An Introduction To Compressive Sampling [A sensing/sampling paradigm that goes against the common knowledge in data acquisition]

This article surveys the theory of compressive sampling, also known as compressed sensing or CS, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition. CS theory asserts that one can recover certain signals and images from far fewer samples or measurements than traditional methods use. To make this possible, CS relies on two principles: sparsity, which pertains to the signals of interest, and incoherence, which pertains to the sensing modality. Our intent in this article is to overview the basic CS theory that emerged in the works [1]–[3], present the key mathematical ideas underlying this theory, and survey a couple of important results in the field. Our goal is to explain CS as plainly as possible, and so our article is mainly of a tutorial nature. One of the charms of this theory is that it draws from various subdisciplines within the applied mathematical sciences, most notably probability theory. In this review, we have decided to highlight this aspect and especially the fact that randomness can — perhaps surprisingly — lead to very effective sensing mechanisms. We will also discuss significant implications, explain why CS is a concrete protocol for sensing and compressing data simultaneously (thus the name), and conclude our tour by reviewing important applications

Optimizing and method development for clinical MR imaging near metallic implants

Metallic hip prosthesis is an implant that gets more common and comes with problems like metallosis (inflammation due to metallic debris). Magnetic resonance imaging (MRI) which is a superior method when imaging soft tissue (compared to other medical imaging techniques) is affected by metal implants and will result in a distorted image. View Angle Tilting (VAT) and Slice Encoding for Metal Artifact Correction (SEMAC) are techniques which can reduce both in-plane and through-plane distortions. Unfortunately do the SEMAC technique come with a drawback of increased scan times. To acheive more acceptable scan times in the clinic,a new method, called Compressed Sensing can be used in combinationwith VAT and SEMAC. This method which reconstructs data using fewersamples than before thought was required will reduce the scan time. A phantom (hip prosthesis surrounded with agarose gel) was used toinvestigate how much the sampling can be reduced, while still retainingan image with good quality. The data was presented in different domainswhich were individually investigated for an optimized performance of thereconstruction algorithm. Fully sampled data was imported into Matlaband afterwards undersampled. Compressed Sensing was used to reconstructthe images and a comparison was done with the original images. Even with low sampling (40% data) Compressed Sensing can reconstructimages with no significant loss of image quality. SEMAC imagestoday fit the restriction of Compressed Sensing and by implementing themethod the SEMAC technique can be more acessible in clinical practice,thereby improving the diagnosis of patients with metallic prosteses

Time-Frequency Signal Representations using Interpolations in Joint-Variable Domains

Abstract-Time-frequency representations are a powerful tool for analyzing Doppler and microDoppler signals. These signals are frequently encountered in various radar applications. Data interpolators play a unique role in time-frequency signal representations under missing samples. When applied in the instantaneous autocorrelation domain over the time variable, the low-pass filter characteristic underlying linear interpolators lends itself to cross-terms reduction in the ambiguity domain. This is in contrast to interpolation performed over the lag variable or a direct interpolation of the raw data. We demonstrate the interpolator performance in both the time-domain and time-lag domain and compare it with sparse signal reconstruction, which exploits the local sparsity property assumed by most Doppler radar signals

Compressed Sensing And Joint Acquisition Techniques In Mri

The relatively long scan times in Magnetic Resonance Imaging (MRI) limits some clinical applications and the ability to collect more information in a reasonable period of time. Practically, 3D imaging requires longer acquisitions which can lead to a reduction in image quality due to motion artifacts, patient discomfort, increased costs to the healthcare system and loss of profit to the imaging center. The emphasis in reducing scan time has been to a large degree through using limited k-space data acquisition and special reconstruction techniques. Among these approaches are data extrapolation methods such as constrained reconstruction techniques, data interpolation methods such as parallel imaging, and more recently another technique known as Compressed Sensing (CS). In order to recover the image components from far fewer measurements, CS exploits the compressible nature of MR images by imposing randomness in k-space undersampling schemes. In this work, we explore some intuitive examples of CS reconstruction leading to a primitive algorithm for CS MR imaging. Then, we demonstrate the application of this algorithm to MR angiography (MRA) with the goal of reducing the scan time. Our results showed reconstructions with comparable results to the fully sampled MRA images, providing up to three times faster image acquisition via CS. The CS performance in recovery of the vessels in MRA, showed slightly shrinkage of both the width of and amplitude of the vessels in 20% undersampling scheme. The spatial location of the vessels however remained intact during CS reconstruction. Another direction we pursue is the introduction of joint acquisition for accelerated multi data point MR imaging such as multi echo or dynamic imaging. Keyhole imaging and view sharing are two techniques for accelerating dynamic acquisitions, where some k-space data is shared between neighboring acquisitions. In this work, we combine the concept of CS random sampling with keyhole imaging and view sharing techniques, in order to improve the performance of each method by itself and reduce the scan time. Finally, we demonstrate the application of this new method in multi-echo spin echo (MSE) T2 mapping and compare the results with conventional methods. Our proposed technique can potentially provide up to 2.7 times faster image acquisition. The percentage difference error maps created from T2 maps generated from images with joint acquisition and fully sampled images, have a histogram with a 5-95 percentile of less than 5% error. This technique can potentially be applied to other dynamic imaging acquisitions such as multi flip angle T1 mapping or time resolved contrast enhanced MRA

Compressive Direct Imaging of a Billion-Dimensional Optical Phase-Space

Optical phase-spaces represent fields of any spatial coherence, and are typically measured through phase-retrieval methods involving a computational inversion, interference, or a resolution-limiting lenslet array. Recently, a weak-values technique demonstrated that a beam's Dirac phase-space is proportional to the measurable complex weak-value, regardless of coherence. These direct measurements require scanning through all possible position-polarization couplings, limiting their dimensionality to less than 100,000. We circumvent these limitations using compressive sensing, a numerical protocol that allows us to undersample, yet efficiently measure high-dimensional phase-spaces. We also propose an improved technique that allows us to directly measure phase-spaces with high spatial resolution and scalable frequency resolution. With this method, we are able to easily measure a 1.07-billion-dimensional phase-space. The distributions are numerically propagated to an object placed in the beam path, with excellent agreement. This protocol has broad implications in signal processing and imaging, including recovery of Fourier amplitudes in any dimension with linear algorithmic solutions and ultra-high dimensional phase-space imaging.Comment: 7 pages, 5 figures. Added new larger dataset and fixed typo

Effect of sparsity-aware time–frequency analysis on dynamic hand gesture classification with radar micro-Doppler signatures

Dynamic hand gesture recognition is of great importance in human-computer interaction. In this study, the authors investigate the effect of sparsity-driven time-frequency analysis on hand gesture classification. The time-frequency spectrogram is first obtained by sparsity-driven time-frequency analysis. Then three empirical micro-Doppler features are extracted from the time-frequency spectrogram and a support vector machine is used to classify six kinds of dynamic hand gestures. The experimental results on measured data demonstrate that, compared to traditional time-frequency analysis techniques, sparsity-driven time-frequency analysis provides improved accuracy and robustness in dynamic hand gesture classification

Time-frequency Signature Sparse Reconstruction using Chirp Dictionary

This paper considers local sparse reconstruction of time-frequency signatures of windowed non-stationary radar returns. These signals can be considered instantaneously narrow-band, thus the local time-frequency behaviour can be recovered accurately with incomplete observations. The typically employed sinusoidal dictionary induces competing requirements on window length. It confronts converse requests on the number of measurements for exact recovery, and sparsity. In this paper, we use chirp dictionary for each window position to determine the signal instantaneous frequency laws. This approach can considerably mitigate the problems of sinusoidal dictionary, and enable the utilization of longer windows for accurate time-frequency representations. It also reduces the picket fence by introducing a new factor, the chirp rate . Simulation examples are provided, demonstrating the superior performance of local chirp dictionary over its sinusoidal counterpart

Compressed Sensing Based Reconstruction Algorithm for X-ray Dose Reduction in Synchrotron Source Micro Computed Tomography

Synchrotron computed tomography requires a large number of angular projections to reconstruct tomographic images with high resolution for detailed and accurate diagnosis. However, this exposes the specimen to a large amount of x-ray radiation. Furthermore, this increases scan time and, consequently, the likelihood of involuntary specimen movements. One approach for decreasing the total scan time and radiation dose is to reduce the number of projection views needed to reconstruct the images. However, the aliasing artifacts appearing in the image due to the reduced number of projection data, visibly degrade the image quality. According to the compressed sensing theory, a signal can be accurately reconstructed from highly undersampled data by solving an optimization problem, provided that the signal can be sparsely represented in a predefined transform domain. Therefore, this thesis is mainly concerned with designing compressed sensing-based reconstruction algorithms to suppress aliasing artifacts while preserving spatial resolution in the resulting reconstructed image. First, the reduced-view synchrotron computed tomography reconstruction is formulated as a total variation regularized compressed sensing problem. The Douglas-Rachford Splitting and the randomized Kaczmarz methods are utilized to solve the optimization problem of the compressed sensing formulation. In contrast with the first part, where consistent simulated projection data are generated for image reconstruction, the reduced-view inconsistent real ex-vivo synchrotron absorption contrast micro computed tomography bone data are used in the second part. A gradient regularized compressed sensing problem is formulated, and the Douglas-Rachford Splitting and the preconditioned conjugate gradient methods are utilized to solve the optimization problem of the compressed sensing formulation. The wavelet image denoising algorithm is used as the post-processing algorithm to attenuate the unwanted staircase artifact generated by the reconstruction algorithm. Finally, a noisy and highly reduced-view inconsistent real in-vivo synchrotron phase-contrast computed tomography bone data are used for image reconstruction. A combination of prior image constrained compressed sensing framework, and the wavelet regularization is formulated, and the Douglas-Rachford Splitting and the preconditioned conjugate gradient methods are utilized to solve the optimization problem of the compressed sensing formulation. The prior image constrained compressed sensing framework takes advantage of the prior image to promote the sparsity of the target image. It may lead to an unwanted staircase artifact when applied to noisy and texture images, so the wavelet regularization is used to attenuate the unwanted staircase artifact generated by the prior image constrained compressed sensing reconstruction algorithm. The visual and quantitative performance assessments with the reduced-view simulated and real computed tomography data from canine prostate tissue, rat forelimb, and femoral cortical bone samples, show that the proposed algorithms have fewer artifacts and reconstruction errors than other conventional reconstruction algorithms at the same x-ray dose