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15 pages, 10503 KiB

Open AccessArticle

MRI Reconstruction Using Markov Random Field and Total Variation as Composite Prior

by Marko Panić, Dušan Jakovetić, Dejan Vukobratović, Vladimir Crnojević and Aleksandra Pižurica

Sensors 2020, 20(11), 3185; https://doi.org/10.3390/s20113185 - 3 Jun 2020

Cited by 1 | Viewed by 2978

Abstract

Reconstruction of magnetic resonance images (MRI) benefits from incorporating a priori knowledge about statistical dependencies among the representation coefficients. Recent results demonstrate that modeling intraband dependencies with Markov Random Field (MRF) models enable superior reconstructions compared to inter-scale models. In this paper, we [...] Read more.

Reconstruction of magnetic resonance images (MRI) benefits from incorporating a priori knowledge about statistical dependencies among the representation coefficients. Recent results demonstrate that modeling intraband dependencies with Markov Random Field (MRF) models enable superior reconstructions compared to inter-scale models. In this paper, we develop a novel reconstruction method, which includes a composite prior based on an MRF model and Total Variation (TV). We use an anisotropic MRF model and propose an original data-driven method for the adaptive estimation of its parameters. From a Bayesian perspective, we define a new position-dependent type of regularization and derive a compact reconstruction algorithm with a novel soft-thresholding rule. Experimental results show the effectiveness of this method compared to the state of the art in the field. Full article

(This article belongs to the Special Issue Compressed Sensing in Biomedical Signal and Image Analysis)

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18 pages, 3506 KiB

Open AccessArticle

Sparse Analyzer Tool for Biomedical Signals

by Stefan Vujović, Andjela Draganić, Maja Lakičević Žarić, Irena Orović, Miloš Daković, Marko Beko and Srdjan Stanković

Sensors 2020, 20(9), 2602; https://doi.org/10.3390/s20092602 - 2 May 2020

Cited by 5 | Viewed by 3335

Abstract

The virtual (software) instrument with a statistical analyzer for testing algorithms for biomedical signals’ recovery in compressive sensing (CS) scenario is presented. Various CS reconstruction algorithms are implemented with the aim to be applicable for different types of biomedical signals and different applications [...] Read more.

The virtual (software) instrument with a statistical analyzer for testing algorithms for biomedical signals’ recovery in compressive sensing (CS) scenario is presented. Various CS reconstruction algorithms are implemented with the aim to be applicable for different types of biomedical signals and different applications with under-sampled data. Incomplete sampling/sensing can be considered as a sort of signal damage, where missing data can occur as a result of noise or the incomplete signal acquisition procedure. Many approaches for recovering the missing signal parts have been developed, depending on the signal nature. Here, several approaches and their applications are presented for medical signals and images. The possibility to analyze results using different statistical parameters is provided, with the aim to choose the most suitable approach for a specific application. The instrument provides manifold possibilities such as fitting different parameters for the considered signal and testing the efficiency under different percentages of missing data. The reconstruction accuracy is measured by the mean square error (MSE) between original and reconstructed signal. Computational time is important from the aspect of power requirements, thus enabling the selection of a suitable algorithm. The instrument contains its own signal database, but there is also the possibility to load any external data for analysis. Full article

(This article belongs to the Special Issue Compressed Sensing in Biomedical Signal and Image Analysis)

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19 pages, 2096 KiB

Open AccessArticle

Deep Compressed Sensing for Learning Submodular Functions

by Yu-Chung Tsai and Kuo-Shih Tseng

Sensors 2020, 20(9), 2591; https://doi.org/10.3390/s20092591 - 2 May 2020

Cited by 9 | Viewed by 2899

Abstract

The AI community has been paying attention to submodular functions due to their various applications (e.g., target search and 3D mapping). Learning submodular functions is a challenge since the number of a function’s outcomes of N sets is

2^{N}

. The state-of-the-art [...] Read more.

The AI community has been paying attention to submodular functions due to their various applications (e.g., target search and 3D mapping). Learning submodular functions is a challenge since the number of a function’s outcomes of N sets is

2^{N}

. The state-of-the-art approach is based on compressed sensing techniques, which are to learn submodular functions in the Fourier domain and then recover the submodular functions in the spatial domain. However, the number of Fourier bases is relevant to the number of sets’ sensing overlapping. To overcome this issue, this research proposed a submodular deep compressed sensing (SDCS) approach to learning submodular functions. The algorithm consists of learning autoencoder networks and Fourier coefficients. The learned networks can be applied to predict

2^{N}

values of submodular functions. Experiments conducted with this approach demonstrate that the algorithm is more efficient than the benchmark approach. Full article

(This article belongs to the Special Issue Compressed Sensing in Biomedical Signal and Image Analysis)

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19 pages, 602 KiB

Open AccessArticle

Enhancing Compression Level for More Efficient Compressed Sensing and Other Lessons from NMR Spectroscopy

by Dariusz Gołowicz, Paweł Kasprzak and Krzysztof Kazimierczuk

Sensors 2020, 20(5), 1325; https://doi.org/10.3390/s20051325 - 28 Feb 2020

Cited by 9 | Viewed by 4187

Abstract

Modern nuclear magnetic resonance spectroscopy (NMR) is based on two- and higher-dimensional experiments that allow the solving of molecular structures, i.e., determine the relative positions of single atoms very precisely. However, rich chemical information comes at the price of long data acquisition times [...] Read more.

Modern nuclear magnetic resonance spectroscopy (NMR) is based on two- and higher-dimensional experiments that allow the solving of molecular structures, i.e., determine the relative positions of single atoms very precisely. However, rich chemical information comes at the price of long data acquisition times (up to several days). This problem can be alleviated by compressed sensing (CS)—a method that revolutionized many fields of technology. It is known that CS performs the most efficiently when measured objects feature a high level of compressibility, which in the case of NMR signal means that its frequency domain representation (spectrum) has a low number of significant points. However, many NMR spectroscopists are not aware of the fact that various well-known signal acquisition procedures enhance compressibility and thus should be used prior to CS reconstruction. In this study, we discuss such procedures and show to what extent they are complementary to CS approaches. We believe that the survey will be useful not only for NMR spectroscopists but also to inspire the broader signal processing community. Full article

(This article belongs to the Special Issue Compressed Sensing in Biomedical Signal and Image Analysis)

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22 pages, 5287 KiB

Open AccessArticle

Suppressing the Spikes in Electroencephalogram via an Iterative Joint Singular Spectrum Analysis and Low-Rank Decomposition Approach

by Zikang Tian, Bingo Wing-Kuen Ling, Xueling Zhou, Ringo Wai-Kit Lam and Kok-Lay Teo

Sensors 2020, 20(2), 341; https://doi.org/10.3390/s20020341 - 7 Jan 2020

Cited by 4 | Viewed by 2843

Abstract

The novelty and the contribution of this paper consists of applying an iterative joint singular spectrum analysis and low-rank decomposition approach for suppressing the spikes in an electroencephalogram. First, an electroencephalogram is filtered by an ideal lowpass filter via removing its discrete Fourier [...] Read more.

The novelty and the contribution of this paper consists of applying an iterative joint singular spectrum analysis and low-rank decomposition approach for suppressing the spikes in an electroencephalogram. First, an electroencephalogram is filtered by an ideal lowpass filter via removing its discrete Fourier transform coefficients outside the

δ

wave band, the

θ

wave band, the

α

wave band, the

β

wave band and the

γ

wave band. Second, the singular spectrum analysis is performed on the filtered electroencephalogram to obtain the singular spectrum analysis components. The singular spectrum analysis components are sorted according to the magnitudes of their corresponding eigenvalues. The singular spectrum analysis components are sequentially added together starting from the last singular spectrum analysis component. If the variance of the summed singular spectrum analysis component under the unit energy normalization is larger than a threshold value, then the summation is terminated. The summed singular spectrum analysis component forms the first scale of the electroencephalogram. The rest singular spectrum analysis components are also summed up together separately to form the residue of the electroencephalogram. Next, the low-rank decomposition is performed on the residue of the electroencephalogram to obtain both the low-rank component and the sparse component. The low-rank component is added to the previous scale of the electroencephalogram to obtain the next scale of the electroencephalogram. Finally, the above procedures are repeated on the sparse component until the variance of the current scale of the electroencephalogram under the unit energy normalization is larger than another threshold value. The computer numerical simulation results show that the spike suppression performance based on our proposed method outperforms that based on the state-of-the-art methods. Full article

(This article belongs to the Special Issue Compressed Sensing in Biomedical Signal and Image Analysis)

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14 pages, 6273 KiB

Open AccessArticle

Reference-Driven Compressed Sensing MR Image Reconstruction Using Deep Convolutional Neural Networks without Pre-Training

by Di Zhao, Feng Zhao and Yongjin Gan

Sensors 2020, 20(1), 308; https://doi.org/10.3390/s20010308 - 6 Jan 2020

Cited by 27 | Viewed by 5549

Abstract

Deep learning has proven itself to be able to reduce the scanning time of Magnetic Resonance Imaging (MRI) and to improve the image reconstruction quality since it was introduced into Compressed Sensing MRI (CS-MRI). However, the requirement of using large, high-quality, and patient-based [...] Read more.

Deep learning has proven itself to be able to reduce the scanning time of Magnetic Resonance Imaging (MRI) and to improve the image reconstruction quality since it was introduced into Compressed Sensing MRI (CS-MRI). However, the requirement of using large, high-quality, and patient-based datasets for network training procedures is always a challenge in clinical applications. In this paper, we propose a novel deep learning based compressed sensing MR image reconstruction method that does not require any pre-training procedure or training dataset, thereby largely reducing clinician dependence on patient-based datasets. The proposed method is based on the Deep Image Prior (DIP) framework and uses a high-resolution reference MR image as the input of the convolutional neural network in order to induce the structural prior in the learning procedure. This reference-driven strategy improves the efficiency and effect of network learning. We then add the k-space data correction step to enforce the consistency of the k-space data with the measurements, which further improve the image reconstruction accuracy. Experiments on in vivo MR datasets showed that the proposed method can achieve more accurate reconstruction results from undersampled k-space data. Full article

(This article belongs to the Special Issue Compressed Sensing in Biomedical Signal and Image Analysis)

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17 pages, 5912 KiB

Open AccessArticle

Improvement of Fast Model-Based Acceleration of Parameter Look-Locker T₁ Mapping

by Michał Staniszewski and Uwe Klose

Sensors 2019, 19(24), 5371; https://doi.org/10.3390/s19245371 - 5 Dec 2019

Cited by 2 | Viewed by 2904

Abstract

Quantitative mapping is desirable in many scientific and clinical magneric resonance imaging (MRI) applications. Recent inverse recovery-look locker sequence enables single-shot T₁ mapping with a time of a few seconds but the main computational load is directed into offline reconstruction, which can [...] Read more.

Quantitative mapping is desirable in many scientific and clinical magneric resonance imaging (MRI) applications. Recent inverse recovery-look locker sequence enables single-shot T₁ mapping with a time of a few seconds but the main computational load is directed into offline reconstruction, which can take from several minutes up to few hours. In this study we proposed improvement of model-based approach for T₁-mapping by introduction of two steps fitting procedure. We provided analysis of further reduction of k-space data, which lead us to decrease of computational time and perform simulation of multi-slice development. The region of interest (ROI) analysis of human brain measurements with two different initial models shows that the differences between mean values with respect to a reference approach are in white matter—0.3% and 1.1%, grey matter—0.4% and 1.78% and cerebrospinal fluid—2.8% and 11.1% respectively. With further improvements we were able to decrease the time of computational of single slice to 6.5 min and 23.5 min for different initial models, which has been already not achieved by any other algorithm. In result we obtained an accelerated novel method of model-based image reconstruction in which single iteration can be performed within few seconds on home computer. Full article

(This article belongs to the Special Issue Compressed Sensing in Biomedical Signal and Image Analysis)

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17 pages, 4109 KiB

Open AccessArticle

A Low-Complexity Compressed Sensing Reconstruction Method for Heart Signal Biometric Recognition

by Jian Xiao, Fang Hu, Qiang Shao and Sizhuo Li

Sensors 2019, 19(23), 5330; https://doi.org/10.3390/s19235330 - 3 Dec 2019

Cited by 13 | Viewed by 3844

Abstract

Biometric systems allow recognition and verification of an individual through his or her physiological or behavioral characteristics. It is a growing field of research due to the increasing demand for secure and trustworthy authentication systems. Compressed sensing is a data compression acquisition method [...] Read more.

Biometric systems allow recognition and verification of an individual through his or her physiological or behavioral characteristics. It is a growing field of research due to the increasing demand for secure and trustworthy authentication systems. Compressed sensing is a data compression acquisition method that has been proposed in recent years. The sampling and compression of data is completed synchronously, avoiding waste of resources and meeting the requirements of small size and limited power consumption of wearable portable devices. In this work, a compression reconstruction method based on compression sensing was studied using bioelectric signals, which aimed to increase the limited resources of portable remote bioelectric signal recognition equipment. Using electrocardiograms (ECGs) and photoplethysmograms (PPGs) of heart signals as research data, an improved segmented weak orthogonal matching pursuit (OMP) algorithm was developed to compress and reconstruct the signals. Finally, feature values were extracted from the reconstructed signals for identification and analysis. The accuracy of the proposed method and the practicability of compression sensing in cardiac signal identification were verified. Experiments showed that the reconstructed ECG and PPG signal recognition rates were 95.65% and 91.31%, respectively, and that the residual value was less than 0.05 mV, which indicates that the proposed method can be effectively used for two bioelectric signal compression reconstructions. Full article

(This article belongs to the Special Issue Compressed Sensing in Biomedical Signal and Image Analysis)

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21 pages, 9707 KiB

Open AccessArticle

3D Tensor Based Nonlocal Low Rank Approximation in Dynamic PET Reconstruction

by Nuobei Xie, Yunmei Chen and Huafeng Liu

Sensors 2019, 19(23), 5299; https://doi.org/10.3390/s19235299 - 1 Dec 2019

Cited by 8 | Viewed by 3492

Abstract

Reconstructing images from multi-view projections is a crucial task both in the computer vision community and in the medical imaging community, and dynamic positron emission tomography (PET) is no exception. Unfortunately, image quality is inevitably degraded by the limitations of photon emissions and [...] Read more.

Reconstructing images from multi-view projections is a crucial task both in the computer vision community and in the medical imaging community, and dynamic positron emission tomography (PET) is no exception. Unfortunately, image quality is inevitably degraded by the limitations of photon emissions and the trade-off between temporal and spatial resolution. In this paper, we develop a novel tensor based nonlocal low-rank framework for dynamic PET reconstruction. Spatial structures are effectively enhanced not only by nonlocal and sparse features, but momentarily by tensor-formed low-rank approximations in the temporal realm. Moreover, the total variation is well regularized as a complementation for denoising. These regularizations are efficiently combined into a Poisson PET model and jointly solved by distributed optimization. The experiments demonstrated in this paper validate the excellent performance of the proposed method in dynamic PET. Full article

(This article belongs to the Special Issue Compressed Sensing in Biomedical Signal and Image Analysis)

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15 pages, 7697 KiB

Open AccessArticle

Single-Pixel Imaging with Origami Pattern Construction

by Wen-Kai Yu and Yi-Ming Liu

Sensors 2019, 19(23), 5135; https://doi.org/10.3390/s19235135 - 23 Nov 2019

Cited by 45 | Viewed by 4530

Abstract

Single-pixel compressive imaging can recover images from fewer measurements, offering many benefits especially for the imaging modalities where array detection is unavailable. However, the widely used random projections fail to explore internal relations between coding patterns and image reconstruction. Here, we propose a [...] Read more.

Single-pixel compressive imaging can recover images from fewer measurements, offering many benefits especially for the imaging modalities where array detection is unavailable. However, the widely used random projections fail to explore internal relations between coding patterns and image reconstruction. Here, we propose a single-pixel imaging method based on a deterministic origami pattern construction that can lead to a more accurate pattern ordering sequence and better imaging quality. It can decrease the sampling ratio, closer to the upper bounds. The experimental realization of this approach is a big step forward towards practical applications. Full article

(This article belongs to the Special Issue Compressed Sensing in Biomedical Signal and Image Analysis)

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Review

Jump to: Research

21 pages, 562 KiB

Open AccessReview

Trends in Compressive Sensing for EEG Signal Processing Applications

by Dharmendra Gurve, Denis Delisle-Rodriguez, Teodiano Bastos-Filho and Sridhar Krishnan

Sensors 2020, 20(13), 3703; https://doi.org/10.3390/s20133703 - 2 Jul 2020

Cited by 39 | Viewed by 5217

Abstract

The tremendous progress of big data acquisition and processing in the field of neural engineering has enabled a better understanding of the patient’s brain disorders with their neural rehabilitation, restoration, detection, and diagnosis. An integration of compressive sensing (CS) and neural engineering emerges [...] Read more.

The tremendous progress of big data acquisition and processing in the field of neural engineering has enabled a better understanding of the patient’s brain disorders with their neural rehabilitation, restoration, detection, and diagnosis. An integration of compressive sensing (CS) and neural engineering emerges as a new research area, aiming to deal with a large volume of neurological data for fast speed, long-term, and energy-saving purposes. Furthermore, electroencephalography (EEG) signals for brain–computer interfaces (BCIs) have shown to be very promising, with diverse neuroscience applications. In this review, we focused on EEG-based approaches which have benefited from CS in achieving fast and energy-saving solutions. In particular, we examine the current practices, scientific opportunities, and challenges of CS in the growing field of BCIs. We emphasized on summarizing major CS reconstruction algorithms, the sparse basis, and the measurement matrix used in CS to process the EEG signal. This literature review suggests that the selection of a suitable reconstruction algorithm, sparse basis, and measurement matrix can help to improve the performance of current CS-based EEG studies. In this paper, we also aim at providing an overview of the reconstruction free CS approach and the related literature in the field. Finally, we discuss the opportunities and challenges that arise from pushing the integration of the CS framework for BCI applications. Full article

(This article belongs to the Special Issue Compressed Sensing in Biomedical Signal and Image Analysis)

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