Fluorescence microscopy has been a significant tool to observe long-term imaging of embryos (in vivo) growth over time. However, cumulative exposure is phototoxic to such sensitive live samples. While techniques like light-sheet fluorescence microscopy (LSFM) allow for reduced exposure, it is not well suited for deep imaging models. Other computational techniques are computationally expensive and often lack restoration quality. To address this challenge, one can use various low-dosage imaging techniques that are developed to achieve the 3D volume reconstruction using a few slices in the axial direction (z-axis); however, they often lack restoration quality. Also, acquiring dense images (with small steps) in the axial direction is computationally expensive. To address this challenge, we present a compressive sensing (CS) based approach to fully reconstruct 3D volumes with the same signal-to-noise ratio (SNR) with less than half of the excitation dosage. We present the theory and experimentally validate the approach. To demonstrate our technique, we capture a 3D volume of the RFP labeled neurons in the zebrafish embryo spinal cord (30um thickness) with the axial sampling of 0.1um using a confocal microscope. From the results, we observe the CS-based approach achieves accurate 3D volume reconstruction from less than 20% of the entire stack optical sections. The developed CS-based methodology in this work can be easily applied to other deep imaging modalities such as two-photon and light-sheet microscopy, where reducing sample photo-toxicity is a critical challenge.
https://arxiv.org/abs/2201.00820
Convolution neural networks (CNNs) have succeeded in compressive image sensing. However, due to the inductive bias of locality and weight sharing, the convolution operations demonstrate the intrinsic limitations in modeling the long-range dependency. Transformer, designed initially as a sequence-to-sequence model, excels at capturing global contexts due to the self-attention-based architectures even though it may be equipped with limited localization abilities. This paper proposes CSformer, a hybrid framework that integrates the advantages of leveraging both detailed spatial information from CNN and the global context provided by transformer for enhanced representation learning. The proposed approach is an end-to-end compressive image sensing method, composed of adaptive sampling and recovery. In the sampling module, images are measured block-by-block by the learned sampling matrix. In the reconstruction stage, the measurement is projected into dual stems. One is the CNN stem for modeling the neighborhood relationships by convolution, and the other is the transformer stem for adopting global self-attention mechanism. The dual branches structure is concurrent, and the local features and global representations are fused under different resolutions to maximize the complementary of features. Furthermore, we explore a progressive strategy and window-based transformer block to reduce the parameter and computational complexity. The experimental results demonstrate the effectiveness of the dedicated transformer-based architecture for compressive sensing, which achieves superior performance compared to state-of-the-art methods on different datasets.
https://arxiv.org/abs/2112.15299
Hyperspectral imaging is an essential imaging modality for a wide range of applications, especially in remote sensing, agriculture, and medicine. Inspired by existing hyperspectral cameras that are either slow, expensive, or bulky, reconstructing hyperspectral images (HSIs) from a low-budget snapshot measurement has drawn wide attention. By mapping a truncated numerical optimization algorithm into a network with a fixed number of phases, recent deep unfolding networks (DUNs) for spectral snapshot compressive sensing (SCI) have achieved remarkable success. However, DUNs are far from reaching the scope of industrial applications limited by the lack of cross-phase feature interaction and adaptive parameter adjustment. In this paper, we propose a novel Hyperspectral Explicable Reconstruction and Optimal Sampling deep Network for SCI, dubbed HerosNet, which includes several phases under the ISTA-unfolding framework. Each phase can flexibly simulate the sensing matrix and contextually adjust the step size in the gradient descent step, and hierarchically fuse and interact the hidden states of previous phases to effectively recover current HSI frames in the proximal mapping step. Simultaneously, a hardware-friendly optimal binary mask is learned end-to-end to further improve the reconstruction performance. Finally, our HerosNet is validated to outperform the state-of-the-art methods on both simulation and real datasets by large margins.
https://arxiv.org/abs/2112.06238
Over the last decades, images have become an important source of information in many domains, thus their high quality has become necessary to acquire better information. One of the important issues that arise is image denoising, which means recovering a signal from inaccurately and/or partially measured samples. This interpretation is highly correlated to the compressive sensing theory, which is a revolutionary technology and implies that if a signal is sparse then the original signal can be obtained from a few measured values, which are much less, than the ones suggested by other used theories like Shannon's sampling theories. A strong factor in Compressive Sensing (CS) theory to achieve the sparsest solution and the noise removal from the corrupted image is the selection of the basis dictionary. In this paper, Discrete Cosine Transform (DCT) and moment transform (Tchebichef, Krawtchouk) are compared in order to achieve image denoising of Gaussian additive white noise based on compressive sensing and sparse approximation theory. The experimental results revealed that the basis dictionaries constructed by the moment transform perform competitively to the traditional DCT. The latter transform shows a higher PSNR of 30.82 dB and the same 0.91 SSIM value as the Tchebichef transform. Moreover, from the sparsity point of view, Krawtchouk moments provide approximately 20-30% more sparse results than DCT.
https://arxiv.org/abs/2111.07254
Recent development in brain-machine interface technology has made seizure prediction possible. However, the communication of large volume of electrophysiological signals between sensors and processing apparatus and related computation become two major bottlenecks for seizure prediction systems due to the constrained bandwidth and limited computation resource, especially for wearable and implantable medical devices. Although compressive sensing (CS) can be adopted to compress the signals to reduce communication bandwidth requirement, it needs a complex reconstruction procedure before the signal can be used for seizure prediction. In this paper, we propose C$^2$SP-Net, to jointly solve compression, prediction, and reconstruction with a single neural network. A plug-and-play in-sensor compression matrix is constructed to reduce transmission bandwidth requirement. The compressed signal can be used for seizure prediction without additional reconstruction steps. Reconstruction of the original signal can also be carried out in high fidelity. Prediction accuracy, sensitivity, false prediction rate, and reconstruction quality of the proposed framework are evaluated under various compression ratios. The experimental results illustrate that our model outperforms the competitive state-of-the-art baselines by a large margin in prediction accuracy. In particular, our proposed method produces an average loss of 0.35 % in prediction accuracy with a compression ratio ranging from 1/2 to 1/16.
https://arxiv.org/abs/2110.13674
Mapping a truncated optimization method into a deep neural network, deep unfolding network (DUN) has attracted growing attention in compressive sensing (CS) due to its good interpretability and high performance. Each stage in DUNs corresponds to one iteration in optimization. By understanding DUNs from the perspective of the human brain's memory processing, we find there exists two issues in existing DUNs. One is the information between every two adjacent stages, which can be regarded as short-term memory, is usually lost seriously. The other is no explicit mechanism to ensure that the previous stages affect the current stage, which means memory is easily forgotten. To solve these issues, in this paper, a novel DUN with persistent memory for CS is proposed, dubbed Memory-Augmented Deep Unfolding Network (MADUN). We design a memory-augmented proximal mapping module (MAPMM) by combining two types of memory augmentation mechanisms, namely High-throughput Short-term Memory (HSM) and Cross-stage Long-term Memory (CLM). HSM is exploited to allow DUNs to transmit multi-channel short-term memory, which greatly reduces information loss between adjacent stages. CLM is utilized to develop the dependency of deep information across cascading stages, which greatly enhances network representation capability. Extensive CS experiments on natural and MR images show that with the strong ability to maintain and balance information our MADUN outperforms existing state-of-the-art methods by a large margin. The source code is available at this https URL.
https://arxiv.org/abs/2110.09766
Aiming at high-dimensional (HD) data acquisition and analysis, snapshot compressive imaging (SCI) obtains the 2D compressed measurement of HD data with optical imaging systems and reconstructs HD data using compressive sensing algorithms. While the Plug-and-Play (PnP) framework offers an emerging solution to SCI reconstruction, its intrinsic denoising process is still a challenging problem. Unfortunately, existing denoisers in the PnP framework either suffer limited performance or require extensive training data. In this paper, we propose an efficient and effective shallow-learning-based algorithm for video SCI reconstruction. Revisiting dictionary learning methods, we empower the PnP framework with a new denoiser, the kernel singular value decomposition (KSVD). Benefited from the advent of KSVD, our algorithm retains a good trade-off among quality, speed, and training difficulty. On a variety of datasets, both quantitative and qualitative evaluations of our simulation results demonstrate the effectiveness of our proposed method. In comparison to a typical baseline using total variation, our method achieves around $2$ dB improvement in PSNR and 0.2 in SSIM. We expect that our proposed PnP-KSVD algorithm can serve as a new baseline for video SCI reconstruction.
https://arxiv.org/abs/2110.04966
This paper presents a scalable approximate Bayesian method for image restoration using total variation (TV) priors. In contrast to most optimization methods based on maximum a posteriori estimation, we use the expectation propagation (EP) framework to approximate minimum mean squared error (MMSE) estimators and marginal (pixel-wise) variances, without resorting to Monte Carlo sampling. For the classical anisotropic TV-based prior, we also propose an iterative scheme to automatically adjust the regularization parameter via expectation-maximization (EM). Using Gaussian approximating densities with diagonal covariance matrices, the resulting method allows highly parallelizable steps and can scale to large images for denoising, deconvolution and compressive sensing (CS) problems. The simulation results illustrate that such EP methods can provide a posteriori estimates on par with those obtained via sampling methods but at a fraction of the computational cost. Moreover, EP does not exhibit strong underestimation of posteriori variances, in contrast to variational Bayes alternatives.
https://arxiv.org/abs/2110.01585
Communication systems at millimeter-wave (mmW) and sub-terahertz frequencies are of increasing interest for future high-data rate networks. One critical challenge faced by phased array systems at these high frequencies is the efficiency of the initial beam alignment, typically using only phase-less power measurements due to high frequency oscillator phase noise. Traditional methods for beam alignment require exhaustive sweeps of all possible beam directions, thus scale communications overhead linearly with antenna array size. For better scaling with the large arrays required at high mmW bands, compressive sensing methods have been proposed as their overhead scales logarithmically with the array size. However, algorithms utilizing machine learning have shown more efficient and more accurate alignment when using real hardware due to array impairments. Additionally, few existing phase-less beam alignment algorithms have been tested over varied secondary path strength in multipath channels. In this work, we introduce a novel, machine learning based algorithm for beam alignment in multipath environments using only phase-less received power measurements. We consider the impacts of phased array sounding beam design and machine learning architectures on beam alignment performance and validate our findings experimentally using 60 GHz radios with 36-element phased arrays. Using experimental data in multipath channels, our proposed algorithm demonstrates an 88\% reduction in beam alignment overhead compared to an exhaustive search and at least a 62\% reduction in overhead compared to existing compressive methods.
毫米波(mmW)和微带波频率的通信系统对于未来的高数据传输网络越来越具有吸引力。在这些高频率下的聚光 array 系统面临的一个重要挑战是初始光束对齐的效率,通常只能使用无相位的能量测量,因为高频率振荡器相位噪声。传统的光束对齐方法需要遍历所有可能光束方向,因此通信 overhead 与天线阵列尺寸呈线性增长。为了与高 mmW Band 所需的大型阵列更好地 scaling,压缩感知方法被提出作为其 overhead 与阵列尺寸的指数级增长相关联。然而,由于 array impairments,使用 real hardware 时利用机器学习算法的光束对齐方法表现出更高效和更准确的对齐。此外, few 现有的无相位光束对齐算法已经在多相通道中进行了测试,其中 secondary path 强度因多种原因而变化。在本文中,我们提出了一种基于机器学习的新颖算法,用于在多相环境中使用的光束对齐,仅使用无相位接收功率测量。我们考虑了聚光 array sounding 光束设计和机器学习架构对光束对齐性能的影响,并使用 60 GHz 并具有 36 element 聚光 array 的通信电台实验验证我们的发现。利用多相通道的实验数据,我们提出的算法表明相较于 exhaustive 搜索,光束对齐 overhead 有 88\% 的减少,并且相较于现有的压缩方法,有至少 62\% 的 overhead 减少。
https://arxiv.org/abs/2109.14689
Dual-view snapshot compressive imaging (SCI) aims to capture videos from two field-of-views (FoVs) using a 2D sensor (detector) in a single snapshot, achieving joint FoV and temporal compressive sensing, and thus enjoying the advantages of low-bandwidth, low-power, and low-cost. However, it is challenging for existing model-based decoding algorithms to reconstruct each individual scene, which usually require exhaustive parameter tuning with extremely long running time for large scale data. In this paper, we propose an optical flow-aided recurrent neural network for dual video SCI systems, which provides high-quality decoding in seconds. Firstly, we develop a diversity amplification method to enlarge the differences between scenes of two FoVs, and design a deep convolutional neural network with dual branches to separate different scenes from the single measurement. Secondly, we integrate the bidirectional optical flow extracted from adjacent frames with the recurrent neural network to jointly reconstruct each video in a sequential manner. Extensive results on both simulation and real data demonstrate the superior performance of our proposed model in a short inference time. The code and data are available at this https URL.
https://arxiv.org/abs/2109.05287
Multilinear Compressive Learning (MCL) is an efficient signal acquisition and learning paradigm for multidimensional signals. The level of signal compression affects the detection or classification performance of a MCL model, with higher compression rates often associated with lower inference accuracy. However, higher compression rates are more amenable to a wider range of applications, especially those that require low operating bandwidth and minimal energy consumption such as Internet-of-Things (IoT) applications. Many communication protocols provide support for adaptive data transmission to maximize the throughput and minimize energy consumption. By developing compressive sensing and learning models that can operate with an adaptive compression rate, we can maximize the informational content throughput of the whole application. In this paper, we propose a novel optimization scheme that enables such a feature for MCL models. Our proposal enables practical implementation of adaptive compressive signal acquisition and inference systems. Experimental results demonstrated that the proposed approach can significantly reduce the amount of computations required during the training phase of remote learning systems but also improve the informational content throughput via adaptive-rate sensing.
https://arxiv.org/abs/2109.01184
Recovering an underlying image from under-sampled measurements, Compressive Sensing Imaging (CSI) is a challenging problem and has many practical applications. Recently, deep neural networks have been applied to this problem with promising results, owing to its implicitly learned prior to alleviate the ill-poseness of CSI. However, existing neural network approaches require separate models for each imaging parameter like sampling ratios, leading to training difficulties and overfitting to specific settings. In this paper, we present a dynamic proximal unrolling network (dubbed DPUNet), which can handle a variety of measurement matrices via one single model without retraining. Specifically, DPUNet can exploit both embedded physical model via gradient descent and imposing image prior with learned dynamic proximal mapping leading to joint reconstruction. A key component of DPUNet is a dynamic proximal mapping module, whose parameters can be dynamically adjusted at inference stage and make it adapt to any given imaging setting. Experimental results demonstrate that the proposed DPUNet can effectively handle multiple CSI modalities under varying sampling ratios and noise levels with only one model, and outperform the state-of-the-art approaches.
https://arxiv.org/abs/2107.11007
Recent deep network-based compressive sensing (CS) methods have achieved great success. However, most of them regard different sampling matrices as different independent tasks and need to train a specific model for each target sampling matrix. Such practices give rise to inefficiency in computing and suffer from poor generalization ability. In this paper, we propose a novel COntrollable Arbitrary-Sampling neTwork, dubbed COAST, to solve CS problems of arbitrary-sampling matrices (including unseen sampling matrices) with one single model. Under the optimization-inspired deep unfolding framework, our COAST exhibits good interpretability. In COAST, a random projection augmentation (RPA) strategy is proposed to promote the training diversity in the sampling space to enable arbitrary sampling, and a controllable proximal mapping module (CPMM) and a plug-and-play deblocking (PnP-D) strategy are further developed to dynamically modulate the network features and effectively eliminate the blocking artifacts, respectively. Extensive experiments on widely used benchmark datasets demonstrate that our proposed COAST is not only able to handle arbitrary sampling matrices with one single model but also to achieve state-of-the-art performance with fast speed. The source code is available on this https URL.
https://arxiv.org/abs/2107.07225
Compressed sensing (CS) is an efficient method to reconstruct MR image from small sampled data in $k$-space and accelerate the acquisition of MRI. In this work, we propose a novel deep geometric distillation network which combines the merits of model-based and deep learning-based CS-MRI methods, it can be theoretically guaranteed to improve geometric texture details of a linear reconstruction. Firstly, we unfold the model-based CS-MRI optimization problem into two sub-problems that consist of image linear approximation and image geometric compensation. Secondly, geometric compensation sub-problem for distilling lost texture details in approximation stage can be expanded by Taylor expansion to design a geometric distillation module fusing features of different geometric characteristic domains. Additionally, we use a learnable version with adaptive initialization of the step-length parameter, which allows model more flexibility that can lead to convergent smoothly. Numerical experiments verify its superiority over other state-of-the-art CS-MRI reconstruction approaches. The source code will be available at \url{this https URL}
https://arxiv.org/abs/2107.04943
Fourier single-pixel imaging (FSI) is a branch of single-pixel imaging techniques. It uses Fourier basis patterns as structured patterns for spatial information acquisition in the Fourier domain. However, the spatial resolution of the image reconstructed by FSI mainly depends on the number of Fourier coefficients sampled. The reconstruction of a high-resolution image typically requires a number of Fourier coefficients to be sampled, and therefore takes a long data acquisition time. Here we propose a new sampling strategy for FSI. It allows FSI to reconstruct a clear and sharp image with a reduced number of measurements. The core of the proposed sampling strategy is to perform a variable density sampling in the Fourier space and, more importantly, the density with respect to the importance of Fourier coefficients is subject to a one-dimensional Gaussian function. Combined with compressive sensing, the proposed sampling strategy enables better reconstruction quality than conventional sampling strategies, especially when the sampling ratio is low. We experimentally demonstrate compressive FSI combined with the proposed sampling strategy is able to reconstruct a sharp and clear image of 256-by-256 pixels with a sampling ratio of 10%. The proposed method enables fast single-pixel imaging and provides a new approach for efficient spatial information acquisition.
https://arxiv.org/abs/2108.02317
Random projection is a common technique for designing algorithms in a variety of areas, including information retrieval, compressive sensing and measuring of outlyingness. In this work, the original random projection outlyingness measure is modified and associated with a neural network to obtain an unsupervised anomaly detection method able to handle multimodal normality. Theoretical and experimental arguments are presented to justify the choices of the anomaly score estimator, the dimensions of the random projections, and the number of such projections. The contribution of adapted dropouts is investigated, along with the affine stability of the proposed method. The performance of the proposed neural network approach is comparable to a state-of-the-art anomaly detection method. Experiments conducted on the MNIST, Fashion-MNIST and CIFAR-10 datasets show the relevance of the proposed approach, and suggest a possible extension to a semi-supervised setup.
https://arxiv.org/abs/2106.15307
We address the detection of material defects, which are inside a layered material structure using compressive sensing based multiple-output (MIMO) wireless radar. Here, the strong clutter due to the reflection of the layered structure's surface often makes the detection of the defects challenging. Thus, sophisticated signal separation methods are required for improved defect detection. In many scenarios, the number of defects that we are interested in is limited and the signaling response of the layered structure can be modeled as a low-rank structure. Therefore, we propose joint rank and sparsity minimization for defect detection. In particular, we propose a non-convex approach based on the iteratively reweighted nuclear and $\ell_1-$norm (a double-reweighted approach) to obtain a higher accuracy compared to the conventional nuclear norm and $\ell_1-$norm minimization. To this end, an iterative algorithm is designed to estimate the low-rank and sparse contributions. Further, we propose deep learning to learn the parameters of the algorithm (i.e., algorithm unfolding) to improve the accuracy and the speed of convergence of the algorithm. Our numerical results show that the proposed approach outperforms the conventional approaches in terms of mean square errors of the recovered low-rank and sparse components and the speed of convergence.
https://arxiv.org/abs/2106.03686
The plug-and-play priors (PnP) and regularization by denoising (RED) methods have become widely used for solving inverse problems by leveraging pre-trained deep denoisers as image priors. While the empirical imaging performance and the theoretical convergence properties of these algorithms have been widely investigated, their recovery properties have not previously been theoretically analyzed. We address this gap by showing how to establish theoretical recovery guarantees for PnP/RED by assuming that the solution of these methods lies near the fixed-points of a deep neural network. We also present numerical results comparing the recovery performance of PnP/RED in compressive sensing against that of recent compressive sensing algorithms based on generative models. Our numerical results suggest that PnP with a pre-trained artifact removal network provides significantly better results compared to the existing state-of-the-art methods.
https://arxiv.org/abs/2106.03668
In this work we introduce a novel stochastic algorithm dubbed SNIPS, which draws samples from the posterior distribution of any linear inverse problem, where the observation is assumed to be contaminated by additive white Gaussian noise. Our solution incorporates ideas from Langevin dynamics and Newton's method, and exploits a pre-trained minimum mean squared error (MMSE) Gaussian denoiser. The proposed approach relies on an intricate derivation of the posterior score function that includes a singular value decomposition (SVD) of the degradation operator, in order to obtain a tractable iterative algorithm for the desired sampling. Due to its stochasticity, the algorithm can produce multiple high perceptual quality samples for the same noisy observation. We demonstrate the abilities of the proposed paradigm for image deblurring, super-resolution, and compressive sensing. We show that the samples produced are sharp, detailed and consistent with the given measurements, and their diversity exposes the inherent uncertainty in the inverse problem being solved.
https://arxiv.org/abs/2105.14951
We address the problem of compressed sensing using a deep generative prior model and consider both linear and learned nonlinear sensing mechanisms, where the nonlinear one involves either a fully connected neural network or a convolutional neural network. Recently, it has been argued that the distribution of natural images do not lie in a single manifold but rather lie in a union of several submanifolds. We propose a sparsity-driven latent space sampling (SDLSS) framework and develop a proximal meta-learning (PML) algorithm to enforce sparsity in the latent space. SDLSS allows the range-space of the generator to be considered as a union-of-submanifolds. We also derive the sample complexity bounds within the SDLSS framework for the linear measurement model. The results demonstrate that for a higher degree of compression, the SDLSS method is more efficient than the state-of-the-art method. We first consider a comparison between linear and nonlinear sensing mechanisms on Fashion-MNIST dataset and show that the learned nonlinear version is superior to the linear one. Subsequent comparisons with the deep compressive sensing (DCS) framework proposed in the literature are reported. We also consider the effect of the dimension of the latent space and the sparsity factor in validating the SDLSS framework. Performance quantification is carried out by employing three objective metrics: peak signal-to-noise ratio (PSNR), structural similarity index metric (SSIM), and reconstruction error (RE).
https://arxiv.org/abs/2105.11956