Accelerated Dynamic MRI Exploiting Sparsity and Low-Rank Structure: k-t SLR

Abstract

We introduce a novel algorithm to reconstruct dynamic MRI data from under-sampled k-t space data. In contrast to classical model based cine MRI schemes that rely on the sparsity or banded structure in Fourier space, we use the compact representation of the data in the Karhunen Louve transform (KLT) domain to exploit the correlations in the dataset. The use of the data-dependent KL transform makes our approach ideally suited to a range of dynamic imaging problems, even when the motion is not periodic. In comparison to current KLT-based methods that rely on a two-step approach to first estimate the basis functions and then use it for reconstruction, we pose the problem as a spectrally regularized matrix recovery problem. By simultaneously determining the temporal basis functions and its spatial weights from the entire measured data, the proposed scheme is capable of providing high quality reconstructions at a range of accelerations. In addition to using the compact representation in the KLT domain, we also exploit the sparsity of the data to further improve the recovery rate. Validations using numerical phantoms and in-vivo cardiac perfusion MRI data demonstrate the significant improvement in performance offered by the proposed scheme over existing methods.

High‐resolution 1H‐MRSI of the brain using SPICE: Data acquisition and image reconstruction

“…Although such a joint subspace pursuit and reconstruction approach has been successfully used in various dynamic imaging applications (e.g., (30)(31)(32)), it is not effective for highresolution in vivo MRSI due to the limited SNR. An alternative is to acquire complementary data sets that allows for determining ϕ l (t) and c l (r) separately.…”

Cardiac diffusion tensor imaging based on compressed sensing using joint sparsity and low-rank approximation

“…To evaluate the performance of the proposed method, a comparison was performed with several stateof-the-art reconstruction methods, including the basic CS method [12], low rank [15], and joint sparsity method [9]. The root mean square errors (RMSE) of fractional anisotropy (FA) and mean diffusivity (MD) were calculated for each method.…”

MRI reconstruction of multi‐image acquisitions using a rank regularizer with data reordering

“…Accelerating multi-image MRI acquisitions is a developing area that can have a high practical impact. Many groups have applied acceleration methods for dynamic (multiple time frame) MRI, [1][2][3][4][5][6][7] although the concepts typically also apply to other multi-image acquisitions. These methods undersample k-space data and then use algorithms beyond the inverse Fourier transform (IFT) to exploit redundancies between images and obtain high quality diagnostic images.…”

“…4 Recent developments in matrix completion theory 8,9 have translated to exciting results from low-rank reconstruction methods applied to MRI. 6,[10][11][12][13][14] Rank constrained reconstructions have been applied in the context of static imaging 15 as well as in dynamic MRI. Promising results have been shown for myocardial perfusion MRI (Ref.…”