Compressive sensing with variable density sampling for 3D imaging

Compressive sampling (CS), or Compressed Sensing , has generated a tremendous amount of excitement in the signal processing community. Compressive sampling, which involves non-traditional samples in the form of randomized projections, can capture most of the salient information in a signal with a relatively small number of samples, often far fewer samples than required using traditional sampling schemes. Adaptive sampling (AS), also called Active Learning , uses information gleaned from previous observations (e.g. , feedback) to focus the sampling process. Theoretical and experimental results have shown that adaptive sampling can dramatically outperform conventional (non-adaptive) sampling schemes. This paper compares the theoretical performance of compressive and adaptive sampling for regression in noisy conditions, and it is shown that for certain classes of piecewise constant signals and high SNR regimes both CS and AS are near optimal. This result is remarkable since it is the first evidence that shows that compressive sampling, which is non-adaptive, cannot be significantly outperformed by any other method (including adaptive sampling procedures), even in the presence of noise. The performance of CS schemes for signal detection is also investigated.© (2006) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Compressed sensing (CS) provides an efficient way to acquire and reconstruct natural images from a reduced number of linear projection measurements at sub-Nyquist sampling rates. A key to the success of CS is the design of the measurement ensemble. This paper addresses the design of a novel variable density sampling strategy, where the “a priori” information about the statistical distributions that natural images exhibit in the wavelet domain is exploited. Compared to the current sampling schemes for compressed image sampling, the proposed variable density sampling has the following advantages: 1) The number of necessary measurements for image reconstruction is reduced; 2) The proposed sampling approach can be applied to several transform domains leading to simple implementations. In particular, the proposed method is applied to the compressed sampling in the 2D ordered discrete Hadamard transform (DHT) domain for spatial domain imaging. Furthermore, to evaluate the incoherence of different sampling schemes, a new metric that incorporates the “a priori” information is also introduced. Extensive simulations show the effectiveness of the proposed sampling methods.

This study proposes and evaluates a novel method for generating efficient undersampling patterns for 3D Cartesian acquisition with compressed sensing (CS) and parallel imaging (PI). Image quality achieved with schemes that accelerate data acquisition, including CS and PI, are sensitive to the design of the specific undersampling scheme used. Ideally random sampling is required to recover MR images from undersampled data with CS. In practice, pseudo-random sampling schemes are usually applied. Radial or spiral sampling either for Cartesian or non-Cartesian acquisitions has been using because of its favorable features such as interleaving flexibility. In this study, we propose to undersample data on the ky-kz plane of the 3D Cartesian acquisition by circularly selecting sampling points in a way that maintains the features of both random and radial or spiral sampling. The proposed sampling scheme is shown to outperform conventional random and radial or spiral samplings for 3D Cartesian acquisition and is found to be comparable to advanced variable-density Poisson-Disk sampling (vPDS) while retaining interleaving flexibility for dynamic imaging, based on the results with retrospective undersampling. Our preliminary results with the prospective implementation of the proposed undersampling strategy demonstrated its favorable features. The proposed undersampling patterns for 3D Cartesian acquisition possess the desirable properties of randomization and radial or spiral trajectories. It provides easy implementation, flexible sampling, and high accuracy of image reconstruction with CS and PI.

Reducing acquisition time is of fundamental importance in various imaging\nmodalities. The concept of variable density sampling provides a nice framework\nto achieve this. It was justified recently from a theoretical point of view in\nthe compressed sensing (CS) literature. Unfortunately, the sampling schemes\nsuggested by current CS theories may not be relevant since they do not take the\nacquisition constraints into account (for example, continuity of the\nacquisition trajectory in Magnetic Resonance Imaging - MRI). In this paper, we\npropose a numerical method to perform variable density sampling with block\nconstraints. Our main contribution is to propose a new way to draw the blocks\nin order to mimic CS strategies based on isolated measurements. The basic idea\nis to minimize a tailored dissimilarity measure between a probability\ndistribution defined on the set of isolated measurements and a probability\ndistribution defined on a set of blocks of measurements. This problem turns out\nto be convex and solvable in high dimension. Our second contribution is to\ndefine an efficient minimization algorithm based on Nesterov's accelerated\ngradient descent in metric spaces. We study carefully the choice of the metrics\nand of the prox function. We show that the optimal choice may depend on the\ntype of blocks under consideration. Finally, we show that we can obtain better\nMRI reconstruction results using our sampling schemes than standard strategies\nsuch as equiangularly distributed radial lines.\n

Compressed sensing (CS) sampling is a sampling method which is based on the signal sparse. Much information can be extracted from as little as possible of the data by applying CS and this method is the idea of great theoretical and applied prospects. In the framework of compressed sensing theory, the sampling rate is no longer decided in the bandwidth of the signal, but it depends on the structure and content of the information in the signal. In this paper, the signal is the sparse in the Fourier transform and random sparse sampling is advanced by programing random observation matrix for peak random base. The signal is successfully restored by the use of Bregman algorithm. The signal is described in the transform space, and a theoretical framework is established with a new signal descriptions and processing. By making the case to ensure that the information loss, signal is sampled at much lower than the Nyquist sampling theorem requiring rate,but also the signal is completely restored in high probability. The random sampling has following advantages: alias-free sampling frequency need not obey the Nyquist limit and higher frequency resolution.

Aiming at improving the computational efficiency of compressed sensing (CS) algorithms for linear array synthetic aperture radar (LASAR) three dimensional (3D) imaging, a fast compressed sensing imaging algorithm via the Otsu algorithm (FCSIO) is proposed in this paper. Firstly, the Grayscale value and initial Grayscale thresholds of LASAR echo signals are obtained to classify the echo signals into echo signals of targets and background echo signals. Secondly, the variance between targets and background's echo signals under every Grayscale threshold is calculated to quantify the difference between targets and background's echo signals, the optimal Grayscale threshold and classification results are obtained under the maximum variance. Finally, the possible targets echo signals are extracted for 3D high-quality imaging by the optimal Grayscale threshold and the Grayscale value of echo signals. Compared with traditional CS algorithms, FCSIO algorithm has translated the 3D imaging with whole echoes into imaging processing according to the possible targets echoes, and reduces the computational complexity effectively. Meanwhile, FCSIO algorithm improves the imaging quality by eliminating the influence of signal noise and false targets. Simulation and experimental results prove the effectiveness of FCSIO algorithm for LASAR 3D sparse imaging.

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) needs high temporal and spatial resolution to accurately estimate quantitative parameters and characterize tumor vasculature. Compressed Sensing (CS) has the potential to accomplish this mutual importance. However, the randomness in CS under-sampling trajectory designed using the traditional variable density (VD) scheme may translate to uncertainty in kinetic parameter estimation when high reduction factors are used. Therefore, accurate parameter estimation using VD scheme usually needs multiple adjustments on parameters of Probability Density Function (PDF), and multiple reconstructions even with fixed PDF, which is inapplicable for DCE-MRI. In this paper, an under-sampling trajectory design which is robust to the change on PDF parameters and randomness with fixed PDF is studied. The strategy is to adaptively segment k-space into low-and high frequency domain, and only apply VD scheme in high-frequency domain. Simulation results demonstrate high accuracy and robustness comparing to VD design.

Compressed Sensing with Gaussian Sampling Kernel for Ultrasound Imaging

The compressive sensing (CS) framework states that a signal that has a sparse representation in a known basis may be reconstructed from samples obtained at a sub-Nyquist sampling rate. The Fourier domain is widely used in CS applications due to its inherent properties. Sparse signal recovery applications using a small number of Fourier transform coefficients have made solutions to large-scale data recovery problems, including image recovery problems, more practical. The sparse reconstruction of 2D images is performed using the sampling patterns generated by taking the general frequency characteristics of the images into account. In this work, instead of forming a general sampling pattern for infrared (IR) images, a special sampling pattern is obtained by gathering a database to extract the frequency characteristics of IR sea-surveillance images. Experimental results show that the proposed sampling pattern provides better sparse recovery results compared to the widely used patterns proposed in the literature. It is also shown that, together with a certain image dataset, the sampling pattern generated by the proposed scheme can be generalized for various image sparse recovery applications.

Towards practical implementation of the compressed sensing framework for multi-element synthetic transmit aperture imaging

Nuclear magnetic resonance (NMR) spectroscopy is widely used across the physical, chemical, and biological sciences. A core component of NMR studies is multidimensional experiments, which enable correlation of properties from one or more NMR‐active nuclei. In high‐resolution biomolecular NMR, common nuclei are 1H, 15N, and 13C, and triple resonance experiments using these three nuclei form the backbone of NMR structural studies. In other fields, a range of other nuclei may be used. Multidimensional NMR experiments provide unparalleled information content, but this comes at the price of long experiment times required to achieve the necessary resolution and sensitivity. Non‐uniform sampling (NUS) techniques to reduce the required data sampling have existed for many decades. Recently, such techniques have received heightened interest due to the development of compressed sensing (CS) methods for reconstructing spectra from such NUS datasets. When applied jointly, these methods provide a powerful approach to dramatically improve the resolution of spectra per time unit and under suitable conditions can also lead to signal‐to‐noise ratio improvements. In this review, we explore the basis of NUS approaches, the fundamental features of NUS reconstruction using CS and applications based on CS approaches including the benefits of expanding the repertoire of biomolecular NMR experiments into higher dimensions. We discuss some of the recent algorithms and software packages and provide practical tips for recording and processing NUS data by CS.

This paper introduces a compressive sampling (CS) scheme for pulse stream images. We adopt a particular sparse sampling matrix, that we call Radon-like CS matrix. Whilst the Radon transform evaluates projections of a given image along different directions, the Radon-like CS matrix evaluates randomly weighted projections of the image along a few directions. We demonstrate that the such CS measurements are invertible and assess the reconstruction accuracy of CS with the Radonlike sampling matrix by numerical trials. The Radon-like CS performs almost as well as state of the art techniques, with a reduced number of operations. As an application example, we show that, when implemented in a resource limited framework such as a Smart Sensors Grid, the sampling matrix significantly reduces inter-node signaling and then the associated energy consumption. © 2012 IEEE.

Compressed sensing (CS) leverages signal sparsity in transform domains to facilitate precise signal reconstruction from restricted incoherent measurements. While effectively applied in turbomachinery flow field measurements, current compressed sensing reconstruction research primarily emphasizes random sampling within limited instrumentation parameters, resulting in a significant knowledge deficit regarding high-frequency reconstruction from time-domain uniformly undersampled data. This study addresses this limitation by developing compressed sensing-enhanced temporal resolution for unsteady flow field measurements in compressor cascades. This research presents and implements a dual low-frequency uniform sampling compressive sensing approach for particle image velocimetry analysis in the near-wake areas of compressor blades. The effectiveness of the strategy was validated through comparative analysis with random sampling CS reconstruction. Second, a sensitivity analysis was performed on the principal factors influencing reconstruction accuracy in dual low-frequency sampling CS, including the orthogonal basis, compression ratio, and modal order. The dual low-frequency uniform sampling strategy is ultimately extended to multi-low-frequency sampling, hence confirming the robustness of generalized multi-frequency CS implementations. The findings indicate that the dual low-frequency uniform sampling CS technique markedly decreases the need for instrumentation frequency responsiveness while maintaining measurement reliability. This study develops a methodological framework for high-resolution physical field measurements in turbomachinery applications, providing theoretical foundations and practical implementation guidelines for CS-enhanced experimental fluid dynamics.

Compressive Sensing (CS) is a stable and robust technique that allows for the sub-sampling of data at a given data rate: ‘compressive sampling’ or ‘compressive sensing’ at rates smaller than the Nyquist sampling rate. It makes it possible to create standalone and net-centric applications with fewer resources required in Internet of Things (IoT). CS-based signal and information acquisition/compression paradigm combines the nonlinear reconstruction algorithm and random sampling on a sparse basis that provides a promising approach to compress signal and data in information systems. In this paper, we investigates how CS can provide new insights into coexisting heterogeneous IoT environments. First, we briefly introduce the CS theory with respect to the sampling through providing a compressed sampling process with low computation costs. Then, a CS-based framework is proposed for IoT, in which the hub nodes measure, transmit, and store the sampled data into the fusion center. Then, an efficient cluster-sparse reconstruction algorithm is proposed for in-network compression aiming at more accurate data reconstruction and lower energy efficiency. Therefore, compression should be performed locally at each Access Point (AP) and reconstruction is executed jointly to consider dependencies in the acquired data by the final fusion center.

The purpose of this study was to compare between compressed sensing (CS) and deep learning (DL) accelerated T1ρ mapping in knee cartilage, a quantitative imaging technique that provides valuable information for disease diagnosis but requires long scan time. Both retrospectively and prospectively undersampled reconstruction were evaluated in nine volunteers including three with diagnosed pathology. For data collection, DESS images were collected for segmentation of six cartilage compartments. T1ρ-weighted 3D MAPSS sequence was used to create T1ρ maps. A 3T MRI scanner was used and GRAPPA 2 accelerated data were collected to provide 8-echo reference T1ρ maps and was retrospectively undersampled for reconstruction with two sampling schemes: 4 TSLs with each echo image undersampled by 4 (UF4_4echo), and 8 TSLs with each echo image undersampled by 8 (UF8_8echo). Separate prospectively undersampled datasets were also collected for reconstruction. Volunteers were scanned and rescanned with repositioning for repeatability comparison. Reference, retrospectively undersampled reconstruction, and prospectively undersampled reconstruction were compared by voxel-wise median normalized absolute differences (MNADs), concordance correlation coefficient (CCC), and coefficient of variation (CV) using cartilage compartment-wise mean value. As a result, for retrospective undersampling, CS showed CCC 0.992, MNAD 10.0%, and CV 1.3% for UF4_4echo, and CCC 0.988, MNAD 9.9%, and CV 1.4% for UF8_8echo. DL showed CCC 0.971, MNAD 9.8%, and CV 1.7% for UF4_4echo, and CCC 0.968, MNAD 10.6%, and CV 1.7% for UF8_8echo. For prospective undersampling, CS showed CCC 0.853 and CV 3.3% for UF4_4echo, and CCC 0.754 and CV 3.9% for UF8_8echo. DL showed CCC 0.939 and CV 2.4% for UF4_4echo and CCC 0.845 and CV 2.8% for UF8_8echo. The maps had 2.57%, 3.80%, 2.79%, 2.29%, and 2.85% scan-rescan CV, respectively, for reference, CS UF4_4echo, CS UF8_8echo, DL UF4_4echo, and DL UF8_8echo reconstructions. As a conclusion, DL provided better results compared to CS in prospectively undersampled reconstruction.