Optimal k-space sampling scheme for compressive sampling MRI
01 Dec 2012-pp 531-534
TL;DR: In this article, a method for optimizing k-space sampling trajectory in compressive sampling MRI (CS-MRI) was presented, where a probability density function (PDF) was proposed to generate sampling trajectories.
Abstract: A method for optimizing k-space sampling trajectory in compressive sampling MRI (CS-MRI) is presented. In k-space, most of the energies are concentrated around the center. When k-space is undersampled, it is required to take most of its higher energy samples for proper CS reconstruction. Therefore more samples are required around the center than the periphery. Using this prior knowledge on k-space energy distribution, a probability density function (PDF) was proposed to generate sampling trajectories. Sampling trajectories were generated for various PDF parameters. These sampling trajectories were applied on the spatial frequency data of fully acquired brain MR images. The optimum sampling trajectory was chosen based on the reconstruction performance. With this optimum trajectory, only 38% of k-space data were required for proper image reconstruction. It was also found that at least 20% of the higher energy samples around the center of k-space were fully required and the rest of the higher energy samples were to be acquired as closely as possible. The optimized sampling trajectory was applied on the simulated k-space data of virtual brain phantom and k-space data of quality assurance phantom. It was verified that the quality of CS reconstructed image matches with the fully reconstructed image.
Citations
More filters
TL;DR: To improve the efficacy of undersampled MRI, a method of designing adaptive sampling functions is proposed that is simple to implement on an MR scanner and yet effectively improves the performance of the sampling functions.
9 citations
01 Aug 2017
TL;DR: Computer simulation results show that the proposed procedure yields better results than other conventional CS-MRI methods in terms of Peak Signal to Noise Ratio (PSNR) and Structural SIMilarity (SSIM) index.
Abstract: In this paper, a hybrid method for acquisition and reconstruction of sparse magnetic resonance images is presented. The method uses conventional spin echo Magnetic Resonance Imaging (MRI) with only a few Phase-encoding steps to obtain the dominant k-space data coefficients. The rest of the k-space data coefficients are estimated using Compressive Sampling (CS). The compressive sampling part of the algorithm uses a random matrix to sample the vectorized k-space data of the image at a sub-Nyquist rate followed by reconstruction of the Discrete Wavelet Transform (DWT) coefficients of the k-space data using Orthogonal Matching Pursuit (OMP). The DWT coefficients are then transformed into the Discrete Fourier Transform (DFT) domain and denoised prior to combination with the dominant DFT coefficients obtained using conventional MRI to yield the whole k-space of the reconstructed image. The reconstructed k-space data is finally transformed into the reconstructed image using inverse DFT. Computer simulation results show that the proposed procedure yields better results than other conventional CS-MRI methods in terms of Peak Signal to Noise Ratio (PSNR) and Structural SIMilarity (SSIM) index.
7 citations
Cites methods from "Optimal k-space sampling scheme for..."
...An optimal k-Space sampling scheme for compressive sampling MRI is proposed in [11]....
[...]
Patent•
25 Feb 2016TL;DR: In this article, a magnetic resonance imaging system (MRI) is used to acquire under-sampled k-space data using a pulse sequence that samples the K-space domain along the derived sampling pattern; apply a compressed sensing reconstruction to the acquired under sampled data to reconstruct an image of the target volume.
Abstract: The present invention relates to a magnetic resonance imaging MRI system (100) for acquiring magnetic resonance data from a target volume in a subject (118), the magnetic resonance imaging system (100) comprises: a memory (136) for storing machine executable instructions; and a processor (130) for controlling the MRI system (100), wherein execution of the machine executable instructions causes the processor (130) to: determine an energy distribution (301-305) over a k-space domain of the target volume; receive a reduction factor representing a degree of under-sampling of the k-space domain; derive from the energy distribution (301-305) and the received reduction factor a sampling density function; derive from the sampling density function an energy dependent sampling pattern of the k-space domain; control the MRI system (100) to acquire under-sampled k-space data using a pulse sequence that samples the k-space domain along the derived sampling pattern; apply a compressed sensing reconstruction to the acquired under-sampled data to reconstruct an image of the target volume.
6 citations
01 Feb 2018
TL;DR: This paper analyses the Cartesian variable density k-space data sampling pattern with the radial sampling scheme and concludes that CS technique violates the Nyquist’s sampling theory by sampling signals at lower rate than conventional sampling rate.
Abstract: Magnetic Resonance (MR) imaging is a non invasive medical imaging technique used widely for diagnosis. The data collected by MRI scanner is placed in the k-space. Various algorithms are developed to sample the k-space and reconstruct the image from the compressive sampled k-space data. The k-space sampling pattern plays an important role in optimizing compressed sensing magnetic resonance imaging. CS technique violates the Nyquist’s sampling theory by sampling signals at lower rate than conventional sampling rate. CS can reduce scanning time in MRI applications by acquiring very few samples. This paper analyses the Cartesian variable density k-space data sampling pattern with the radial sampling scheme. Qualitative and quantitative analysis are performed on the reconstructed MR Image for different sampling percentages.
5 citations
Cites methods from "Optimal k-space sampling scheme for..."
...Generation of Cartesian under sampling pattern The energy distribution of k-space elements is considered for the design the variable density random undersampling technique [7]....
[...]
01 Dec 2018
TL;DR: This paper proposes a robust, fast Magnetic Resonance Imaging (MRI) reconstruction algorithm based on Compressive Sampling, profile of the k-space coefficients and sparsity in the wavelet transform domain, which implies reduction in scan time by approximately 10% for a given image quality.
Abstract: This paper proposes a robust, fast Magnetic Resonance Imaging (MRI) reconstruction algorithm. The method is based on Compressive Sampling (CS), profile of the k-space coefficients and sparsity in the wavelet transform domain. It commences with partial acquisition of the k-space of the image followed by random sampling prior to reconstruction in the wavelet transform domain using a greedy algorithm. The reconstructed wavelet coefficients vector is transformed into the full k-space vector of the image by determining its Inverse Discrete Wavelet Transform (IDWT) domain. The vectorized form of the k-space reveals the reconstruction artifacts which makes it easy to design a denoising filter. The artifacts are then suppressed using an apodization function. The denoised coefficients are then reshaped into a k-space matrix prior to being transformed into the reconstructed image using two-dimensional Inverse Discrete Fourier Transform (2D-IDFT). The Structural SIMilarity (SSIM) and the Peak Signal to Noise Ratio (PSNR) quality metrics are used for quality assessment of the output images. Experimental results show that the proposed method yields an average PSNR improvement of 1.4 dB over the Orthogonal Matching Pursuit (OMP) method at 40% measurements. The improvement implies reduction in scan time by approximately 10% for a given image quality.
2 citations
Cites methods from "Optimal k-space sampling scheme for..."
...A k-space sampling method for CS-MRI is proposed in [21]....
[...]
...It incorporates an apodization function to suppress the reconstruction artifacts that are experienced in the method presented in [21]....
[...]
References
More filters
TL;DR: In this paper, the authors considered the model problem of reconstructing an object from incomplete frequency samples and showed that with probability at least 1-O(N/sup -M/), f can be reconstructed exactly as the solution to the lscr/sub 1/ minimization problem.
Abstract: This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal f/spl isin/C/sup N/ and a randomly chosen set of frequencies /spl Omega/. Is it possible to reconstruct f from the partial knowledge of its Fourier coefficients on the set /spl Omega/? A typical result of this paper is as follows. Suppose that f is a superposition of |T| spikes f(t)=/spl sigma//sub /spl tau//spl isin/T/f(/spl tau/)/spl delta/(t-/spl tau/) obeying |T|/spl les/C/sub M//spl middot/(log N)/sup -1/ /spl middot/ |/spl Omega/| for some constant C/sub M/>0. We do not know the locations of the spikes nor their amplitudes. Then with probability at least 1-O(N/sup -M/), f can be reconstructed exactly as the solution to the /spl lscr//sub 1/ minimization problem. In short, exact recovery may be obtained by solving a convex optimization problem. We give numerical values for C/sub M/ which depend on the desired probability of success. Our result may be interpreted as a novel kind of nonlinear sampling theorem. In effect, it says that any signal made out of |T| spikes may be recovered by convex programming from almost every set of frequencies of size O(|T|/spl middot/logN). Moreover, this is nearly optimal in the sense that any method succeeding with probability 1-O(N/sup -M/) would in general require a number of frequency samples at least proportional to |T|/spl middot/logN. The methodology extends to a variety of other situations and higher dimensions. For example, we show how one can reconstruct a piecewise constant (one- or two-dimensional) object from incomplete frequency samples - provided that the number of jumps (discontinuities) obeys the condition above - by minimizing other convex functionals such as the total variation of f.
14,587 citations
TL;DR: Practical incoherent undersampling schemes are developed and analyzed by means of their aliasing interference and demonstrate improved spatial resolution and accelerated acquisition for multislice fast spin‐echo brain imaging and 3D contrast enhanced angiography.
Abstract: The sparsity which is implicit in MR images is exploited to significantly undersample k -space. Some MR images such as angiograms are already sparse in the pixel representation; other, more complicated images have a sparse representation in some transform domain–for example, in terms of spatial finite-differences or their wavelet coefficients. According to the recently developed mathematical theory of compressedsensing, images with a sparse representation can be recovered from randomly undersampled k -space data, provided an appropriate nonlinear recovery scheme is used. Intuitively, artifacts due to random undersampling add as noise-like interference. In the sparse transform domain the significant coefficients stand out above the interference. A nonlinear thresholding scheme can recover the sparse coefficients, effectively recovering the image itself. In this article, practical incoherent undersampling schemes are developed and analyzed by means of their aliasing interference. Incoherence is introduced by pseudo-random variable-density undersampling of phase-encodes. The reconstruction is performed by minimizing the 1 norm of a transformed image, subject to data
6,653 citations
"Optimal k-space sampling scheme for..." refers methods in this paper
...So, the researchers used variable density random undersampling technique which is based on the energy distribution of k-space [3] [4]....
[...]
...The reconstruction of the image from the undersampled kspace was performed using the nonlinear reconstruction method [4]:...
[...]
...The problem was solved using Conjugate Gradient (CG) method [4]....
[...]
TL;DR: It is shown that ‘1 minimization recovers x 0 exactly when the number of measurements exceeds m Const ·µ 2 (U) ·S · logn, where S is the numberof nonzero components in x 0, and µ is the largest entry in U properly normalized: µ(U) = p n · maxk,j |Uk,j|.
Abstract: We consider the problem of reconstructing a sparse signal x 0 2 R n from a limited number of linear measurements. Given m randomly selected samples of Ux 0 , where U is an orthonormal matrix, we show that ‘1 minimization recovers x 0 exactly when the number of measurements exceeds m Const ·µ 2 (U) ·S · logn, where S is the number of nonzero components in x 0 , and µ is the largest entry in U properly normalized: µ(U) = p n · maxk,j |Uk,j|. The smaller µ, the fewer samples needed. The result holds for “most” sparse signals x 0 supported on a fixed (but arbitrary) set T. Given T, if the sign of x 0 for each nonzero entry on T and the observed values of Ux 0 are drawn at random, the signal is recovered with overwhelming probability. Moreover, there is a sense in which this is nearly optimal since any method succeeding with the same probability would require just about this many samples.
2,187 citations
TL;DR: Simulations, phantom images and in vivo cardiac images show that the variable‐density sampling method can significantly reduce the total energy of aliasing artifacts and can be applied to all types of k‐space sampling trajectories.
Abstract: A variable-density k-space sampling method is proposed to reduce aliasing artifacts in MR images. Because most of the energy of an image is concentrated around the k-space center, aliasing artifacts will contain mostly low-frequency components if the k-space is uniformly undersampled. On the other hand, because the outer k-space region contains little energy, undersampling that region will not contribute severe aliasing artifacts. Therefore, a variable-density trajectory may sufficiently sample the central k-space region to reduce low-frequency aliasing artifacts and may undersample the outer k-space region to reduce scan time and to increase resolution. In this paper, the variable-density sampling method was implemented for both spiral imaging and two-dimensional Fourier transform (2DFT) imaging. Simulations, phantom images and in vivo cardiac images show that this method can significantly reduce the total energy of aliasing artifacts. In general, this method can be applied to all types of k-space sampling trajectories.
260 citations
TL;DR: SIMRI, a new 3D MRI simulator based on the Bloch equation, proposes an efficient management of the T2* effect, and in a unique simulator integrates most of the simulation features that are offered in different simulators.
199 citations
"Optimal k-space sampling scheme for..." refers methods in this paper
...The simulated k-space data was obtained using SIMRI simulator [7]....
[...]