Compressed sensing (CS) requires undersampled projection data, but CT x-ray tubes cannot be pulsed quickly enough to achieve reduced-view undersampling. We propose an alternative within-view undersampling strategy, named SparseCT, as a practical CS technique to reduce CT radiation dose. SparseCT uses a multi-slit collimator (MSC) to interrupt the x-ray beam, thus acquiring undersampled projection data directly. This study evaluated the feasibility of SparseCT via simulations using a standardized patient dataset. Because the projection data in the dataset are fully sampled, we retrospectively undersample the projection data to simulate SparseCT acquisitions in three steps. First, two photon distributions were simulated, representing the cases with and without the MSC. Second, by comparing the two distributions, detector regions with more than 80% of x-ray blocked by the MSC were identified and the corresponding projection data were not used. Third, noise was inserted into the rest of the projection data to account for the increase in quantum noise due to reduced flux (partial MSC blockage). The undersampled projection data were then reconstructed iteratively using a penalized weighted least squares cost function with the conjugate gradient algorithm. The image reconstruction problem promotes sparsity in the solution and incorporates the undersampling model. Weighting factors were applied to the projection data during the reconstruction to account for the noise variation in the undersampled projection. Compared to images acquired with reduced tube current (provided in the standardized patient dataset), SparseCT undersampling presented less image noise while preserving pathologies and fine structures such as vessels in the reconstructed images.
State-of-the-art low-dose CT methods reduce the x-ray tube current and use iterative reconstruction methods to denoise the resulting images. However, due to compromises between denoising and image quality, only moderate dose reductions up to 30-40% are accepted in clinical practice. An alternative approach is to reduce the number of x-ray projections and use compressed sensing to reconstruct the full-tube-current undersampled data. This idea was recognized in the early days of compressed sensing and proposals for CT dose reduction appeared soon afterwards. However, no practical means of undersampling has yet been demonstrated in the challenging environment of a rapidly rotating CT gantry. In this work, we propose a moving multislit collimator as a practical incoherent undersampling scheme for compressed sensing CT and evaluate its application for radiation dose reduction. The proposed collimator is composed of narrow slits and moves linearly along the slice dimension (z), to interrupt the incident beam in different slices for each x-ray tube angle (θ). The reduced projection dataset is then reconstructed using a sparse approach, where 3D image gradients are employed to enforce sparsity. The effects of the collimator slits on the beam profile were measured and represented as a continuous slice profile. SparseCT was tested using retrospective undersampling and compared against commercial current-reduction techniques on phantoms and in vivo studies. Initial results suggest that SparseCT may enable higher performance than current-reduction, particularly for high dose reduction factors.
The task of imaging is to gather spatiotemporal information which can be organized into a coherent map. Tomographic imaging in particular involves the use of multiple projections, or other interactions of a probe (light, sound, etc.) with a body, in order to determine cross-sectional information. Though the probes and the corresponding imaging modalities may vary, and though the methodology of particular imaging approaches is in constant ferment, the conceptual underpinnings of tomographic imaging have in many ways remained fixed for many decades. Recent advances in applied mathematics, however, have begun to roil this intellectual landscape. The advent of compressed sensing, anticipated in various algorithms dating back many years but unleashed in full theoretical force in the last decade, has changed the way imagers have begun to think about data acquisition and image reconstruction. The power of incoherent sampling and sparsity-enforcing reconstruction has been demonstrated in various contexts and, when combined with other modern fast imaging techniques, has enabled unprecedented increases in imaging efficiency. Perhaps more importantly, however, such approaches have spurred a shift in perspective, prompting us to focus less on nominal data sufficiency than on information content. Beginning with examples from MRI, then proceeding through selected other modalities such as CT and PET, as well as multimodality combinations, this paper explores the potential of newly evolving acquisition and reconstruction paradigms to change the way we do imaging in the lab and in the clinic.
L+S matrix decomposition finds the low-rank (L) and sparse (S) components of a matrix M by solving the following
convex optimization problem: min‖L‖<sub>*</sub>L+S matrix decomposition finds the low-rank (L) and sparse (S) components of a matrix M by solving the following convex optimization problem: ‖L ‖<sub>*</sub> + λ‖S‖<sub>1</sub>, subject to M=L+S, where ‖L‖<sub>*</sub> is the nuclear-norm or sum of singular values of L and ‖S‖<sub>1</sub> is the 1<sub>1</sub>-norm| or sum of absolute values of S. This work presents the application of the L+S
decomposition to reconstruct incoherently undersampled dynamic MRI data as a superposition of a slowly or coherently changing background and sparse innovations. Feasibility of the method was tested in several accelerated dynamic MRI experiments including cardiac perfusion, time-resolved peripheral angiography and liver perfusion using Cartesian and radial sampling. The high acceleration and background separation enabled by L+S reconstruction promises to enhance spatial and temporal resolution and to enable background suppression without the need of subtraction or modeling.
Parallel MRI can achieve increased spatiotemporal resolution in MRI by simultaneously sampling reduced k-space data
with multiple receiver coils. One requirement that different parallel MRI techniques have in common is the need to
determine spatial sensitivity information for the coil array. This is often done by smoothing the raw sensitivities obtained
from low-resolution calibration images, for example via polynomial fitting. However, this sensitivity post-processing
can be both time-consuming and error-prone. Another important factor in Parallel MRI is noise amplification in the
reconstruction, which is due to non-unity transformations in the image reconstruction associated with spatially correlated
coil sensitivity profiles. Generally, regularization approaches, such as Tikhonov and SVD-based methods, are applied to
reduce SNR loss, at the price of introducing residual aliasing. In this work, we present a regularization approach using in
vivo coil sensitivities in parallel MRI to overcome these potential errors into the reconstruction. The mathematical
background of the proposed method is explained, and the technique is demonstrated with phantom images. The
effectiveness of the proposed method is then illustrated clinically in a whole-heart 3D cardiac MR acquisition within a
single breath-hold. The proposed method can not only overcome the sensitivity calibration problem, but also suppress a
substantial portion of reconstruction-related noise without noticeable introduction of residual aliasing artifacts.