Adaptive sparsity level and dictionary size estimation for image reconstruction in accelerated 2D radial cine MRI.

Marie‐Christine Pali,Christoph Kolbitsch,Tobias Schaeffter,Andreas Kofler

doi:10.1002/mp.14547

Abstract

In the past, dictionary learning (DL) and sparse coding (SC) have been proposed for the regularization of image reconstruction problems. The regularization is given by a sparse approximation of all image patches using a learned dictionary, that is, an overcomplete set of basis functions learned from data. Despite its competitiveness, DL and SC require the tuning of two essential hyperparameters: the sparsity level S - the number of basis functions of the dictionary, called atoms, which are used to approximate each patch, and K - the overall number of such atoms in the dictionary. These two hyperparameters usually have to be chosen a priori and are determined by repetitive and computationally expensive experiments. Furthermore, the final reported values vary depending on the specific situation. As a result, the clinical application of the method is limited, as standardized reconstruction protocols have to be used. In this work, we use adaptive DL and propose a novel adaptive sparse coding algorithm for two-dimensional (2D) radial cine MR image reconstruction. Using adaptive DL and adaptive SC, the optimal dictionary size K as well as the optimal sparsity level S are chosen dependent on the considered data. Our three main results are the following: First, adaptive DL and adaptive SC deliver results which are comparable or better than the most widely used nonadaptive version of DL and SC. Second, the time needed for the regularization is accelerated due to the fact that the sparsity level S is never overestimated. Finally, the a priori choice of S and K is no longer needed but is optimally chosen dependent on the data under consideration. Adaptive DL and adaptive SC can highly facilitate the application of DL- and SC-based regularization methods. While in this work we focused on 2D radial cine MR image reconstruction, we expect the method to be applicable to different imaging modalities as well.

Highlights

Acquisition process due to physical limits imposed by the scanner
We have that the adaptive combination aITKrM + aOMP achieved the best results with respect to all reported measures when compared to the nonadaptive combinations for the best choices of S and K
Because aITKrM is approximately 10 times faster than K-singular value decomposition (K-SVD), allowing aITKrM to take the same amount of time as K-SVD, it is possible to surpass K-SVD + orthogonal matching pursuit (OMP) in terms of peak signal-to-noise ratio (PSNR) and to obtain the same normalized root mean squared error (NRMSE), for the case where the dictionary is learned during the reconstruction, see Table III

Summary

Introduction

Acquisition process due to physical limits imposed by the scanner. In particular, typical cardiac MR scans are per-. Since the acquisition is often slow, dimensional (2D) images showing the heart movement can undersampling in k-space is used to shorten scan times. The regularization of the solution is achieved by the fact that, given the incoherent undersampling scheme applied in k-space, the artifacts resulting from the direct reconstruction of an image are high dimensional and suppressed by the low-dimensional representation, which suffices to capture the important features. Performing an S-sparse approximation of all image patches is computationally quite expensive, especially when S is chosen relatively high These two issues make the method prohibitive for the application in the clinical routine where standardized reconstruction protocols have to be used

Methods

Results

Discussion

Conclusion