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Compressive Sensing by Random Convolution

Justin Romberg
2009 SIAM Journal of Imaging Sciences  
This paper demonstrates that convolution with random waveform followed by random time-domain subsampling is a universally efficient compressive sensing strategy.  ...  The time-domain subsampling can be done in one of two ways: in the first, we simply observe m samples of the random convolution, in the second, we break the random convolution into m blocks, and summarize  ...  Random convolution for compressive sensing has been explored in several other places in the literature.  ... 
doi:10.1137/08072975x fatcat:e5pembab7vhsfkv2xv5nco3oye

Compressive sensing by white random convolution [article]

Yin Xiang, Lianlin Li, Fang Li
2009 arXiv   pre-print
A different compressive sensing framework, convolution with white noise waveform followed by subsampling at fixed (not randomly selected) locations, is studied in this paper.  ...  convolution.  ...  Related works Application of a random filter for compressive sensing was first mentioned by J. Tropp et al.  ... 
arXiv:0909.2737v2 fatcat:leee6h33ordvrmggvtfegfvuma

An Efficient Compressive Convolutional Network for Unified Object Detection and Image Compression

Xichuan Zhou, Lang Xu, Shujun Liu, Yingcheng Lin, Lei Zhang, Cheng Zhuo
The proposed Compressive Convolutional Network (CCN) is basically a compressive-sensing-enabled convolutional neural network.  ...  the CCN convolution kernels learned by training over the VOC and COCO image set can be used for data embedding and image compression.  ...  Romberg found that, the convolution between the data and a random embedding matrix is an efficient compressive sensing strategy, and the image compressed by random convolution can be recovered via L1-norm  ... 
doi:10.1609/aaai.v33i01.33015949 fatcat:qkmdsodzjfh6tlq2zxzuf7ss7m

Snapshot spectral imaging via compressive random convolution

Yao Wu, Gonzalo Arce
2011 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
The new method, based on the theory of compressive sensing via random convolutions, is shown to outperform traditional CASSI systems in terms of PSNR spectral image cube reconstructions.  ...  The spectral cube is then attained using a compressive sensing reconstruction algorithm. In this paper, we explore a new approach referred to as random convolution snapshot spectral imaging (RCSSI).  ...  The systems is based on the concept of random convolution recently proposed in the field of compressive sensing.  ... 
doi:10.1109/icassp.2011.5946769 dblp:conf/icassp/WuA11 fatcat:2lqtvdx2tzfgheclpbqvpvrnkq

CMOS compressed imaging by Random Convolution

L. Jacques, P. Vandergheynst, A. Bibet, V. Majidzadeh, A. Schmid, Y. Leblebici
2009 2009 IEEE International Conference on Acoustics, Speech and Signal Processing  
We present a CMOS imager with built-in capability to perform Compressed Sensing coding by Random Convolution. It is achieved by a shift register set in a pseudo-random configuration.  ...  The feasibility of the imager and its robustness under noise and non-linearities have been confirmed by computer simulations, as well as the reconstruction tools supporting the Compressed Sensing theory  ...  The random convolution of an image x ∈ RN by a random filter a ∈ RN is mathematically described by y i = (Φx) i = i a r(i)−j x j = (x * a) r(i) , (1) where r(i) ∈ {1, · · · ,N } is selected uniformly at  ... 
doi:10.1109/icassp.2009.4959783 dblp:conf/icassp/JacquesVBMSL09 fatcat:meyzrrohmfc2beniptdfdswx3u

Sensing by Random Convolution

Justin Romberg
2007 2007 2nd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing  
In particular, we will show that taking measurements by subsampling a convolution with a random pulse is in some sense a universal compressive sampling strategy.  ...  Several recent results in Compressive Sampling (CS) show that a sparse signal (i.e. one which can be compressed in a known orthobasis) can be efficiently acquired by taking linear measurements against  ...  That is, sampling a random convolution is in some sense a universal compressive sampling strategy. Other universal compressive sampling strategies have been proposed [1, 4] .  ... 
doi:10.1109/camsap.2007.4497984 fatcat:lcpc7jjxnng2dg43sazrkaew64

State of the art and prospects of structured sensing matrices in compressed sensing

Kezhi Li, Shuang Cong
2015 Frontiers of Computer Science  
However, the pure random sensing matrices usually require huge memory for storage and high computational cost for signal reconstruction.  ...  Compressed sensing (CS) enables people to acquire the compressed measurements directly and recover sparse or compressible signals faithfully even when the sampling rate is much lower than the Nyquist rate  ...  Random Convolution The random convolution (RC) model was first proposed by Romberg in 2007 [25, 26] . In the RC, the construction has two steps.  ... 
doi:10.1007/s11704-015-3326-8 fatcat:ftl6hdkjdvaqflxcjo2imcn26a

On the Acceleration of Deep Neural Network Inference using Quantized Compressed Sensing [article]

Meshia Cédric Oveneke
2021 arXiv   pre-print
The present paper therefore proposes a novel binary quantization function based on quantized compressed sensing (QCS).  ...  To alleviate this, DNN binary quantization for faster convolution and memory savings is one of the most promising strategies despite its serious drop in accuracy.  ...  The function Q B defined in Quantized Compressed Sensing Despite the above-mentioned strategies for quantizing DNNs by finding the optimal scaling factor α, none of these strategies is proven to inherently  ... 
arXiv:2108.10101v1 fatcat:fxbxzx425zh4tazluapfrovjaq

Compressive Sensing Based Robust Signal Sampling

Lianlin Li, Fang Li
2012 Applied Physics Research  
Recently, compressive sensing (CS) has made a paradigmatic step in the way information is presented, stored, transmitted and recovered, by which we can acquire and reconstruct sparse signals from sub-Nyquist  ...  Three key ingredients of successfully implementing compressed sampling technique are sparsible/compressible probed signal, reliable hardware design, and low-cost computational algorithm.  ...  Application of a random filter for compressive sensing was first mentioned by Tropp et al. who proposed two equivalent realization structures of a random filter: 1) convolution with a random waveform  ... 
doi:10.5539/apr.v4n1p30 fatcat:qlhqel7h4zcbndixmmficid2uq

Single-Shot Compressed Imaging via Random Phase Modulation

Cheng Zhang, Ru Zhang, Yuanyuan Zhu, Hairong Yang, Chuan Shen, Sui Wei
2022 Applied Sciences  
mask (CI-SSRPM). (4) Single-shot compressed imaging with a random convolution using a double random phase mask (CI-DRPM). (5) Single-shot compressed imaging with Fourier-domain single random phase mask  ...  applied in compressed sensing or compressed imaging: (1) Fundamentals of compressed sensing. (2) Principles of phase modulation. (3) Single-shot compressed imaging with spatial-domain single random phase  ...  the forward measurement operator (i.e., measurement matrix) in compressed sensing via random convolution followed by random demodulation.  ... 
doi:10.3390/app12094536 fatcat:6yjalidk4rep7i2kvitmqf4y4q

ConvCSNet: A Convolutional Compressive Sensing Framework Based on Deep Learning [article]

Xiaotong Lu, Weisheng Dong, Peiyao Wang, Guangming Shi, Xuemei Xie
2018 arXiv   pre-print
Compressive sensing (CS), aiming to reconstruct an image/signal from a small set of random measurements has attracted considerable attentions in recent years.  ...  In this paper, we propose a convolutional CS framework that senses the whole image using a set of convolutional filters.  ...  Proposed convolutional compressive sensing Unlike existing BCS and convolutional CS, we propose to sense an image by convolving it with a set of random filters, followed by spatial subsampling of the convolved  ... 
arXiv:1801.10342v1 fatcat:b7gregurm5gjdp3yzdygk6lbhe

Compressed Learning: A Deep Neural Network Approach [article]

Amir Adler, Michael Elad, Michael Zibulevsky
2016 arXiv   pre-print
In this paper we present an end-to-end deep learning approach for CL, in which a network composed of fully-connected layers followed by convolutional layers perform the linear sensing and non-linear inference  ...  Compressed Learning (CL) is a joint signal processing and machine learning framework for inference from a signal, using a small number of measurements obtained by linear projections of the signal.  ...  This research is supported in part by ERC Grant agreement no. 320649, and in part by the Intel Collaborative Research Institute for Computational Intelligence (ICRI-CI).  ... 
arXiv:1610.09615v1 fatcat:ll37te3jq5gd5h5hld76ce572i

ATP-Net: An Attention-based Ternary Projection Network For Compressed Sensing [article]

Guanxiong Nie, Yajian Zhou
2021 arXiv   pre-print
Compressed Sensing (CS) theory simultaneously realizes the signal sampling and compression process, and can use fewer observations to achieve accurate signal recovery, providing a solution for better and  ...  Furthermore, a compressed sensing algorithm especially for image reconstruction is implemented, on the basis of the ternary sampling matrix, which is called ATP-Net, i.e., Attention-based ternary projection  ...  In traditional compressed sensing way, random matrices are often used as the measurement matrices, such as random Gaussian matrix, random Bernoulli matrix, which meet the Restricted Isometry Property (  ... 
arXiv:2106.12728v1 fatcat:y7533tb2tzdw5bsqdbdwbmwjyi

Compressive sensing based privacy for fall detection [article]

Ronak Gupta, Prashant Anand, Santanu Chaudhury, Brejesh Lall, Sanjay Singh
2020 arXiv   pre-print
The proposed architecture is a custom version of Inflated 3D (I3D) architecture, that takes compressed measurements of video sequence as spatio-temporal input, obtained from compressive sensing framework  ...  , rather than video sequence as input, as in the case of I3D convolutional neural network.  ...  In compressive sensing, random Gaussian matrix or random Bernoulli matrix has been widely used to generate linear measurements of natural images, frames of video, etc. [9] .  ... 
arXiv:2001.03463v1 fatcat:hvgu32hipvau3b5bymtd3nuia4

Compressed Sensing using Chaos Filters

Nguyen Linh-Trung, Dinh Van Phong, Zahir M. Hussain, Huu Tue Huynh, Victoria L. Morgan, John C. Gore
2008 2008 Australasian Telecommunication Networks and Applications Conference  
Compressed sensing, viewed as a type of random undersampling, considers the acquisition and reconstruction of sparse or compressible signals at a rate significantly lower than that of Nyquist.  ...  , outperforms random filters.  ...  ACKNOWLEDGEMENT This article was funded in part by a grant from the Vietnam Education Foundation (VEF).  ... 
doi:10.1109/atnac.2008.4783326 fatcat:uvpgvm7yabajtevoqtvqcr3np4
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