1000/1000

Hot
Most Recent

Submitted Successfully!

To reward your contribution, here is a gift for you: A free trial for our video production service.

Thank you for your contribution! You can also upload a video entry or images related to this topic.

Do you have a full video?

Are you sure to Delete?

Cite

If you have any further questions, please contact Encyclopedia Editorial Office.

Zhou, J.; Yang, J. Compressive Sensing in Image/Video Compression. Encyclopedia. Available online: https://encyclopedia.pub/entry/54860 (accessed on 11 August 2024).

Zhou J, Yang J. Compressive Sensing in Image/Video Compression. Encyclopedia. Available at: https://encyclopedia.pub/entry/54860. Accessed August 11, 2024.

Zhou, Jinjia, Jian Yang. "Compressive Sensing in Image/Video Compression" *Encyclopedia*, https://encyclopedia.pub/entry/54860 (accessed August 11, 2024).

Zhou, J., & Yang, J. (2024, February 07). Compressive Sensing in Image/Video Compression. In *Encyclopedia*. https://encyclopedia.pub/entry/54860

Zhou, Jinjia and Jian Yang. "Compressive Sensing in Image/Video Compression." *Encyclopedia*. Web. 07 February, 2024.

Copy Citation

Compressive Sensing (CS) has emerged as a transformative technique in image compression, offering innovative solutions to challenges in efficient signal representation and acquisition.

compressive sensing
sampling
measurement coding
reconstruction algorithm

In the era of rapid technological advancement, the sheer volume of data generated and exchanged daily has become staggering. This influx of information, from high-resolution images to bandwidth-intensive videos, has posed unprecedented challenges to conventional methods of data transmission and storage. As we grapple with the ever-growing demand for the efficient handling of these vast datasets, a groundbreaking concept emerges—Compressive Sensing ^{[1]}.

Traditionally, the Nyquist–Shannon sampling theorem ^{[2]} has governed our approach to capturing and reconstructing signals, emphasizing the need to sample at twice the rate of the signal’s bandwidth to avoid information loss. However, in the face of escalating data sizes and complexities, this theorem’s practicality is increasingly strained. Compressive Sensing, as a disruptive force, challenges the assumptions of Nyquist–Shannon by advocating for a selective and strategic sampling technique.

In general, CS is a revolutionary signal-processing technique that hinges on the idea that sparse signals can be accurately reconstructed from a significantly reduced set of measurements. The principle of CS involves capturing a compressed version of a signal, enabling efficient data acquisition and transmission. As the **Figure 1** shows, in the field of image processing, numerous works have been proposed in each of various domains, exploring innovative techniques and algorithms to harness the potential of compressive imaging ^{[3]}^{[4]}^{[5]}^{[6]}^{[7]}^{[8]}^{[9]}^{[10]}^{[11]}, efficient communication systems ^{[12]}^{[13]}^{[14]}^{[15]}^{[16]}^{[17]}^{[18]}^{[19]}^{[20]}, pattern recognition ^{[21]}^{[22]}^{[23]}^{[24]}^{[25]}^{[26]}^{[27]}^{[28]}^{[29]}, and video processing tasks ^{[30]}^{[31]}^{[32]}^{[33]}^{[34]}^{[35]}^{[36]}^{[37]}^{[38]}. The versatility and effectiveness of CS make it a compelling area of study with broad implications across different fields of signal processing and information retrieval.

Consider an original signal X, which is an N-length vector that can be sparsely represented as S in a transformed domain using a specific 𝑁×𝑁 transform matrix Ψ, where K-sparse implies that only K elements are non-zero, and the remaining are close to or equal to zero. This relationship is expressed by the equation:

$${X}_{N\times 1}={\mathsf{\Psi}}_{N\times N}{S}_{N\times 1}.$$

The sensing matrix, also known as the sampling matrix A, is derived by multiplying an 𝑀×𝑁 measurement matrix Φ by the transform matrix Ψ, where 𝐾≪𝑀≪𝑁:

$${A}_{M\times N}={\mathsf{\Phi}}_{M\times N}{\mathsf{\Psi}}_{N\times N}.$$

The sampling rate, or Compressed Sensing (CS) ratio, denoted as the number of measurements M divided by the signal length N, indicates the fraction of the signal that is sampled:

$$\mathrm{Sampling}\phantom{\rule{4.pt}{0ex}}\mathrm{Rate}\phantom{\rule{4.pt}{0ex}}(\mathrm{CS}\phantom{\rule{4.pt}{0ex}}\mathrm{ratio})=\frac{M}{N}.$$

Finally, the measurement vector Y is obtained by multiplying the sensing matrix A with the sparse signal S:

$${Y}_{M\times 1}={\mathsf{\Phi}}_{M\times N}{\mathsf{\Psi}}_{N\times N}{S}_{N\times 1}.$$

Since the CS reconstruction is an ill-posed problem ^{[39]}, to obtain a reliable reconstruction, the conventional optimization-based CS methods commonly solve an energy function as:

$$\widehat{X}=\underset{X}{argmin}\frac{1}{2}{\parallel \mathsf{\Phi}X-y\parallel}_{2}^{2}+\lambda \mathcal{R}\left(X\right),$$

One of the fascinating aspects of compressive sensing focuses on the development of measurement matrices. The construction of these matrices is crucial, as they need to meet specific constraints. They should align coherently with the sparsifying matrix to efficiently capture essential information from the initial signal with the least number of projections. On the other hand, the matrix needs to satisfy the restricted isometry property (RIP) to preserve the original signal’s main information in the compression process. However, in the research of ^{[40]}^{[41]}, they verified the possibility that maintaining sparsity levels in a compressive sensing environment does not necessarily require the presence of the RIP, and also demonstrated that it is not a mandatory requirement for adhering to the random model of a signal. Moreover, designing a measurement matrix with low complexity and hardware-friendly characteristics has become more and more crucial in the context of real-time applications and low-power requirements.

In CS-related research a decade ago, random matrices like Gaussian or Bernoulli matrices were often selected as the measurement matrices, which satisfied the RIP conditions of CS. Although these random matrices are easy to implement and contribute to improved reconstruction performance, they come with several notable disadvantages, such as the requirement for significant storage resources and the challenging recovery while dealing with large signal dimensions ^{[42]}. Therefore, the issue of the measurement matrix has been widely discussed in recent works.

Conventional measurement matrices encompass multiple categories, ranging from random matrices to deterministic matrices, each contributing uniquely to the applications in CS. Random matrices are constructed by randomly selecting elements from a certain probability distribution, such as the random Gaussian matrix (RGM) ^{[43]} and random binary matrix (RBM) ^{[44]}. The well-known traditional deterministic matrices include the Bernoulli matrix ^{[45]}, Hadamard matrix ^{[46]}, Walsh matrix ^{[47]}, and Toplitz matrix ^{[48]}. **Figure 3** gives an example of two famous deterministic matrices.

Although these deterministic matrices have been extensively researched and successfully applied to the CS camera, because of their good sensing performance, fast reconstruction, and hardware-friendly properties, they are insupportable when applied to the ultra-low CS ratio ^{[49]}. Moreover, for instance, in the work of ^{[44]}, the information of the pixel domain can be obtained by changing a few rows in the matrix, but the modified matrix results in an unacceptable reconstruction performance, posing enormous challenges for practical applications. In recent years, some studies have been carried out to investigate the effect of Hadamard and Walsh projection order selection on image reconstruction quality by reordering orthogonal matrices ^{[50]}^{[51]}^{[52]}^{[53]}^{[54]}. A Hadamard-based Russian-doll ordering matrix is proposed in ^{[50]}, which sorts the projection patterns by increasing the number of zero-crossing components. In the works of ^{[51]}^{[52]}, the authors present a matrix, called the cake-cutting ordering of Hadamard, which can optimally reorder the deterministic Hadamard basis. More recently, the work of ^{[54]} designs a novel hardware-friendly matrix named the Zigzag-ordered Walsh (ZoW). Specifically, the ZoW matrix uses the zigzag to reorder the blocks from the Walsh matrix, and, finally, vectored them. The illustration of the process is shown in **Figure 4**.

In the proposed matrix of ^{[54]}, the low-frequency patterns are in the upper-left corner, and the frequency increases according to the zigzag scan order. Therefore, across different sampling rates, ZoW consistently retains the lowest frequency patterns, which are pivotal for determining the image quality. This allows ZoW to extract features effectively from low to high-frequency components.

Recently, there has been a surge in the development of image CS algorithms based on deep neural networks. These algorithms aim to acquire features from training data to comprehend the underlying representation and subsequently reconstruct test data from their CS measurements. Therefore, some learning-based algorithms are developed to jointly optimize the sampling matrix and the non-linear recovery operator ^{[55]}^{[56]}^{[57]}^{[58]}^{[59]}^{[60]}^{[61]}. Ref. ^{[55]}’s first attempt leads into a fully connected layeras the sampling matrix for simultaneous sampling and recovery. In the works of ^{[56]}^{[57]}, the authors present the idea of adopting a convolution layer to mimic the sampling process and utilize all-convolutional networks for CS reconstruction. These methods not only train the sampling and recovery stages jointly but are also non-iterative, leading to a significant reduction in time complexity compared to their optimization-based counterparts. However, only utilizing the fully connected or repetitive convolutional layers for the joint learning of the sampling matrix and recovery operator lacks structural diversity, which can be the bottleneck for a further performance improvement. To address this drawback, Ref. ^{[59]} proposes a novel optimization-inspired deep-structured network (OPINE-Net), which includes a data-driven and adaptively learned matrix. Specifically, the measurement matrix Φ∈ℝ^{𝑀×𝑁} is a trainable parameter and is adaptively learned by the training dataset. Two constraints are applied to attain the trained matrix simultaneously. Firstly, the orthogonal constraint is designed into a loss term and then enforced into the total loss, as follows:

$${\mathcal{L}}_{\mathrm{orth}\phantom{\rule{4.pt}{0ex}}}=\frac{1}{{M}^{2}}{\parallel \mathsf{\Phi}{\mathsf{\Phi}}^{\top}-I\parallel}_{F}^{2}$$

$$BinarySign\left(z\right)=1\phantom{\rule{4.pt}{0ex}}\mathrm{if}\phantom{\rule{4.pt}{0ex}}z\ge 0\phantom{\rule{4.pt}{0ex}}\mathrm{or}\phantom{\rule{4.pt}{0ex}}-1\phantom{\rule{4.pt}{0ex}}\mathrm{if}\phantom{\rule{4.pt}{0ex}}z<0$$

Experiments show that their proposed learnable matrix can achieve a superior reconstruction performance with constraint incorporation when compared to conventional measurement matrices.

In general, by learning the features of signals, learning-based measurement matrices can more effectively capture the sparse representation of signals. This personalized adaptability enables learning-based measurement matrices to outperform traditional construction methods in certain scenarios. Another strength of learning-based measurement matrices is their adaptability. By adjusting training data and algorithm parameters, customized measurement matrices can be generated for different types of signals and application scenarios, enhancing the applicability of compressed sensing in diverse tasks. However, obtaining these trainable matrices usually needs a substantial amount of training data and complex algorithms.

It is noticed that the data reduction from the original signal to CS measurement does not completely equal signal compression, and these measurements can indeed be transmitted directly, but still require a substantial bandwidth. To alleviate the transmitter’s load further, the CS-based CMOS image sensor can collaborate with a compressor to produce a compressed bitstream. However, due to the high complexity, the conventional pixel-based compressor is not suitable for CS systems aiming at reducing the computational complexity and power consumption of the encoder ^{[1]}. The difference between conventional image sensors and CS-based sensors is shown in **Figure 5**.

Therefore, to further compress measurements, several well-designed measurement matrices for better measurement coding have been recently proposed ^{[62]}^{[63]}. Wherein, a novel framework for measurement coding is proposed in ^{[63]}, and designs an adjacent pixels-based measurement matrix (APMM) to obtain measurements of each block, which contains block boundary information as a reference for intra prediction. Specifically, a set of four directional prediction modes is employed to generate prediction candidates for each block, from which the optimal prediction is selected for further processing. The residuals represent the difference between measurements and predictions and undergo quantization and Huffman coding to create a coded bit sequence for transmission. Importantly, each encoding step corresponds to a specific operation in the decoding process, ensuring a coherent and reversible transformation. Extensive experimental results show that ^{[63]} can obtain a superior trade-off between the bit-rate and reconstruction quality. **Table 1** illustrates the comparison of different introduced measurement matrices that are commonly used in CS.

Image | CS Ratio | Measurement Matrices | ||||
---|---|---|---|---|---|---|

RGM ^{[43]} |
Hadamard ^{[44]} |
Bernoulli ^{[45]} |
Toplitz ^{[48]} |
APMM ^{[63]} |
||

Lenna | 30% | 33.24 | 28.25 | 29.87 | 28.26 | 33.98 |

40% | 34.76 | 29.71 | 31.24 | 30.83 | 36.04 | |

50% | 36.39 | 30.92 | 32.48 | 33.91 | 37.69 | |

Clown | 30% | 32.15 | 24.59 | 28.36 | 26.85 | 32.79 |

40% | 33.52 | 26.94 | 30.49 | 28.93 | 35.17 | |

50% | 35.46 | 28.03 | 30.67 | 31.42 | 37.08 | |

Peppers | 30% | 33.59 | 27.78 | 30.24 | 30.40 | 33.83 |

40% | 34.82 | 28.03 | 32.18 | 32.75 | 35.50 | |

50% | 36.14 | 30.17 | 33.52 | 33.35 | 36.74 |

- Donoho, D.L. Compressed sensing. IEEE Trans. Inf. Theory 2006, 52, 1289–1306.
- Por, E.; van Kooten, M.; Sarkovic, V. Nyquist–Shannon Sampling Theorem; Leiden University: Leiden, The Netherlands, 2019; Volume 1.
- Arildsen, T.; Oxvig, C.S.; Pedersen, P.S.; Østergaard, J.; Larsen, T. Reconstruction algorithms in undersampled AFM imaging. IEEE J. Sel. Top. Signal Process. 2015, 10, 31–46.
- Li, J.; Liu, Y.; Yuan, Y.; Huang, B. Applications of atomic force microscopy in immunology. Front. Med. 2021, 15, 43–52.
- Lerner, B.E.; Flores-Garibay, A.; Lawrie, B.J.; Maksymovych, P. Compressed sensing for scanning tunnel microscopy imaging of defects and disorder. Phys. Rev. Res. 2021, 3, 043040.
- Otazo, R.; Candes, E.; Sodickson, D.K. Low-rank plus sparse matrix decomposition for accelerated dynamic MRI with separation of background and dynamic components. Magn. Reson. Med. 2015, 73, 1125–1136.
- Quan, T.M.; Nguyen-Duc, T.; Jeong, W.K. Compressed sensing MRI reconstruction using a generative adversarial network with a cyclic loss. IEEE Trans. Med. Imaging 2018, 37, 1488–1497.
- Feng, C.M.; Yan, Y.; Wang, S.; Xu, Y.; Shao, L.; Fu, H. Specificity-preserving federated learning for MR image reconstruction. IEEE Trans. Med. Imaging 2022, 42, 2010–2021.
- Zhang, L.; Xing, M.; Qiu, C.W.; Li, J.; Sheng, J.; Li, Y.; Bao, Z. Resolution enhancement for inversed synthetic aperture radar imaging under low SNR via improved compressive sensing. IEEE Trans. Geosci. Remote Sens. 2010, 48, 3824–3838.
- Giusti, E.; Cataldo, D.; Bacci, A.; Tomei, S.; Martorella, M. ISAR image resolution enhancement: Compressive sensing versus state-of-the-art super-resolution techniques. IEEE Trans. Aerosp. Electron. Syst. 2018, 54, 1983–1997.
- Huang, Y.; Chen, Z.; Wen, C.; Li, J.; Xia, X.G.; Hong, W. An efficient radio frequency interference mitigation algorithm in real synthetic aperture radar data. IEEE Trans. Geosci. Remote Sens. 2022, 60, 1–12.
- Priya, G.; Ghosh, D. An Effectual Video Compression Scheme for WVSNs Based on Block Compressive Sensing. IEEE Trans. Netw. Sci. Eng. 2023.
- Rajpoot, P.; Dwivedi, P. Optimized and load balanced clustering for wireless sensor networks to increase the lifetime of WSN using MADM approaches. Wirel. Netw. 2020, 26, 215–251.
- Okada, H.; Suzaki, S.; Kato, T.; Kobayashi, K.; Katayama, M. Link quality information sharing by compressed sensing and compressed transmission for arbitrary topology wireless mesh networks. IEICE Trans. Commun. 2017, 100, 456–464.
- Rao, P.S.; Jana, P.K.; Banka, H. A particle swarm optimization based energy efficient cluster head selection algorithm for wireless sensor networks. Wirel. Netw. 2017, 23, 2005–2020.
- Ali, I.; Ahmedy, I.; Gani, A.; Munir, M.U.; Anisi, M.H. Data collection in studies on Internet of things (IoT), wireless sensor networks (WSNs), and sensor cloud (SC): Similarities and differences. IEEE Access 2022, 10, 33909–33931.
- Gai, K.; Qiu, M. Optimal resource allocation using reinforcement learning for IoT content-centric services. Appl. Soft Comput. 2018, 70, 12–21.
- Garcia, N.; Wymeersch, H.; Larsson, E.G.; Haimovich, A.M.; Coulon, M. Direct localization for massive MIMO. IEEE Trans. Signal Process. 2017, 65, 2475–2487.
- Björnson, E.; Sanguinetti, L.; Wymeersch, H.; Hoydis, J.; Marzetta, T.L. Massive MIMO is a reality—What is next?: Five promising research directions for antenna arrays. Digit. Signal Process. 2019, 94, 3–20.
- Guo, J.; Wen, C.K.; Jin, S.; Li, G.Y. Convolutional neural network-based multiple-rate compressive sensing for massive MIMO CSI feedback: Design, simulation, and analysis. IEEE Trans. Wirel. Commun. 2020, 19, 2827–2840.
- Nagesh, P.; Li, B. A compressive sensing approach for expression-invariant face recognition. In Proceedings of the 2009 IEEE Conference on Computer Vision and Pattern Recognition, Miami, FL, USA, 20–25 June 2009; pp. 1518–1525.
- Andrés, A.M.; Padovani, S.; Tepper, M.; Jacobo-Berlles, J. Face recognition on partially occluded images using compressed sensing. Pattern Recognit. Lett. 2014, 36, 235–242.
- Jaber, A.K.; Abdel-Qader, I. Hybrid Histograms of Oriented Gradients-compressive sensing framework feature extraction for face recognition. In Proceedings of the 2016 IEEE International Conference on Electro Information Technology (EIT), Grand Forks, ND, USA, 19–21 May 2016; pp. 442–447.
- Akl, A.; Feng, C.; Valaee, S. A novel accelerometer-based gesture recognition system. IEEE Trans. Signal Process. 2011, 59, 6197–6205.
- Wang, Z.W.; Vineet, V.; Pittaluga, F.; Sinha, S.N.; Cossairt, O.; Bing Kang, S. Privacy-preserving action recognition using coded aperture videos. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, Long Beach, CA, USA, 16–17 June 2019.
- Zhuang, H.; Yang, M.; Cui, Z.; Zheng, Q. A method for static hand gesture recognition based on non-negative matrix factorization and compressive sensing. IAENG Int. J. Comput. Sci. 2017, 44, 52–59.
- Sivapalan, S.; Rana, R.K.; Chen, D.; Sridharan, S.; Denmon, S.; Fookes, C. Compressive sensing for gait recognition. In Proceedings of the 2011 International Conference on Digital Image Computing: Techniques and Applications, Noosa, QLD, Australia, 6–8 December 2011; pp. 567–571.
- Pant, J.K.; Krishnan, S. Compressive sensing of foot gait signals and its application for the estimation of clinically relevant time series. IEEE Trans. Biomed. Eng. 2015, 63, 1401–1415.
- Wu, J.; Xu, H. An advanced scheme of compressed sensing of acceleration data for telemonintoring of human gait. Biomed. Eng. Online 2016, 15, 27.
- Yoshida, M.; Torii, A.; Okutomi, M.; Taniguchi, R.i.; Nagahara, H.; Yagi, Y. Deep Sensing for Compressive Video Acquisition. Sensors 2023, 23, 7535.
- Zhao, C.; Ma, S.; Zhang, J.; Xiong, R.; Gao, W. Video compressive sensing reconstruction via reweighted residual sparsity. IEEE Trans. Circuits Syst. Video Technol. 2016, 27, 1182–1195.
- Shi, W.; Liu, S.; Jiang, F.; Zhao, D. Video compressed sensing using a convolutional neural network. IEEE Trans. Circuits Syst. Video Technol. 2020, 31, 425–438.
- Veeraraghavan, A.; Reddy, D.; Raskar, R. Coded strobing photography: Compressive sensing of high speed periodic videos. IEEE Trans. Pattern Anal. Mach. Intell. 2010, 33, 671–686.
- Martel, J.N.; Mueller, L.K.; Carey, S.J.; Dudek, P.; Wetzstein, G. Neural sensors: Learning pixel exposures for HDR imaging and video compressive sensing with programmable sensors. IEEE Trans. Pattern Anal. Mach. Intell. 2020, 42, 1642–1653.
- Dong, D.; Rui, G.; Tian, W.; Liu, G.; Zhang, H. A Multi-Task Bayesian Algorithm for online Compressed Sensing of Streaming Signals. In Proceedings of the 2019 IEEE International Conference on Signal, Information and Data Processing (ICSIDP), Chongqing, China, 11–13 December 2019; pp. 1–5.
- Edgar, M.P.; Sun, M.J.; Gibson, G.M.; Spalding, G.C.; Phillips, D.B.; Padgett, M.J. Real-time 3D video utilizing a compressed sensing time-of-flight single-pixel camera. In Proceedings of the Optical Trapping and Optical Micromanipulation XIII, San Diego, CA, USA, 28 August–1 September 2016; Volume 9922, pp. 171–178.
- Edgar, M.; Johnson, S.; Phillips, D.; Padgett, M. Real-time computational photon-counting LiDAR. Opt. Eng. 2018, 57, 031304.
- Musarra, G.; Lyons, A.; Conca, E.; Villa, F.; Zappa, F.; Altmann, Y.; Faccio, D. 3D RGB non-line-of-sight single-pixel imaging. In Proceedings of the Imaging Systems and Applications, Munich, Germany, 24–27 June 2019; p. IM2B–5.
- Song, J.; Mou, C.; Wang, S.; Ma, S.; Zhang, J. Optimization-Inspired Cross-Attention Transformer for Compressive Sensing. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, Vancouver, BC, Canada, 18–22 June 2023; pp. 6174–6184.
- Candes, E.J.; Plan, Y. A probabilistic and RIPless theory of compressed sensing. IEEE Trans. Inf. Theory 2011, 57, 7235–7254.
- Foucart, S.; Rauhut, H.; Foucart, S.; Rauhut, H. An Invitation to Compressive Sensing; Springer: Berlin/Heidelberg, Germany, 2013.
- Nguyen, T.L.N.; Shin, Y. Deterministic sensing matrices in compressive sensing: A survey. Sci. World J. 2013, 2013, 192795.
- Li, L.; Wen, G.; Wang, Z.; Yang, Y. Efficient and secure image communication system based on compressed sensing for IoT monitoring applications. IEEE Trans. Multimed. 2019, 22, 82–95.
- Zhou, J.; Zhou, D.; Guo, L.; Yoshimura, T.; Goto, S. Framework and vlsi architecture of measurement-domain intra prediction for compressively sensed visual contents. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 2017, 100, 2869–2877.
- Yu, N.Y. Indistinguishability and energy sensitivity of Gaussian and Bernoulli compressed encryption. IEEE Trans. Inf. Forensics Secur. 2018, 13, 1722–1735.
- Moshtaghpour, A.; Bioucas-Dias, J.M.; Jacques, L. Close encounters of the binary kind: Signal reconstruction guarantees for compressive Hadamard sampling with Haar wavelet basis. IEEE Trans. Inf. Theory 2020, 66, 7253–7273.
- Zhuoran, C.; Honglin, Z.; Min, J.; Gang, W.; Jingshi, S. An improved Hadamard measurement matrix based on Walsh code for compressive sensing. In Proceedings of the 2013 9th International Conference on Information, Communications & Signal Processing, Tainan, Taiwan, 10–13 December 2013; pp. 1–4.
- Rauhut, H. Circulant and Toeplitz matrices in compressed sensing. arXiv 2009, arXiv:0902.4394.
- Boyer, C.; Bigot, J.; Weiss, P. Compressed sensing with structured sparsity and structured acquisition. Appl. Comput. Harmon. Anal. 2019, 46, 312–350.
- Sun, M.J.; Meng, L.T.; Edgar, M.P.; Padgett, M.J.; Radwell, N. A Russian Dolls ordering of the Hadamard basis for compressive single-pixel imaging. Sci. Rep. 2017, 7, 3464.
- Yu, W.K. Super sub-Nyquist single-pixel imaging by means of cake-cutting Hadamard basis sort. Sensors 2019, 19, 4122.
- Yu, W.K.; Liu, Y.M. Single-pixel imaging with origami pattern construction. Sensors 2019, 19, 5135.
- López-García, L.; Cruz-Santos, W.; García-Arellano, A.; Filio-Aguilar, P.; Cisneros-Martínez, J.A.; Ramos-García, R. Efficient ordering of the Hadamard basis for single pixel imaging. Opt. Express 2022, 30, 13714–13732.
- Zhou, J.; Xu, J.; Peetakul, J.; Zhou, J. Zigzag Ordered Walsh Matrix for Compressed Sensing Image Sensor. In Proceedings of the 2023 Data Compression Conference (DCC), Snowbird, UT, USA, 21–24 March 2023; p. 346.
- Kulkarni, K.; Lohit, S.; Turaga, P.; Kerviche, R.; Ashok, A. Reconnet: Non-iterative reconstruction of images from compressively sensed measurements. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA, 27–30 June 2016; pp. 449–458.
- Shi, W.; Jiang, F.; Liu, S.; Zhao, D. Image compressed sensing using convolutional neural network. IEEE Trans. Image Process. 2019, 29, 375–388.
- Du, J.; Xie, X.; Wang, C.; Shi, G.; Xu, X.; Wang, Y. Fully convolutional measurement network for compressive sensing image reconstruction. Neurocomputing 2019, 328, 105–112.
- Zhang, Z.; Liu, Y.; Liu, J.; Wen, F.; Zhu, C. AMP-Net: Denoising-based deep unfolding for compressive image sensing. IEEE Trans. Image Process. 2020, 30, 1487–1500.
- Zhang, J.; Zhao, C.; Gao, W. Optimization-inspired compact deep compressive sensing. IEEE J. Sel. Top. Signal Process. 2020, 14, 765–774.
- Zhou, S.; He, Y.; Liu, Y.; Li, C.; Zhang, J. Multi-channel deep networks for block-based image compressive sensing. IEEE Trans. Multimed. 2020, 23, 2627–2640.
- Song, J.; Chen, B.; Zhang, J. Memory-augmented deep unfolding network for compressive sensing. In Proceedings of the 29th ACM International Conference on Multimedia, Virtual Event, 20–24 October 2021; pp. 4249–4258.
- Gao, X.; Zhang, J.; Che, W.; Fan, X.; Zhao, D. Block-based compressive sensing coding of natural images by local structural measurement matrix. In Proceedings of the 2015 Data Compression Conference, Snowbird, UT, USA, 7–9 April 2015; pp. 133–142.
- Wan, R.; Zhou, J.; Huang, B.; Zeng, H.; Fan, Y. Measurement Coding Framework with Adjacent Pixels Based Measurement Matrix for Compressively Sensed Images. In Proceedings of the ICASSP 2021—2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Toronto, ON, Canada, 6–11 June 2021; pp. 1435–1439.

More

Information

Contributors
MDPI registered users' name will be linked to their SciProfiles pages. To register with us, please refer to https://encyclopedia.pub/register
:

View Times:
342

Update Date:
08 Feb 2024