After inquiring about it, Cagdas Bilen sent me the following:
Hi Igor,We now have our simulation codes published in our website (http://vision.poly.edu/cbilen/index.php?n=Main.Research) for anybody interested. The same website also has a link to and information about our other work on compressed sensing reconstruction with the aid of (simultaneous) motion estimation/compensation, the codes for which will also be published in the same website soon.I hope your readers find it interesting.Best,Cagdas
The paper is: High Speed Compressed Sensing Reconstruction in Dynamic Parallel MRI Using Augmented Lagrangian and Parallel Processing by Cagdas Bilen , Yao Wang and Ivan Selesnick. The abstract reads:
Magnetic Resonance Imaging (MRI) is one of the ﬁelds that the compressed sensing theory is well utilized to reduce the scan time signiﬁcantly leading to faster imaging or higher resolution images. It has been shown that a small fraction of the overall measurements are sufﬁcient to reconstruct images with the combination of compressed sensing and parallel imaging. Various reconstruction algorithms has been proposed for compressed sensing, among which Augmented Lagrangian based methods have been shown to often perform better than others for many different applications. In this paper, we propose new Augmented Lagrangian based solutions to the compressed sensing reconstruction problem with analysis and synthesis prior formulations. We also propose a computational method which makes use of properties of the sampling pattern to signiﬁcantly improve the speed of the reconstruction for the proposed algorithms in Cartesian sampled MRI. The proposed algorithms are shown to outperform earlier methods especially for the case of dynamic MRI for which the transfer function tends to be a very large matrix and signiﬁcantly ill conditioned. It is also demonstrated that the proposed algorithm can be accelerated much further than other methods in case of a parallel implementation with graphics processing units (GPUs).
also of related interest: Compressed Sensing for Moving Imagery in Medical Imaging by Cagdas Bilen, Yao Wang and Ivan Selesnick. The abstract reads:
Numerous applications in signal processing have beneﬁted from the theory of compressed sensing which shows that it is possible to reconstruct signals sampled below the Nyquist rate when certain conditions are satisﬁed. One of these conditions is that there exists a known transform that represents the signal with a sufﬁciently small number of non-zero coefﬁcients. However when the signal to be reconstructed is composed of moving images or volumes, it is challenging to form such regularization constraints with traditional transforms such as wavelets. In this paper, we present a motion compensating prior for such signals that is derived directly from the optical ﬂow constraint and can utilize the motion information during compressed sensing reconstruction. Proposed regularization method can be used in a wide variety of applications involving compressed sensing and images or volumes of moving and deforming objects. It is also shown that it is possible to estimate the signal and the motion jointly or separately. Practical examples from magnetic resonance imaging has been presented to demonstrate the beneﬁt of the proposed method.
Thanks Cagdas !
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