Gabriel Rilling

Carotid blood flow measurement accelerated by compressed sensing: validation in healthy volunteers

Measurement of blood flow by cine phase-contrast MRI is a valuable technique in the study of arterial disease but is time consuming, especially for multi-slice (4D) studies. Compressed sensing is a modern signal processing technique that exploits sparse signal representations to enable sampling at lower than the conventional Nyquist rate. It is emerging as a powerful technique for the acceleration of MRI acquisition. In this study we evaluated the accuracy of phase-contrast carotid blood flow measurement in healthy volunteers using threefold undersampling of kt-space and compressed sensing reconstruction. Sixteen healthy volunteers were scanned at 1.5T with a retrospectively gated 2D cine phase-contrast sequence. Both fully sampled and three-fold accelerated scans were carried out to measure blood flow velocities in the common carotid arteries. The accelerated scans used a k-t variable density randomised sampling scheme and standard compressed sensing reconstruction. Flow rates were determined by integration of velocities within the manually segmented arteries. Undersampled measurements were compared with fully sampled results. Bland-Altman analysis found that peak velocities and flow rates determined from the compressed sensing scans were underestimated by 5% compared with fully sampled scanning. The corresponding figure for time-averaged flow was 3%. These acceptably small errors with a threefold reduction in scan time will facilitate future extension to 4D flow studies in clinical research and practice.

Advanced image formation and processing of partial synthetic aperture radar data

The authors propose an advanced synthetic aperture radar (SAR) image formation framework based on iterative inversion algorithms that approximately solve a regularised least squares problem. The framework provides improved image reconstructions, compared to the standard methods, in certain imaging scenarios, for example when the SAR data are under-sampled. Iterative algorithms also allow prior information to be used to solve additional problems such as the correction of unknown phase errors in the SAR data. However, for an iterative inversion framework to be feasible, fast algorithms for the generative model and its adjoint must be available. The authors demonstrate how fast, N2 log2 N complexity, (re/back)-projection algorithms can be used as accurate approximations for the generative model and its adjoint, without the limiting geometric approximations of other N2 log2 N methods, for example, the polar format algorithm. Experimental results demonstrate the effectiveness of their framework using publicly available SAR datasets.

Greedy algorithms for compressed sensing

Compressed Sensing (CS) is often synonymous with l1 based optimization. How- ever, when choosing an algorithm for a particular application, there are a range of different properties that have to be considered and weighed against each other. Important algorithm properties, such as speed and storage requirements, ease of implementation, flexibility and recovery performance have to be compared. In this chapter we will therefore present a range of alternative algorithms that can be used to solve the CS recovery problem and which outperform convex optimization based methods in some of these areas. These methods therefore add important versatility to any CS recovery toolbox

Iterative image formation using fast (Re/Back)-projection for spotlight-mode SAR

Iterative SAR image formation can visually improve image reconstructions from under-sampled phase histories by approximately solving a regularised least squares problem. For iterative inversion to be computationally feasible, fast algorithms for the observation matrix and its adjoint must be available. We demonstrate how fast, N2 log2 N complexity, (re/back)-projection algorithms can be used as accurate approximations for the observation matrix and its adjoint, without the limiting assumptions of other N2 log2 N methods, e.g. the polar format algorithm. Experimental results demonstrate the effectiveness of iterative methods using a publicly available SAR dataset. Matlab/C code implementations of the fast (re/back)-projection algorithms used in this paper have been made available.

Multilattice sampling strategies for region of interest dynamic MRI

A multilattice sampling approach is proposed for dynamic MRI with Cartesian trajectories. It relies on the use of sampling patterns composed of several different lattices and exploits an image model where only some parts of the image are dynamic, whereas the rest is assumed static. Given the parameters of such an image model, the methodology followed for the design of a multilattice sampling pattern adapted to the model is described. The multi‐lattice approach is compared to single‐lattice sampling, as used by traditional acceleration methods such as UNFOLD (UNaliasing by Fourier‐Encoding the Overlaps using the temporal Dimension) or k‐t BLAST, and random sampling used by modern compressed sensing‐based methods. On the considered image model, it allows more flexibility and higher accelerations than lattice sampling and better performance than random sampling. The method is illustrated on a phase‐contrast carotid blood velocity mapping MR experiment. Combining the multilattice approach with the KEYHOLE technique allows up to 12× acceleration factors. Simulation and in vivo undersampling results validate the method. Compared to lattice and random sampling, multilattice sampling provides significant gains at high acceleration factors. Magn Reson Med 70:392–403, 2013.

Compressed sensing in k-space: from magnetic resonance imaging and synthetic aperture radar

We consider two imaging applications of compressed sensing where the acquired data corresponds to samples in the Fourier domain (aka k- space). The rst one is magnetic resonance imaging (MRI), which has been one of the standard examples in the compressed sensing literature. The second one is synthetic aperture radar (SAR). We consider the practical issues of applying compressed sensing ideas in these two applications noting that the physical prossesses involved in these two sensing modalities are very different. We consider the issues of: appropriate image models and sampling strategies, dealing with noise, and the need for calibration.

Automatic target recognition from highly incomplete SAR data

The automatic target recognition (ATR) performance of SAR with subsampled raw data is investigated in this paper. Two schemes are investigated. In scheme A, SAR images are reconstructed from subsampled data by applying compressed sensing (CS) techniques and then targets are classified using either the mean-squared error (MSE) classifier or the point-feature-based classifier. Both classifiers recognize a target by using the magnitude information of dominant scatterers in the image. They fit nicely with the CS framework considering that CS approaches can efficiently recover the bright pixels in SAR images. In scheme B, the smashed-filter classifier is employed without image formation. Instead it makes the classification decision by directly comparing the observed subsampled data with data simulated from reference images. The impact of various subsampling patterns on ATR is investigated since CS theory suggests that some patterns lead to better performance than others. Simulation results show that compared with images formed by the conventional SAR imaging algorithm, CS reconstructed images always lead to much higher recognition rates for both the classifiers in scheme A. The MSE classifier works better than the point-feature-based classifier because the former takes into account both the magnitudes and locations of bright pixels while the latter uses the locations only. The smashed-filter classifier is computationally efficient and can accurately recognize a target even with strong subsampling if appropriate reference images are available. Its application in practice is difficult because it is sensitive to the phases of complex-valued SAR images, which vary too much for different observation angles.

Proceedings of SPIE 8051, 805115

The automatic target recognition (ATR) performance of SAR with subsampled raw data is investigated in this paper. Two schemes are investigated. In scheme A, SAR images are reconstructed from subsampled data by applying compressed sensing (CS) techniques and then targets are classified using either the mean-squared error (MSE) classifier or the point-feature-based classifier. Both classifiers recognize a target by using the magnitude information of dominant scatterers in the image. They fit nicely with the CS framework considering that CS approaches can efficiently recover the bright pixels in SAR images. In scheme B, the smashed-filter classifier is employed without image formation. Instead it makes the classification decision by directly comparing the observed subsampled data with data simulated from reference images. The impact of various subsampling patterns on ATR is investigated since CS theory suggests that some patterns lead to better performance than others. Simulation results show that compared with images formed by the conventional SAR imaging algorithm, CS reconstructed images always lead to much higher recognition rates for both the classifiers in scheme A. The MSE classifier works better than the point-feature-based classifier because the former takes into account both the magnitudes and locations of bright pixels while the latter uses the locations only. The smashed-filter classifier is computationally efficient and can accurately recognize a target even with strong subsampling if appropriate reference images are available. Its application in practice is difficult because it is sensitive to the phases of complex-valued SAR images, which vary too much for different observation angles.

Automatic target recognition fromhighly incomplete SAR data

The automatic target recognition (ATR) performance of SAR with subsampled raw data is investigated in this paper. Two schemes are investigated. In scheme A, SAR images are reconstructed from subsampled data by applying compressed sensing (CS) techniques and then targets are classified using either the mean-squared error (MSE) classifier or the point-feature-based classifier. Both classifiers recognize a target by using the magnitude information of dominant scatterers in the image. They fit nicely with the CS framework considering that CS approaches can efficiently recover the bright pixels in SAR images. In scheme B, the smashed-filter classifier is employed without image formation. Instead it makes the classification decision by directly comparing the observed subsampled data with data simulated from reference images. The impact of various subsampling patterns on ATR is investigated since CS theory suggests that some patterns lead to better performance than others. Simulation results show that compared with images formed by the conventional SAR imaging algorithm, CS reconstructed images always lead to much higher recognition rates for both the classifiers in scheme A. The MSE classifier works better than the point-feature-based classifier because the former takes into account both the magnitudes and locations of bright pixels while the latter uses the locations only. The smashed-filter classifier is computationally efficient and can accurately recognize a target even with strong subsampling if appropriate reference images are available. Its application in practice is difficult because it is sensitive to the phases of complex-valued SAR images, which vary too much for different observation angles.