arXiv subjects

Mikko Kettunen

Publications and source records attributed to Mikko Kettunen.

4 recordsLinked to original sources

arXiv2026

Sparse Dictionary-Based Solution of Dynamic Inverse Problems

In ill-posed dynamic inverse problems expected spatial features and temporal correlation between frames can be leveraged to improve the quality of the computed solution, in particular when the available data are limited and the dimensionality of the unknown is large. One way to take advantage of the spatial and temporal traits believed to characterize the solution is to encode them into the entries of a dictionary, and to seek the solution as a sparse linear combination of the dictionary atoms. To promote a vector of coefficients with mostly vanishing entries, we consider a stochastic extension of the dictionary coding problem model with a random hierarchical sparsity promoting prior. We compute the Maximum A Posteriori (MAP) estimate of the coefficient vector using the Iterative Alternating Sequential Algorithm (IAS), which has been demonstrated to efficiently solve inverse problems with minimal need for parameter tuning. The proposed methodology is tested on real-world dynamic Computed Tomography and MRI datasets, where it is compared to the popular Alternating Direction Method of Minimizers (ADMM). The computed examples show the that proposed methodology is competitive with the ADMM for compressed sensing, with a significantly lower sensitivity to hyper-parameter selection.

math.NA↗

arXiv2020

Data-driven regularization parameter selection in dynamic MRI

In dynamic MRI, sufficient time resolution can often only be obtained using imaging protocols which produce undersampled data for each image in the time series. This has led to the popularity of compressed sensing (CS) based image reconstruction approaches. One of the problems in CS approaches is determining the regularization parameters, which control the balance between data fidelity the spatial and temporal regularization terms. A data-driven approach is proposed for the total variation regularization parameter selection such that the reconstructions yield expected sparsity levels in the regularization domains. The expected sparsity levels are obtained from the measurement data for the temporal regularization and from a reference image for the spatial regularization. Two formulations are proposed. The first is a 2D search for a parameter pair which produces expected sparsity in both the temporal and spatial regularization domains. In the second approach, the sparsity-based parameter selection is split to two 1D searches using the S-curve method. The approaches are evaluated using simulated and experimental DCE-MRI. In the simulated test case, both proposed methods produce a parameter pair that is close to the RMSE optimal pair, and the reconstruction error is also close to minimum. In the experimental test case, the methods produce almost similar parameter selection, and the reconstructions are of high perceived quality. Both approaches lead to a highly feasible selection of the temporal and spatial regularization parameters in both the simulated and experimental test cases while the sequential method is computationally more efficient.

physics.med-ph↗

arXiv2020

Temporal Huber regularization for DCE-MRI

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is used to study microvascular structure and tissue perfusion. In DCE-MRI a bolus of gadolinium based contrast agent is injected into the blood stream and spatiotemporal changes induced by the contrast agent flow are estimated from a time series of MRI data. Sufficient time resolution can often only be obtained by using an imaging protocol which produces undersampled data for each image in the time series. This has led to the popularity of compressed sensing based image reconstruction approaches, where all the images in the time series are reconstructed simultaneously, and temporal coupling between the images is introduced into the problem by a sparsity promoting regularization functional. We propose the use of Huber penalty for temporal regularization in DCE-MRI, and compare it to total variation, total generalized variation and smoothness based temporal regularization models. We also study the effect of spatial regularization to the reconstruction and compare the reconstruction accuracy with different temporal resolutions due to varying undersampling. The approaches are tested using simulated and experimental radial golden angle DCE-MRI data from a rat brain specimen. The results indicate that Huber regularization produces similar reconstruction accuracy with the total variation based models, but the computation times are significantly faster.

physics.med-ph↗

arXiv2017

Dynamic MRI Reconstruction from Undersampled Data with an Anatomical Prescan

The goal of dynamic magnetic resonance imaging (dynamic MRI) is to visualize tissue properties and their local changes over time that are traceable in the MR signal. We propose a new variational approach for the reconstruction of subsampled dynamic MR data, which combines smooth, temporal regularization with spatial total variation regularization. In particular, it furthermore uses the infimal convolution of two total variation Bregman distances to incorporate structural a-priori information from an anatomical MRI prescan into the reconstruction of the dynamic image sequence. The method promotes the reconstructed image sequence to have a high structural similarity to the anatomical prior, while still allowing for local intensity changes which are smooth in time. The approach is evaluated using artificial data simulating functional magnetic resonance imaging (fMRI), and experimental dynamic contrast-enhanced magnetic resonance data from small animal imaging using radial golden angle sampling of the k-space.

math.NA↗