Sunday, June 15, 2008

CS: CS for Multimedia Communications in Wireless Sensor Networks, Sherpa/Romeo, SIAM, FUSION and ISMRM CS centered abstracts.

Here is a presentation for an EE class at University of Texas (Austin) by Wael Barakat Rabih Saliba entitled Compressive Sensing for Multimedia Communications in Wireless Sensor Networks

If some of you are wondering about your ability to put your paper in preprint form on your webpage, you might want to check this SHERPA/ROMEO tool out. Given a journal, it gives you the policy of that paper with regards to making your own material available on your site for fair use.

With the months of July and August coming up I expect less traffic mostly because of the expected decrease in new preprints/publications. I also expect to see more conferences. I will try to list the ones that have papers on Compressive Sensing. Today, there is the SIAM and Fusion meeting in July. I also wanted to list the papers presented at the International Society for Magnetic Resonance in Medicine annual meeting last May.

The International Conferences on Information Fusion 2008 will feature one presentation with CS:

Signal Extraction Using Compressed Sensing for Passive Radar with OFDM Signals by Christian Berger, Shengli Zhou and Peter Willett.

There is the SIAM conference on Imaging Science on July 7-9th. The IS08 abstracts can be found here, I have listed the ones related to CS below. It should be nice being there:

Image Processing with Manifold Models
In this talk I will study the manifold structure of sets of patches extracted from natural images. The local manifold constraint is chained into a global one since the whole image traces a smooth surface on the features manifold. We detail this manifold structure for various ensembles suitable for natural images and textures modeling. These manifolds offer a low-dimensional parameterization of geometric patterns that can be found in such datasets. One can use these manifold models in order to regularize inverse problems in signal and image processing. In this framework, one searches for a smooth surface traced on the feature manifold that matches the forward measurements. In the discrete setting, the manifold can be either known analytically or estimated from exemplars using a graph structure. Numerical simulations on inpainting and compressive sampling inversion show how such manifolds models bring an improvement for datasets with geometrical features.
Gabriel Peyre

Nonconvex Compressive Sensing
We will examine theoretical and numerical results demonstrating that replacing the convex optimization problems of compressive sensing with nonconvex ones allows sparse signals to be reconstructed from many fewer measurements. Surprisingly, very simple algorithms are able to reconstruct signals successfully, despite the huge numbers of local minima. We will see striking examples of the recovery performance of these algorithms under a variety of circumstances,
and discuss the state of the underlying theory.

Rick Chartrand
Los Alamos National Laboratory

CoSaMP: Iterative Signal Recovery from Incomplete and Inaccurate Measurements
Compressive Sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthobasis. The major algorithmic challenge is to approximate a compressible signal from noisy samples. Until recently, all provably correct reconstruction techniques have relied on large-scale optimization, which tends to be computationally burdensome. This talk describes a new iterative, greedy recovery algorithm, called CoSaMP that delivers the same guarantees as the best optimization-based approaches. Moreover, this algorithm offers rigorous bounds
on computational cost and storage. It is likely to be extremely efficient for practical problems because it requires only matrix–vector multiplies with the sampling matrix. For some cases of interest, the running time is just O(N ∗ log2(N)), where N is the length of the signal.

Joel Tropp
Applied and Computational Mathematics

Deanna Needell
Mathematics, UC Davis

Distributed Compressive Sensing with the Dirichlet Process
In many applications, one is interested in simultaneously performing inversion of multiple CS measurements. We propose a novel multi-task compressive sensing framework based on a Bayesian formalism, where a sparseness prior is adopted. The key challenge is that not all of the measured data are necessarily appropriate for sharing when performing inversion, and one must therefore infer what sharing of data across the multiple CS measurements is appropriate.
Toward this end, a Dirichlet process (DP) prior is employed.

Larry Carin
Electrical & Computer Engineering
Duke University

Compressive Imaging for Increased Field-of-view Exploitation
We consider the application of compressive imaging to the problem of wide-area persistent surveillance. There are cases under study where optical architectures have been developed which require the incorporation of compressive imaging to perform the indicated exploitation. We utilize one such architecture to show a dramatic increase in performance for wide-area persistent surveillance. This architecture is described as a field-of-view multiplexing imager
and its relation to compressive imaging is discussed and exploited.
Robert Muise
Lockheed Martin

Difference Imaging from Linear Spatial-Domain Projections
Using compressive optical measurements, we consider direct reconstruction of the difference between two images taken at different time instants. We first show that the linear MMSE reconstruction operator depends on the crosscorrelation between the two images. We then consider reconstruction performance when the measurements consist of a finite number of linear spatial projections of the two images. We also quantify performance when a time series of difference images is reconstructed from a series of linear projections. Various projection operators are compared.

Nathan Goodman, Mark Neifeld, Shikhar Shikhar
Department of Electrical and Computer Engineering
University of Arizona

Manifold-based Image Understanding from Compressive Measurements
The emerging theory of Compressive Sensing (CS) states that an image obeying a sparse model can be reconstructed from a small number of random linear measurements. In this talk we will explore manifold-based models as a generalization of sparse representations, and we will discuss
the possible applications of these models not only in single and multi-image recovery from compressive measurements, but also in scalable inference settings, where a detection, estimation, or classification can be made using far fewer compressive measurements than would be required for recovery.

Michael Wakin
Department of Electrical Engineering and Computer Science
University of Michigan

Seismic Imaging Meets Compressive Sampling
Compressive sensing has led to fundamental new insights in the recovery of compressible signals from sub-Nyquist samplings. It is shown how jittered subsampling can be used to create favorable recovery conditions. Applications include mitigation of incomplete acquisitions and wavefield computations. While the former is a direct adaptation of compressive sampling, the latter application represents a new way of compressing wavefield extrapolation operators. Operators are not diagonalized but are compressively sampled reducing the computational costs.

Felix J. Herrmann
The University of British Columbia
Department of Earth and Ocean Sciences

Fast BV + Texture Decomposition
In this talk based on a joint work with Triet Le and Luminita Vese we will review former work on the problem of decomposing a digital image into an oscillatory part and a BV part. This problem was posed by Yves Meyer as a variational problem, and is also (partially) adressed by compressive sensing techniques. We shall discuss several implementations and variants, including a fast one, which gives a nonlinear version of the classical low-pass, high-pass

Antoni Buades
MAP5, Universite Paris Descartes

Jean-Michel Morel
ENS Cachan

Adaptive Non-local Transforms for Image/video Denoising, Restoration, and Enhancement, and for Compressive Sensing Image Reconstruction
The talk is devoted to a powerful and effective extension of the non-local filtering paradigm. We replace the conventional non-parametric image modeling based on the sample mean or weighted mean by a transform-domain representation where multiple patches from different spatial locations are collectively represented in higher-dimensional data structures. This corresponds to a non-local image transform which is adaptive with respect to the image content. We illustrate this approach and give an overview of its successful application to several image processing problems. The common point is enforcing sparsity within this overcomplete non-local representation. In most of the presented examples, the BM3D (Block-Matching and 3D filtering)
denoising algorithm [Dabov et al., IEEE TIP 16(9) 2007] is used as a pragmatical way to generate the adaptive representation and to then enforce sparsity via shrinkage. Besides the basic image and video denoising problem, we will address image restoration (deblurring), image
enhancement (sharpening), and compressive sensing image reconstruction (inverse tomography, image upsampling/ zooming, and image interpolation). The presented methods are expression of the state-of-the-art, in terms of both objective and subjective visual quality. This quality
is achieved at a competitive computational cost. We conclude the talk highlighting few open problems. The material of the talk is joint work with Kostadin Dabov, Aram Danielyan, Vladimir Katkovnik, and Karen Egiazarian.

Alessandro Foi
Tampere University of Technology
Tempere, Finland

Compressive Sensing for Multi-Static Radar Imaging: Theory and Numerical Experiments
The compressive-sensing framework assumes the scene is relatively sparse in some (unknown) basis and the measurements are made in another basis with the appropriate properties. We address (i) the discrete sampling approximation of the image space, (ii) the satisfaction of the
”restricted isometry property” as a function of waveform design and collection geometry, and (iii) robustness to clutter/noise. Finally, we present some illustrative numerical experiments related to this theory.
Mark Stuff, Brian Thelen, Nikola Subotic, Kyle Cooper,
William Buller

New Results in Sparse Representation
Sparse image representation benefits tremendously from L-1 based methodology. Recently, new modification (that utilizes reweighting) was proposed in both statistics and compressive sensing communities. We report theoretical and experimental results in this line of research.
Xiaoming Huo
Georgia Institute of Technology

Image Reconstruction from Incomplete Data in xray Projection-based Tomographic Imaging
In the field of compressive sensing there has been much recent progress in sparse image recovery from sparse Fourier transform data, using L1-norm or total variation (TV)
minimization of the estimated image. These theoretical advances have implications for tomographic image reconstruction such as Computed Tomography (CT). We have
recently been investigating the possibility of image reconstruction from sparse or incomplete x-ray projection data. We will report on recent results for image reconstruction
in CT and tomosynthesis.
Emil Sidky
Department of Radiology
The University of Chicago

Xiaochuan Pan
The University of Chicago
Department of Radiology

Estimating Tumor Bounds in Bioluminescence Tomography
Bioluminescence tomography is an emerging small animal imaging modality that has many important applications in biomedical research, from drug development to studies of tumor metastasis. The prototypical model for this inverse source problem is based on the time-independent diffusion equation. While a general inversion algorithm is not feasible, the task of estimating a tumor volume can be approached using principles of compressive sensing and
Ikehatas enclosure method.
Matthew A. Lewis
UT Southwestern Medical Center at Dallas

Orthant-Wise Gradient Projection Method for Compressive Sampling
The compressive sampling problem can be formulated as l1-regularized least square problem. The objective function can be reformulated as a quadratic approximation orthantwise. We efficiently apply orthant-wise gradient projection method to solve this optimization problem, and prove its convergence to the global optimal solution. Computational experiments demonstrate that the proposed method outperforms other methods in previous literatures.
Qiu Wu
Electrical and Computer Engineering
The University of Texas at Austin

Foundations of Compressed Sensing
We will give an introduction to the emerging field of Compressed Sensing. The main objective of this new paradigm in signal processing is to capture a signal with the smallest number of measurements. We shall emphasize ways to decide what are the best sensing systems and describe how to construct near optimal systems.

Ronald DeVore
Department of Mathematics
University of South Carolina

Sparse Approximations in Image Processing
The search for the ”best basis” (or even good enough) in which to approximate, to denoise, or, more generally, to analyze images has led to a flurry of activity in the construction of orthonormal, bi-orthogonal, and finally, redundant or overcomplete dictionaries. With these constructions, came heuristic algorithms for how best to use them in the nonlinear approximation and analysis of images. We will survey the combined efforts of the engineering, statistics, mathematics, and computer science communities to put these heuristics on solid theoretical footing, as well as their performance in practice. The final part of the tutorial will show how a number of these techniques are used in compressed sensing.

Anna Gilbert
Department of Mathematics
University of Michigan

Image Super-Resolution via Sparse Representation
In this talk, we address the problem of generating a superresolution (SR) image from a single low-resolution input image. We approach this problem from the perspective of compressed sensing. The low-resolution image is viewed as downsampled version of a high-resolution image, whose patches are assumed to have a sparse representation with respect to an over-complete dictionary of prototype signalatoms. The principle of compressed sensing ensures that under mild conditions, the sparse representation can be correctly recovered from the downsampled signal. We will demonstrate the effectiveness of sparsity as a prior for regularizing the otherwise ill-posed super-resolution problem. We further show that a small set of randomly chosen raw patches from training images of similar statistical nature to the input image generally serve as a good dictionary, in the sense that the computed representation is sparse and the recovered high-resolution image is competitive or even superior in quality to images produced by other SR methods.

Jianchao Yang, John Wright, Yi Ma
Department of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign

Separable Approximation for Sparse Reconstruction
We discuss practical algorithms for large scale unconstrained optimization problems in which the objective consists of a smooth data-fitting term added to a regularization term, which is often nonsmooth and separable. We discuss several applications of the method, highlighting why it is
particularly effective on compressed sensing problems.

Stephen J. Wright
University of Wisconsin
Dept. of Computer Sciences

Mario T. Figueiredo
Instituto Superior Tecnico
Instituto de Telecomunicacoes

Selecting Good Fourier Measurements for Compressed Sensing
We consider the problem of constructing good Fourier compressed sensing matrices by selecting rows of the DFT matrix. While random selection produces good matrices with high probability, particular selections can result in failure to recover certain sparse signals. Using efficiently computable bounds on the admissible signal sparsity for a given sensing matrix, we propose a method to find universally good deterministic Fourier compressed sensing matrices, without compromising average performance.
Kiryung Lee
University of Illinois at Urbana-Champaign

Analog and Digital Sparse Approximation with Applications to Compressed Sensing
In the compressed sensing (CS) framework, the sampling phase is resource constrained, taking a small number of linear samples. However, the price paid for this simplicity is a computationally expensive reconstruction algorithm that forms a bottleneck in using the sensed data. We will present a sparse approximation framework that both unifies many of the recently proposed digital algorithms and introduces novel analog architectures that solve the same problems. We will demonstrate how these analog systems solve CS recovery problems orders of magnitude faster than current digital systems, at speeds limited only by the underlying hardware components.
Chris Rozell
Georgia Institute of Technology

Advances in Compressed Sensing for MRI
Recent developments in Compressive Sensing (CS) theory offer the potential for significant advances in diagnostic medical imaging, and especially magnetic resonance imaging (MRI). Here, we review some of the key works on the application of CS theory and its extensions to both single
and multi-coil or parallel MR imaging and discuss practical benefits such as improved patient comfort, reduced susceptibility to physiological motion, and increased clinical throughput.
Joshua D. Trzasko
Mayo Clinic

Fourier Sketching: Low Complexity Computation of Sparse DFT
I will present a greedy, randomized algorithm that computes the DFT of length N when only S coefficients are nonzero but have unknown location, in the spirit of recent work by Gilbert, Strauss, and co-workers. The complexity is empirically sublinear and scales like S(logN)2. While
some elements of the algorithm are directly taken from Gilbert et al., some steps such as the coefficient estimation are novel. Applications include fast decoding for compressed sensing, without even formulating an ell-1 problem or expliciting the measurement matrix.
Laurent Demanet
Mathematics, Stanford

One Sketch for All: Fast Algorithms for Compressed Sensing
Compressed Sensing is a new paradigm for acquiring the compressible signals that arise in many applications. These signals can be approximated using an amount of information much smaller than the nominal dimension of the signal. Traditional approaches acquire the entire signal and
process it to extract the information. The new approach acquires a small number of nonadaptive linear measurements of the signal and uses sophisticated algorithms to determine its information content. Emerging technologies can compute these general linear measurements of a signal at unit cost per measurement. This paper exhibits a randomized measurement ensemble and a signal reconstruction algorithm that satisfy four requirements: (1) The measurement ensemble succeeds for all signals, with high probability over the random choices in its construction. (2) The number of measurements of the signal is optimal, except for a factor polylogarithmic in the signal length. (3) The running time of the algorithm is polynomial in the amount of information in the signal and polylogarithmic in the signal length. (4) The recovery algorithm offers the strongest possible type of error guarantee. Moreover, it is a fully polynomial approximation scheme with respect to this type of error bound. Emerging applications demand this level of performance. Yet no other algorithm in the literature simultaneously achieves all four of these desiderata. This talk will present and update work that originally appeared in ACM STOC 2007. It is joint work with Anna C. Gilbert, Joel A. Tropp, and Roman Vershynin.

Martin Strauss
Mathematics and EECS
University of Michigan

Bregman Iterative Algorithms for l1-Minimization with Applications to Compressed Sensing
We propose simple and extremely efficient methods for solving the Basis Pursuit problem
min{u1 : Au = f, u ∈ Rn}, which is used in compressed sensing. Our methods are based on Bregman iterative regularization and they give a very accurate solution after solving only a very small number of instances of the unconstrained problem min u∈Rn μu1 +1 2 Au − fk22,
for given matrix A and vector fk. We show analytically that this iterative approach yields exact solutions in a finite number of steps. We were able to solve huge instances of compressed sensing problems quickly on a standard PC. We demonstrate the effectiveness of the algorithm by experiments of compressed MR imaging.
Wotao Yin
Rice University

Stanley J. Osher
University of California
Department of Mathematics

Donald Goldfarb
Columbia University

Jerome Darbon

Image Analysis Through Unknown Random Compressed Sensing Using Diffusion Geometry
We indicate that diffusion geometric analysis can be used to intrinsically process images which have been acquired as randomly encoded patches. In particular we show that for hyperspectral imagery the results are intrinsic and independent of the choice of randomized spectra. Diffusion
Geometry considers the data base of all measurements, and proceeds to organize them enabling compressed sensing through local randomizers.

Ronald Coifman
Yale University
Department of Computer Science

Monotone Operator Splitting and Fast Solutions to Inverse Problems with Sparse Representations
This work focuses on several constrained optimization problems involved in sparse solutions of linear inverse problems. We formalize all these problems within the same framework of convex optimization theory, and invoke tools from convex analysis (proximity operators) and maximal monotone operator splitting. We characterize all these optimization problems, and to solve them, we propose fast iterative splitting algorithms, namely forward-backward and Peaceman/Douglas-Rachford splitting iterations. This framework includes some previously proposed algorithms as a special case. With non-differentiable sparsity-promoting penalties, the proposed algorithms are essentially based on iterative shrinkage. Furthermore, the computational burden of all our algorithms is one application of fast analysis and synthesis operators at each iteration. This makes them very competitive for large-scale problems. Applications to several inverse problems such as denoising, super-resolution and compressed sensing are also reported to demonstrate the wide range of applicability of our approach.

Jalal Fadili
CNRS, Univ. of Caen, France

Bregman Iterative Algorithms for Compressed Sensing
Bregman iterative regularization (1967) was introduced by Osher, Burger, Goldfarb, Xu and Yin as a device for improving TV based image restoration (2004) and was used by Xu and Osher in (2006) to analyze and improve wavelet shrinkage. In recent work by Yin, Osher, Goldfarb and
Darbon we devised simple and extremely efficient methods for solving the basis pursuit problem which is used in compressed sensing. A linearized version of Bregman iteration was also done by Osher, Dong, Mao and Yin. This requires two lines of MATLAB code and is remarkably efficient.
This means we rapidly and easily solve the problem: minimize the L1 norm of u so that Au = f for a given k by n matrix A, with k << style="font-weight: bold;">A Taste of Compressed Sensing
Compressed sensing seeks to capture a signal/image with as few measurements as possible. We shall give a brief discussion of this fascinating field with the emphasis on the accuracy of representation in the compressed sensing setting.

Ronald DeVore
Department of Mathematics
University of South Carolina.

In the International Society for Magnetic Resonance in Medicine annual meeting last May here are the papers that were presented:

MRA: Contrast Without the Agent
726. Improving Non-Contrast Enhanced SSFP Angiography with Compressed Sensing

Tolga Çukur1, Michael Lustig1, Dwight Georger Nishimura1

1Stanford University, Stanford, California , USA

Flow-independent angiography offers the ability to produce vessel images without contrast agents. 3D magnetization-prepared balanced SSFP can be used to acquire these angiograms, where the phase encodes are interleaved and preparation is repeated prior to the start of each interleave. However, frequent repetition of the preparation significantly reduces the scan efficiency. The sparsity of the angiograms allows for the use of compressed sensing to undersample the phase encodes and save scan time. These savings can be allotted for preparing the magnetization more often, or alternatively, improving resolution.

Imaging in the Post-Nyquist Era

333. Dynamic Functional Volumetric Magnetic Resonance K-Space Inverse Imaging of Human Visual System

Fa-Hsuan Lin1, 2, Thomas Witzel1, 3, Graham Wiggins1, Lawrence Wald1, John Belliveau1

1Massachusetts General Hospital, Charlestown, Massachusetts, USA; 2National Taiwan University, Taipei, Taiwan; 3Harvard-MIT Division of Health Sciences and Technology, Cambridge, Massachusetts, USA

We propose a K-space magnetic resonance Inverse Imaging (K-InI) approach to use a highly parallel radio-frequency coil array to achieve high temporal resolution MRI. K-InI solves an under-determined linear system using regularization in parallel MRI reconstruction. K-InI uses auto-calibration technique to estimate the reconstruction coefficients and it can provide coil-by-coil reconstruction to allow for more flexible combination of different channels in the coil array. We demonstrate K-InI using a 3D visual fMRI experiment to achieve 100 ms temporal resolution.

334. High Spatial High Temporal Resolution MR-Encephalography Using Constraint Reconstruction Based on Regularization with Arbitrary Projections (COBRA)

Thimo Grotz1, Benjamin Zahneisen1, Arsène Ella1, Jürgen Hennig1

1University Hospital Freiburg, Freiburg, Germany

MREG, also called inverse imaging, was introduced as a new approach to measure activation related MR-signal changes in the brain, with very high temporal resolu-tion. We present a constraint reconstruction based on regularization with arbitrary projections to localize the activation. The results demonstrate that COBRA with very low number of projections can be used to acquire activation maps with reasonable spatial resolution at very high temporal resolution. Signal time courses show excel-lent contrast-to-noise for the observed BOLD response.

335. Quantitative 23-Sodium and 17-Oxygen MR Imaging in Human Brain at 9.4 Tesla Enhanced by Constrained K-Space Reconstruction

Ian C. Atkinson1, Keith R. Thulborn1, Aiming Lu1, Justin Haldar2, X J. Zhou1, Ted Claiborne1, Zhi-Pei Liang2

1University of Illinois-Chicago, Chicago, Illinois, USA; 2University of Illinois-Urbana-Champaign, Urbana, Illinois, USA

The sensitivity of ultra-high field MRI enables quantitative imaging of non-proton species such as 23-sodium and 17-oxygen. Constrained k-space reconstruction techniques can be used to improve the spatial resolution of the acquired data without compromising the ability to quantify the final image. This approach of enhanced image reconstruction combined with the improved sensitivity of high field broadens the human applications of metabolic MR imaging by minimizing otherwise long acquisition times to achieve adequate spatial resolution for the anatomy and SNR performance for quantification.

336. Highly Undersampled 3D Golden Ratio Radial Imaging with Iterative Reconstruction

Mariya Doneva1, Holger Eggers2, Jürgen Rahmer2, Peter Börnert2, Alfred Mertins1

1University of Luebeck, Luebeck, Germany; 2Philips Research Europe, Hamburg, Germany

We illustrate the feasibility of Compressed Sensing for 3D dynamic imaging using highly undersampled 3D radial acquisition with golden ratio profile ordering. Image reconstruction from a low number of measurements could be very useful for dynamic 3D imaging, to reduce the often long acquisition times and thus improve temporal resolution in 3D MRI. Using CS, the aliasing artifacts were significantly reduced and a high frame rate was achieved, allowing dynamic imaging with good temporal resolution. The described approach could be particularly useful for dynamic studies of joint motion.

337. Three-Dimensional Compressed Sensing for Dynamic MRI

Ali Bilgin1, 2, Ted P. Trouard1, Maria I. Altbach1, Natarajan Raghunand1

1University of Arizona, Tucson, Arizona , USA

Compressed Sensing (CS) theory illustrates that a small number of linear measurements can be sufficient to reconstruct sparse or compressible signals. we introduce a CS theory based method for reconstruction of time-varying radial k-space data by exploiting the spatio-temporal sparsity of Dynamic Contrast Enhanced (DCE) MRI images. The proposed method significantly reduces undersampling artifacts and can provide high temporal and spatial resolution.

338. Constrained Compressed Sensing for Fast 3D Visualization of Active Catheters

Carsten Oliver Schirra1, 2, Sascha Krueger3, Steffen Weiss3, Reza Razavi1, Tobias Schaeffter1, Sebastian Kozerke2

1King's College London, London, UK; 2University and ETH Zurich, Zurich, Switzerland; 3Philips Medical Systems, Hamburg, Germany

With standard dynamic 3D imaging methods sufficient spatial resolution is difficult to achieve at the required temporal rates when visualizing interventional devices. Active catheters lend themselves well to undersampling methods given their confined sensitivity volume. Compressed Sensing allows exploiting the image sparseness inherent to images acquired with active catheter antennae, however the associated iterative reconstruction algorithms are time-expensive. In this work, the feasibility of using Compressed Sensing for accelerating 3D imaging of active catheters is investigated. Dedicated constraints are introduced taking into account the known catheter length and position in order to minimize the number of iterations in reconstruction.

339. HYPR-Constrained Compressed Sensing Reconstruction for Accelerated Time Resolved Imaging

Huimin Wu1, Walter F. Block1, Alexey A. Samsonov1

1University of Wisconsin-Madison, Madison, USA

Constrained reconstruction methods have been shown to produce significant accelerations to date, but suffer some temporal inaccuracy when vessels with different temporal behaviors are nearby or as the sparsity of the image volume decreases. We present simulated comparisons of a single pass reconstruction method (Highly constrained Projection Local Reconstruction or HYPRLR) and an iterative constrained reconstruction method termed HYPR Reconstruction by Iterative Estimation (HYPRIT). We demonstrate increased temporal accuracy for HYPRIT relative to HYPR LR, but also demonstrate how HYPRIT’s performance improves when using the HYPR LR image as a constraining image. Finally, rapid CE-MRA capabilities are demonstrated.

340. A Comparison of L1 and L2 Norms as Temporal Constraints for Reconstruction of Undersampled Dynamic Contrast Enhanced Cardiac Scans with Respiratory Motion

Ganesh Adluru1, 2, Edward VR DiBella1

1University of Utah, Salt Lake City, USA

Constrained reconstruction methods can be used to accelerate the acquisition of cardiac dynamic contrast-enhanced MRI data. The temporal constraint term is important for determining the quality of reconstructions from undersampled data. Here we compare and evaluate reconstructions obtained by using an L2-norm and an L1-norm as temporal constraints. The reconstructions were compared using data with simulated undersampling and using actual undersampled radial data acquired from the scanner. Using an L1-norm in the temporal constraint helps in obtaining better reconstructions as compared to using an L2-norm in the temporal constraint especially when there is respiratory motion in the data.

341. Accelerated Dynamic Imaging by Reconstructing Sparse Differences Using Compressed Sensing

André Fischer1, 2, Felix Breuer2, Martin Blaimer2, Nicole Seiberlich1, Peter Michael Jakob1, 2

1University of Wuerzburg, Wuerzburg, Germany; 2Research Center for Magnetic Resonance Bavaria e.V., Wuerzburg, Germany

The concept of Compressed Sensing offers a new perspective for accelerated magnet resonance imaging. We demonstrate the use of CS in connection with dynamic imaging. The proposed method reconstructs the differences between a certain timeframe and the composite image of a dynamic dataset. By choosing a radial trajectory, the artifacts in the undersampled image are incoherent, and, therefore, beneficial for the CS algorithm. We achieved good reconstructions with as less as 14 projections (192 x 192 matrix size). Hence, this technique is promising for future real-time dynamic applications.

342. MRI Compressed Sensing Via Sparsifying Images

Alexey Samsonov1, Youngkyoo Jung1, Andrew L. Alexander1, Walter F. Block1, Aaron S. Field1

1University of Wisconsin, Madison, Wisconsin, USA

Recently, there has been an emerging interest to accelerate MRI through iterative reconstruction of undersampled data based on compressed sensing theory. We extend the compressed sensing framework via sparsifying images. The new method utilizes the recent idea in HYPR methods to use sliding window composite images to constrain reconstruction. At the same time, such enhancement is done within the compressed sensing framework. We demonstrate that the new method, HighlY constrained back PRojection by Iterative esTimation (HYPRIT), may be a powerful tool for image reconstruction from highly undersampled data. We demonstrate its potential for accelerated radial diffusion tensor imaging.

Image Credit: NASA/JPL/Space Science Institute, W00046494.jpg was taken on June 15, 2008 and received on Earth June 17, 2008. The camera was pointing toward SATURN-RINGS at approximately 800,600 kilometers away, and the image was taken using the CL1 and CL2 filters. This image has not been validated or calibrated. A validated/calibrated image will be archived with the NASA Planetary Data System in 2009.

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