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Juan M. Santos

Bio: Juan M. Santos is an academic researcher from Stanford University. The author has contributed to research in topics: Real-time MRI & Aliasing. The author has an hindex of 20, co-authored 45 publications receiving 3773 citations. Previous affiliations of Juan M. Santos include Pontifical Catholic University of Chile.

Papers
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Journal ArticleDOI
TL;DR: The authors emphasize on an intuitive understanding of CS by describing the CS reconstruction as a process of interference cancellation, and there is also an emphasis on the understanding of the driving factors in applications.
Abstract: This article reviews the requirements for successful compressed sensing (CS), describes their natural fit to MRI, and gives examples of four interesting applications of CS in MRI. The authors emphasize on an intuitive understanding of CS by describing the CS reconstruction as a process of interference cancellation. There is also an emphasis on the understanding of the driving factors in applications, including limitations imposed by MRI hardware, by the characteristics of different types of images, and by clinical concerns.

2,134 citations

01 Jan 2006
TL;DR: A method for high frame-rate dynamic imaging based on similar ideas, now exploiting both spatial and temporal sparsity of dynamic MRI image sequences (dynamic scene) by exploiting sparsity by constraining the reconstruction to have a sparse representation and be consistent with the measured data by solving the constrained optimization problem.
Abstract: M. Lustig, J. M. Santos, D. L. Donoho, J. M. Pauly Electrical Engineering, Stanford University, Stanford, CA, United States, Statistics, Stanford University, Stanford, CA, United States Introduction Recently rapid imaging methods that exploit the spatial sparsity of images using under-sampled randomly perturbed spirals and non-linear reconstruction have been proposed [1,2]. These methods were inspired by theoretical results in sparse signal recovery [1-5] showing that sparse or compressible signals can be recovered from randomly under-sampled frequency data. We propose a method for high frame-rate dynamic imaging based on similar ideas, now exploiting both spatial and temporal sparsity of dynamic MRI image sequences (dynamic scene). We randomly under-sample k-t space by random ordering of the phase encodes in time (Fig. 1). We reconstruct by minimizing the L1 norm of a transformed dynamic scene subject to data fidelity constraints. Unlike previously suggested linear methods [7, 8], our method does not require a known spatio-temporal structure nor a training set, only that the dynamic scene has a sparse representation. We demonstrate a 7-fold frame-rate acceleration both in simulated data and in vivo non-gated Cartesian balanced-SSFP cardiac MRI . Theory Dynamic MR images are highly redundant in space and time. By using linear transformations (such as wavelets, Fourier etc.), we can represent a dynamic scene using only a few sparse transform coefficients. Inadequate sampling of the spatial-frequency -temporal space (k-t space) results in aliasing in the spatial -temporal-frequency space (x-f space). The aliasing artifacts due to random under-sampling are incoherent as opposed to coherent artifacts in equispaced under sampling. More importantly the artifacts are incoherent in the sparse transform domain. By using the non-linear reconstruction scheme in [1-5] we can recover the sparse transform coefficients and as a consequence, recover the dynamic scene. We exploit sparsity by constraining our reconstruction to have a sparse representation and be consistent with the measured data by solving the constrained optimization problem: minimize ||Ψm||1 subject to: ||Fm – y||2 < e. Here m is the dynamic scene, Ψ transforms the scene into a sparse representation, F is randomized phase encode ordering Fourier matrix, y is the measured k-space data and e controls fidelity of the reconstruction to the measured data. e is usually set to the noise level. Methods For dynamic heart imaging, we propose using the wavelet transform in the spatial dimension and the Fourier transform in the temporal. Wavelets sparsify medical images [1] whereas the Fourier transform sparsifies smooth or periodic temporal behavior. Moreover, with random k-t sampling, aliasing is extremely incoherent in this particular transform domain. To validate our approach we considered a simulated dynamic scene with periodic heart-like motion. A random phase-encode ordered Cartesian acquisition (See Fig. 2) was simulated with a TR=4ms, 64 pixels, acquiring a total of 1024 phase encodes (4.096 sec). The data was reconstructed at a frame rate of 15FPS (a 4-fold acceleration factor) using the L1 reconstruction scheme implemented with non-linear conjugate gradients. The result was compared to a sliding window reconstruction (64 phase encodes in length). To further validate our method we considered a Cartesian balanced-SSFP dynamic heart scan (TR=4.4, TE=2.2, α=60°, res=2.5mm, slice=9mm). 1152 randomly ordered phase encodes (5sec) where collected and reconstructed using the L1 scheme at a 7-fold acceleration (25FPS). Result was compared to a sliding window (64 phase encodes) reconstruction. The experiment was performed on a 1.5T GE Signa scanner using a 5inch surface coil. Results and discussion Figs. 2 and 3 illustrate the simulated phantom and actual dynaic heart scan reconstructions. Note, that even at 4 to 7-fold acceleration, the proposed method is able to recover the motion, preserving the spatial frequencies and suppressing aliasing artifacts. This method can be easily extended to arbitrary trajectories and can also be easily integrated with other acceleration methods such as phase constrained partial k-space and SENSE [1]. In the current, Matlab implementation we are able to reconstruct a 64x64x64 scene in an hour. This can be improved by using newly proposed reconstruction techniques [5,6]. Previously proposed linear methods [7,8] exploit known or measured spatio-temporal structure. The advantage of the proposed method is that the signal need not have a known structure, only sparsity, which is a very realistic assumption in dynamic medical images [1,7,8]. Therefore, a training set is not required. References [1] Lustig et al. 13th ISMRM 2004:p605 [2] Lustig et al. ” Rapid MR Angiography ...” Accepted SCMR06’ [3] Candes et al. ”Robust Uncertainty principals". Manuscript. [4] Donoho D. “Compressesed Sensing”. Manuscript. [5] Candes et al. “Practical Signal Recovery from Random Projections” Manuscript. [6] M. Elad, "Why Simple Shrinkage is Still Relevant?" Manuscript. [7] Tsao et al.. Magn Reson Med. 2003 Nov;50(5):1031-42. [8] Madore et al. Magn Reson Med. 1999 Nov;42(5):813-28. Figure 2: Simulated dynamic data. (a) The transform domain of the cross section is truly sparse. (b) Ground truth crosssection. (c) L1 reconstruction from random phase encode ordering, 4-fold acceleration (d) Sliding window (64) reconstruction from random phase encode ordering.. Figure 1: (a) Sequential phase encode ordering. (b) Random Phase encode ordering. The k-t space is randomly sampled, which enables recovery of sparse spatio-temporal dynamic scenes using the L1 reconstruction.

379 citations

Journal ArticleDOI
TL;DR: A new image-based approach for prospective motion correction is described, which utilizes three orthogonal two‐dimensional spiral navigator acquisitions, along with a flexible image‐based tracking method based on the extended Kalman filter algorithm for online motion measurement.
Abstract: Artifacts caused by patient motion during scanning remain a serious problem in most MRI applications The prospective motion correction technique attempts to address this problem at its source by keeping the measurement coordinate system fixed with respect to the patient throughout the entire scan process In this study, a new image-based approach for prospective motion correction is described, which utilizes three orthogonal two-dimensional spiral navigator acquisitions, along with a flexible image-based tracking method based on the extended Kalman filter algorithm for online motion measurement The spiral navigator/extended Kalman filter framework offers the advantages of image-domain tracking within patient-specific regions-of-interest and reduced sensitivity to off-resonance-induced corruption of rigid-body motion estimates The performance of the method was tested using offline computer simulations and online in vivo head motion experiments In vivo validation results covering a broad range of staged head motions indicate a steady-state error of less than 10% of the motion magnitude, even for large compound motions that included rotations over 15 deg A preliminary in vivo application in three-dimensional inversion recovery spoiled gradient echo (IR-SPGR) and three-dimensional fast spin echo (FSE) sequences demonstrates the effectiveness of the spiral navigator/extended Kalman filter framework for correcting three-dimensional rigid-body head motion artifacts prospectively in high-resolution three-dimensional MRI scans

362 citations

Journal ArticleDOI
TL;DR: It is indicated that some subjects with patellofemoral pain exhibit abnormal weight‐bearing joint kinematics and that braces may be effective in reducing patellar maltracking in these subjects.

140 citations

Journal ArticleDOI
TL;DR: Real‐time cardiac and coronary MRI at 1.5T is demonstrated with high blood SNR, blood‐myocardium CNR, resolution, and image quality, using new spectral‐spatial RF pulses and fast spiral gradient echo pulse sequences.
Abstract: Real-time cardiac and coronary MRI at 1.5T is relatively "signal starved" and the 3T platform is attractive for its immediate factor of two increase in magnetization. Cardiac imaging at 3T, however, is both subtly and significantly different from imaging at 1.5T because of increased susceptibility artifacts, differences in tissue relaxation, and RF homogeneity issues. New RF excitation and pulse sequence designs are presented which deal with the fat-suppression requirements and off-resonance issues at 3T. Real-time cardiac imaging at 3T is demonstrated with high blood SNR, blood-myocardium CNR, resolution, and image quality, using new spectral-spatial RF pulses and fast spiral gradient echo pulse sequences. The proposed sequence achieves 1.5 mm in-plane resolution over a 20 cm FOV, with a 5.52 mm measured slice thickness and 32 dB of lipid suppression. Complete images are acquired every 120 ms and are reconstructed and displayed at 24 frames/sec using a sliding window. Results from healthy volunteers show improved image quality, a 53% improvement in blood SNR efficiency, and a 232% improvement in blood-myocardium CNR efficiency compared to 1.5T.

116 citations


Cited by
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Journal ArticleDOI
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

Journal ArticleDOI
TL;DR: A simple costless modification to iterative thresholding is introduced making the sparsity–undersampling tradeoff of the new algorithms equivalent to that of the corresponding convex optimization procedures, inspired by belief propagation in graphical models.
Abstract: Compressed sensing aims to undersample certain high-dimensional signals yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a known basis. Currently, the best known sparsity–undersampling tradeoff is achieved when reconstructing by convex optimization, which is expensive in important large-scale applications. Fast iterative thresholding algorithms have been intensively studied as alternatives to convex optimization for large-scale problems. Unfortunately known fast algorithms offer substantially worse sparsity–undersampling tradeoffs than convex optimization. We introduce a simple costless modification to iterative thresholding making the sparsity–undersampling tradeoff of the new algorithms equivalent to that of the corresponding convex optimization procedures. The new iterative-thresholding algorithms are inspired by belief propagation in graphical models. Our empirical measurements of the sparsity–undersampling tradeoff for the new algorithms agree with theoretical calculations. We show that a state evolution formalism correctly derives the true sparsity–undersampling tradeoff. There is a surprising agreement between earlier calculations based on random convex polytopes and this apparently very different theoretical formalism.

2,412 citations

Journal ArticleDOI
TL;DR: The aim of this paper is to introduce a few key notions and applications connected to sparsity, targeting newcomers interested in either the mathematical aspects of this area or its applications.
Abstract: A full-rank matrix ${\bf A}\in \mathbb{R}^{n\times m}$ with $n

2,372 citations

BookDOI
07 May 2015
TL;DR: Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underlying signal in a set of data and extract useful and reproducible patterns from big datasets.
Abstract: Discover New Methods for Dealing with High-Dimensional Data A sparse statistical model has only a small number of nonzero parameters or weights; therefore, it is much easier to estimate and interpret than a dense model. Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underlying signal in a set of data. Top experts in this rapidly evolving field, the authors describe the lasso for linear regression and a simple coordinate descent algorithm for its computation. They discuss the application of 1 penalties to generalized linear models and support vector machines, cover generalized penalties such as the elastic net and group lasso, and review numerical methods for optimization. They also present statistical inference methods for fitted (lasso) models, including the bootstrap, Bayesian methods, and recently developed approaches. In addition, the book examines matrix decomposition, sparse multivariate analysis, graphical models, and compressed sensing. It concludes with a survey of theoretical results for the lasso. In this age of big data, the number of features measured on a person or object can be large and might be larger than the number of observations. This book shows how the sparsity assumption allows us to tackle these problems and extract useful and reproducible patterns from big datasets. Data analysts, computer scientists, and theorists will appreciate this thorough and up-to-date treatment of sparse statistical modeling.

2,275 citations

Journal ArticleDOI
TL;DR: The authors emphasize on an intuitive understanding of CS by describing the CS reconstruction as a process of interference cancellation, and there is also an emphasis on the understanding of the driving factors in applications.
Abstract: This article reviews the requirements for successful compressed sensing (CS), describes their natural fit to MRI, and gives examples of four interesting applications of CS in MRI. The authors emphasize on an intuitive understanding of CS by describing the CS reconstruction as a process of interference cancellation. There is also an emphasis on the understanding of the driving factors in applications, including limitations imposed by MRI hardware, by the characteristics of different types of images, and by clinical concerns.

2,134 citations