillermo Sapiro

We develop a Bayesian framework for sensing which adapts the sensing time and/or basis functions to the instantaneous sensing quality measured in terms of the expected posterior mean-squared error. For sparse Gaussian sources a significant…

Information Theory · Computer Science 2018-02-12 Ralf R. Müller , Ali Bereyhi , Christoph F. Mecklenbräuker

Linear encoding of sparse vectors is widely popular, but is commonly data-independent -- missing any possible extra (but a priori unknown) structure beyond sparsity. In this paper we present a new method to learn linear encoders that adapt…

In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation…

Information Theory · Computer Science 2021-08-25 Hanshen Xiao , Yaowen Zhang , Guoqiang Xiao

Image recovery from compressive measurements requires a signal prior for the images being reconstructed. Recent work has explored the use of deep generative models with low latent dimension as signal priors for such problems. However, their…

Computer Vision and Pattern Recognition · Computer Science 2021-03-02 Niklas Smedemark-Margulies , Jung Yeon Park , Max Daniels , Rose Yu , Jan-Willem van de Meent , Paul Hand

Deep networks can be trained to map images into a low-dimensional latent space. In many cases, different images in a collection are articulated versions of one another; for example, same object with different lighting, background, or pose.…

Computer Vision and Pattern Recognition · Computer Science 2023-03-14 Rakib Hyder , M. Salman Asif