Haut PDF Anisotropic compressed sensing for non-Cartesian MRI acquisitions

Anisotropic compressed sensing for non-Cartesian MRI acquisitions

Anisotropic compressed sensing for non-Cartesian MRI acquisitions

j=1 ka ∗ j k 2 ∞ s ln(n/ε). It was shown experimentally, however, that this result is not sufficient to explain the success of CS in applications such as MRI [1]. It is in particular due to the fact that in the above result we do not assume any structure (apart from sparsity) in the signals to be recovered. A natural extension would be to consider the structured sparsity approach, where one assumes that some prior information on the support S is known, e.g. sparsity by level in the wavelet domain (see [1] for a comprehensive theory for Fourier sampling, based on isolated measurements under a sparsity-by-levels assumption in the wavelet domain). This strategy allows to incorporate any kind of prior information on the structure of S and to study its influence on the quality of CS reconstructions.
En savoir plus

12 En savoir plus

Physically plausible K-space trajectories for Compressed Sensing in MRI: From simulations to real acquisitions

Physically plausible K-space trajectories for Compressed Sensing in MRI: From simulations to real acquisitions

References Conclusions In this work, we have proposed an original computer-intensive approach to design efficient sampling schemes complying with the hardware constraints of MRI gradient systems. On the reconstructed images we have shown significant improvements in terms of image quality (pSNR) in very high resolution anatomical imaging, which makes sense for in-vivo exams at ultra-high magnetic field (ISEULT Project@NeuroSpin). MR acquisitions on 7T MR scanner showed superiority of developed sampling schemes and suggest the feasibility of very high acceleration factor at very high resolution in CS-MRI.
En savoir plus

2 En savoir plus

Calibrationless oscar-based image reconstruction in compressed sensing parallel MRI

Calibrationless oscar-based image reconstruction in compressed sensing parallel MRI

has been successfully applied to MRI [ 3 ], first using Poisson-Disk sampling and then considering more efficient non-Cartesian trajec- tories (e.g. spirals, radial [ 4 ], Sparkling [ 5 , 6 ] ...) that allow to break down the coherence barrier [ 7 , 8 ] using 2D variable density sampling [ 9 , 8 ]. The resulting acceleration factor (e.g. 6 to 10) is larger than those resulting from standard parallel imaging (PI) accel- eration methods. However, for a given image resolution, the max- imum acceleration factor depends on the input Signal-to-Noise Ra- tio (SNR) [ 10 ]. Therefore, to ensure a certain level of SNR, CS has been combined with multiple receiver coils (e.g. parallel imaging or PI [ 11 ]). In this context, many algorithms have been proposed to re- construct MR images from subsampled measurements collected over
En savoir plus

6 En savoir plus

Online MR image reconstruction for compressed sensing acquisition in T2* imaging

Online MR image reconstruction for compressed sensing acquisition in T2* imaging

Reducing acquisition time is a major challenge in high-resolution MRI that has been successfully addressed by Compressed Sensing (CS) theory. While the scan time has been massively accelerated by a factor up to 20 in 2D imaging, the complexity of image recovery algorithms has strongly increased, resulting in slower reconstruction processes. In this work we propose an online approach to shorten image reconstruction times in the CS setting. We leverage the segmented acquisition in multiple shots of k-space data to interleave the MR acquisition and im- age reconstruction steps. This approach is particularly appealing for 2D high-resolution T ∗ 2 -weighted anatomical imaging as the largest timing interval (i.e. Time of Repetition) between consecutive shots arises for this kind of imaging. During the scan, acquired shots are stacked together to form mini-batches and image reconstruction may start from incomplete data. For each newly available mini-batch, the previous partial solution is used as warm restart for the next sub-problem to be solved in a timing window compatible with the given TR and the number of shots stacked in a mini-batch. We demonstrate the interest and time savings of using online MR image reconstruction for Cartesian and non-Cartesian sampling strategies combined with a single receiver coil. Next, we extend the online formalism to address the more general multi-receiver phased array acquisition scenario. In this setting, calibrationless image reconstruction is adopted to remain compatible with the timing constraints of online delivery. Our retrospective and prospective results on ex-vivo 2D T ∗ 2 -weighted brain imaging show that high-quality MR images are recovered by the end of acquisition for single receiver acquisition and that additional iterations are required when parallel imaging is adopted. Overall, our approach implemented through the Gadgetron framework may be compatible with the data workflow on the scanner to provide the physician with reliable MR images for diagnostic purposes.
En savoir plus

16 En savoir plus

Compressed Sensing in MRI : optimization-based design of k-space filling curves for accelerated MRI

Compressed Sensing in MRI : optimization-based design of k-space filling curves for accelerated MRI

There may be two obstacles to the enhanced performance of the proposed strategy for 2D imaging. First, the modest SNR associated with 2D acquisitions may reduce the effectiveness of our method, as for any other subsampled trajectory. Although our exper- iments benefited from relatively good SNR conditions owing to a strong magnetic field and the use of a multiple receiver coil, SNR limitations appeared beyond the highest presented in-plane resolution of 390 µm. The second potential limitation is the hard- ware capacity, namely, the maximum gradient amplitude, the maximum slew rate and the gradient and readout bandwidths, which together control the flexibility and thus, the efficiency of the k-space trajectory. In particular, the gradient raster time plays a critical role and should be as short as possible. Assuming a readout bandwidth larger or equal to the gradient bandwidth, the following practical rule for best SPARKLING use should be observed: the ratio of the number of gradient steps per shot to the image size should be as high as possible. As regards high resolution, long-readout scenarios will maximize this ratio and thus optimize SPARKLING performance, while short-readout acquisitions allow for less departure from simple geometric trajectories. When considering lower resolutions however, our method remains applicable and promising. Moreover, in view of the considerable efforts that are currently being invested to push the limits of gra- dient systems (Weiger et al., 2018) , it is reasonable to expect further improvement of SPARKLING performance.
En savoir plus

157 En savoir plus

High spatiotemporal cineMRI films using compressed sensing for acquiring articulatory data

High spatiotemporal cineMRI films using compressed sensing for acquiring articulatory data

INRIA/CNRS/universit´e de Lorraine † IADI, Universit´e de Lorraine, Nancy, France U947, INSERM, Nancy, France Abstract—The paper presents a method to acquire articulatory data from a sequence of MRI images at a high framerate. The acquisition rate is enhanced by partially collecting data in the kt-space. The combination of compressed sensing technique, along with homodyne reconstruction, enables the missing data to be recovered. The good reconstruction is guaranteed by an appropriate design of the sampling pattern. It is based on a pseudo-random Cartesian scheme, where each line is partially acquired for use of the homodyne reconstruction, and where the lines are pseudo-randomly sampled: central lines are constantly acquired and the sampling density decreases as the lines are far from the center. Application on real speech data show that the framework enables dynamic sequences of vocal tract images to be recovered at a framerate higher than 30 frames per second and with a spatial resolution of 1 mm. A method to extract articulatory data from contour identification is presented. It is intended, in fine, to be used for the creation of a large database of articulatory data.
En savoir plus

6 En savoir plus

An Empirical Study of the Maximum Degree of Undersampling in Compressed Sensing for T2*-weighted MRI

An Empirical Study of the Maximum Degree of Undersampling in Compressed Sensing for T2*-weighted MRI

Regarding the practical utilization of this work, our experimental results appeared to be in good agreement with simulations performed on the analyti- 380 cal brain phantom, which corroborates the validity of our approach to derive a maximum undersampling factor for a given acquisition-reconstruction setup. Our work may thus aid the design of undersampled 3D acquisitions using CS and even 4D MRI, even though prospective performance of compressed MR ac- quisitions may be slightly lower than predicted due to unconsidered MR system

32 En savoir plus

NC-PDNet: a Density-Compensated Unrolled Network for 2D and 3D non-Cartesian MRI Reconstruction

NC-PDNet: a Density-Compensated Unrolled Network for 2D and 3D non-Cartesian MRI Reconstruction

I. I NTRODUCTION Magnetic Resonance Imaging (MRI) is the reference ima- ging technique used to probe soft tissues in the human body non-invasively. The data acquisition process in MRI is inher- ently slow due to the sequential measurements collection in the Fourier domain, also called k-space. This slow acquisition causes many issues such as motion-corrupted scans, limited image resolution in a scan time compatible with clinical routine, non-applicability to certain patients and limited patient throughput. To reduce the scan time as a means to offset the limiting factors, the main solution proposed was to diminish the number of measurements in the k-space. It was exploited for parallel imaging (PI) [2], [3] as well as for the use of Compressed Sensing (CS) in MRI [4]. In this last framework, a manually crafted decomposition basis is used to express the sparsity of the image to be reconstructed in a transform domain. From this sparsity prior, an optimization problem, whose solution should be close to the image of interest, can be constructed.
En savoir plus

11 En savoir plus

Analysis vs Synthesis-based Regularization for combined Compressed Sensing and Parallel MRI Reconstruction at 7 Tesla

Analysis vs Synthesis-based Regularization for combined Compressed Sensing and Parallel MRI Reconstruction at 7 Tesla

VI. C ONCLUSIONS In this paper, we have compared analysis and synthesis- based formulations for compressed sensing MR image recon- struction in the parallel imaging context, i.e. when multiple receivers are combined within the same phased array coil. As already known in the literature, we have shown that translation invariant overcomplete decomposition outperform orthogonal wavelet transforms especially at low input SNR. Well known optimization algorithms have been respectively implemented to minimize the cost functions associated with the analysis and synthesis formulations. We have also pointed out the superiority of the Sparkling under-sampling scheme over the Radial one in terms of quality assessed by SSIM scores. We also provide a Python package, called Pysap, for CS image reconstruction in MRI and astrophysics, interfaced with the pynfft package to deal with non-Cartesian Fourier sampling.
En savoir plus

6 En savoir plus

Quantitative DLA-based compressed sensing for T1-weighted acquisitions.

Quantitative DLA-based compressed sensing for T1-weighted acquisitions.

3 Introduction Recent advances in the static magnetic field strength of magnetic resonance scanners and in the radio-frequency (RF) detector designs has allowed magnetic resonance microscopy (MRM) to reach spatial resolutions suitable for functional imaging of single cells (1,2). However, in order to reach the full potential of MRM it is necessary to reduce the currently long acquisition times required for obtaining high resolution images. Based on the fact that MR images, among other types of images, are compressible, an image can be reconstructed from a small number of random measurements (3). This finding opened the field of Compressed Sensing (CS) which can significantly reduce the MRI scan time and found numerous applications in preclinical (4) and clinical (5) imaging.
En savoir plus

14 En savoir plus

Blind calibration for compressed sensing: State evolution and an online algorithm

Blind calibration for compressed sensing: State evolution and an online algorithm

An ensuing question is whether the calibration could be performed online, that is when different observations are received successively instead of being treated at once. In learning applications, it is sometimes advantageous for speed concerns to only treat a subset of training examples at a time. Sometimes also, the size of the current data sets may exceed the available memory. Methods implementing a step-by-step learning, as the data arrives, are referred to as online, streaming or mini-batch learning, as opposed to offline or batch learning. For instance, in deep learning, Stochastic Gradient Descent is the most popular training algorithm [12]. From the theoretical point of view, the restriction to the fully online case, where a single data point is used at a time, offers interesting possibilities of analysis, as demonstrated in different machine learning problems by [13, 14, 15]. Here we will consider the Bayesian online learning of the calibration variables.
En savoir plus

30 En savoir plus

Exact Performance Analysis of the Oracle Receiver for Compressed Sensing Reconstruction

Exact Performance Analysis of the Oracle Receiver for Compressed Sensing Reconstruction

4. NUMERICAL RESULTS In this section, we show the validity of the results of The- orem 1 by comparing the equations to the results of simu- lations. Here and in the following sections, signal length is N = 512 with sparsity K = 16. M = 128 measurements are taken. The nonzero elements of the signal are distributed as N (0, 1). The sparsity basis Ψ is the DCT matrix. The sensing matrix is composed by i.i.d. elements distributed as zero–mean Gaussian with variance 1/M . The noise vector is Gaussian with zero mean, while the covariance matrix de- pends on the specific test and will be discussed later. The reconstructed signal x is obtained using the oracle estimator. b A different realization of the signal, noise and sensing matrix is drawn for each trial, and the reconstruction error, evaluated as E h k b x − xk 2 2 i , is averaged over 1,000 trials.
En savoir plus

6 En savoir plus

Efficient compressed sensing based non-sample spaced sparse channel estimation in OFDM system

Efficient compressed sensing based non-sample spaced sparse channel estimation in OFDM system

τ ∈T |< f τ , r l−1 >| is not sufficient for accurate delay tracking and channel estimation with high precision. In other words, the delay points within a delay sub- set where the corresponding bases have high coherence with the residual vector, should be considered. With these delay points, the reference delay grid (RDG) guided RNM method is proposed in this paper to effectively fight against the non- uniform pilot arrangement and realize the near optimal delay searching of the l th channel tap, which will be discussed after the DT method in this section.

10 En savoir plus

Anisotropic Fast-Marching on Cartesian Grids Using Lattice Basis Reduction

Anisotropic Fast-Marching on Cartesian Grids Using Lattice Basis Reduction

Denote by y a trial point which minimizes d, and set b(y) ← accepted. For all x ∈ V [y], set d(x) ← min{d(x), Λ(d, x; b, y)}. Output: The map d : Z → IR. We denoted by Λ(d, x; b, y) the modification of the Hopf-Lax update operator (4) in which the minimum is only taken over faces (of any dimension) of ∂V (x) which vertices (i) contain y, and (ii) are all accepted. Regarding the FM-LBR complexity O(N ln N + N ln κ(M)), we refer for details to the classical analysis in [26, 23, 1] and simply point out that (i) each FM-LBR causal stencil costs O(ln κ(M)) to construct, (ii) maintaining a list of Ω∩Z, sorted by increasing values of the mutable map d, costs O(ln N) for each modification of a single value of d, with a proper heap sort implementation, and (iii) the optimization problem defining the Hopf-Lax update (4), or its variant Λ(d, x; b, y), has an explicit solution: the minimum associated to each face of ∂V (x) is the root of a simple univariate quadratic polynomial, see Appendix of [23]. Memory usage is discussed in detail in Remark 1.10.
En savoir plus

29 En savoir plus

Algorithmic solutions toward applications of compressed sensing for optical imaging

Algorithmic solutions toward applications of compressed sensing for optical imaging

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

133 En savoir plus

Analysis of weighted l̳₁-minimization for model based compressed sensing

Analysis of weighted l̳₁-minimization for model based compressed sensing

Specifically we consider the case when the probabilities pi mentioned above are values of a continuous function at uniformly spaced points on a given interval. In t[r]

76 En savoir plus

Multichannel Compressed Sensing and its Application in Radioastronomy

Multichannel Compressed Sensing and its Application in Radioastronomy

the MC method cannot correctly interpolate the data, which means that the following source separation procedure performs badly. Comparing the perfor- mance of DecGMCA with MC+GMCA at its turning points (30% and 60% for the number of channels 20 and 10, respectively), we can see that DecGMCA conserves well the continuity of both criteria and outperforms MC+GMCA even when the mask is very ill-conditioned. One should notice that when mask is relatively good, DecGMCA still outperforms MC+GMCA. This is due to the fact that DecGMCA takes all of the data into account and simultane- ously processes source separation and subsampling effect, while MC+GMCA considers them separately. Consequently, the BSS in MC+GMCA relies on the quality of matrix completion, which in fact approximates the data in- terpolation and produces a negligible bias. Interestingly, the separation per- formances of the DecGMCA seem to degrade when the average number of available measurements per frequency in the Fourier domain (i.e., the product of the subsampling ratio and the total number of observations) is roughly of the order of the number of sources. In that case, the resulting problem is close to an under-determined BSS problem. In that case the identifiability of the sources is not guaranteed unless additional assumptions about the sources are made. In this setting, it is customary to assume that the sources have disjoint supports in the sparse domain, which is not a valid assumption in the present work. Additionally, radio-interferometric measurements are generally composed of a large amount of observations for few sources to be retrieved. Furthermore, in contrast to the fully random masks we considered in these experiments, real interferometric masks exhibit a denser amount of data at low frequency and their evolution across channels is mainly a dilation of the sampling mask in the Fourier domain. This entails that the sampling process across wavelegengths is highly correlated, which is a more favorable setting for BSS. Altogether, these different points highly mitigate the limitations of the DecGMCA algorithm due to subsampling in a realistic inferometric imaging setting.
En savoir plus

203 En savoir plus

Regularized Bayesian compressed sensing in ultrasound imaging

Regularized Bayesian compressed sensing in ultrasound imaging

Index Terms— Ultrasound imaging, compressed sens- ing, Bayesian inference, Markov random field. 1. INTRODUCTION Ultrasound (US) imaging is one of the most popular medi- cal imaging techniques and represents the gold standard in many crucial diagnostic exams such as obstetrics and cardi- ology. The main advantages of US imaging are its relatively low cost, its innocuity for the patient, its ease of use and real time nature. However, the real-time property is sometimes limited by the acquisition time or by the high amount of ac- quired data, especially in 3D ultrasound imaging. Even in 2D applications, a higher frame rate could be beneficial, i.e., for cardiac US monitoring. For this reason, a few research groups have recently started to evaluate the feasibility of US acquisitions using the compressive sampling (CS) framework [1, 2]. In particular, Friboulet et al. have presented in [3] a method for randomly sub-sampling the US raw data (sig- nals before beamforming and classically used in US imag- ing for obtaining the radiofrequency (RF) lines). The idea
En savoir plus

6 En savoir plus

Sampling by blocks of measurements in compressed sensing

Sampling by blocks of measurements in compressed sensing

guide to construct sampling patterns and not as a requirement for perfect recovery. Surprisingly, a better drawing probability distribution reducing the required number of measurements is not the uniform one, as commonly used in [8], [4], but the one depending on the ℓ ∞ -norm of the considered row. B. Block diagonal case

5 En savoir plus

Compressed sensing for the extraction of atrial fibrillation patterns from surface electrocardiograms

Compressed sensing for the extraction of atrial fibrillation patterns from surface electrocardiograms

The results show that the accuracy of CS is lower than ASVC in terms of NMSE when performing on full long recordings. However, a breakthrough finding is the ability of CS to extract AA from a short ECG recording containing only one heartbeat, which is impossible with ASVC, that is said to perform well for significantly longer recordings of at least 10 heartbeats. Based on the observation that CS performs well on short recordings, it is adapted to an online process, where it estimates the AA beat-by-beat from the ECG. This way, our CS approach handles better long recordings. On the other

6 En savoir plus

Show all 10000 documents...