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Register a new userA Divide-and-Conquer Approach to Compressed Sensing MRI
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Xinghao Ding
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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Compressed sensing (CS) theory assures us that we can accurately reconstruct magnetic resonance images using fewer k-space measurements than the Nyquist sampling rate requires. In traditional CS-MRI inversion methods, the fact that the energy within the Fourier measurement domain is distributed non-uniformly is often neglected during reconstruction. As a result, more densely sampled low-frequency information tends to dominate penalization schemes for reconstructing MRI at the expense of high-frequency details. In this paper, we propose a new framework for CS-MRI inversion in which we decompose the observed k-space data into subspaces via sets of filters in a lossless way, and reconstruct the images in these various spaces individually using off-the-shelf algorithms. We then fuse the results to obtain the final reconstruction. In this way we are able to focus reconstruction on frequency information within the entire k-space more equally, preserving both high and low frequency details. We demonstrate that the proposed framework is competitive with state-of-the-art methods in CS-MRI in terms of quantitative performance, and often improves an algorithms results qualitatively compared with its direct application to k-space.
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Virtual memory (VM) is critical to the usability and programmability of hardware accelerators. Unfortunately, implementing accelerator VM efficiently is challenging because the area and power constraints make it difficult to employ the large multi-level TLBs used in general-purpose CPUs. Recent research proposals advocate a number of restrictions on virtual-to-physical address mappings in order to reduce the TLB size or increase its reach. However, such restrictions are unattractive because they forgo many of the original benefits of traditional VM, such as demand paging and copy-on-write. We propose SPARTA, a divide and conquer approach to address translation. SPARTA splits the address translation into accelerator-side and memory-side parts. The accelerator-side translation hardware consists of a tiny TLB covering only the accelerators cache hierarchy (if any), while the translation for main memory accesses is performed by shared memory-side TLBs. Performing the translation for memory accesses on the memory side allows SPARTA to overlap data fetch with translation, and avoids the replication of TLB entries for data shared among accelerators. To further improve the performance and efficiency of the memory-side translation, SPARTA logically partitions the memory space, delegating translation to small and efficient per-partition translation hardware. Our evaluation on index-traversal accelerators shows that SPARTA virtually eliminates translation overhead, reducing it by over 30x on average (up to 47x) and improving performance by 57%. At the same time, SPARTA requires minimal accelerator-side translation hardware, reduces the total number of TLB entries in the system, gracefully scales with memory size, and preserves all key VM functionalities.
Compressed sensing for magnetic resonance imaging (CS-MRI) exploits image sparsity properties to reconstruct MRI from very few Fourier k-space measurements. The goal is to minimize any structural errors in the reconstruction that could have a negative impact on its diagnostic quality. To this end, we propose a deep error correction network (DECN) for CS-MRI. The DECN model consists of three parts, which we refer to as modules: a guide, or template, module, an error correction module, and a data fidelity module. Existing CS-MRI algorithms can serve as the template module for guiding the reconstruction. Using this template as a guide, the error correction module learns a convolutional neural network (CNN) to map the k-space data in a way that adjusts for the reconstruction error of the template image. Our experimental results show the proposed DECN CS-MRI reconstruction framework can considerably improve upon existing inversion algorithms by supplementing with an error-correcting CNN.
We develop a Bayesian nonparametric model for reconstructing magnetic resonance images (MRI) from highly undersampled k-space data. We perform dictionary learning as part of the image reconstruction process. To this end, we use the beta process as a nonparametric dictionary learning prior for representing an image patch as a sparse combination of dictionary elements. The size of the dictionary and the patch-specific sparsity pattern are inferred from the data, in addition to other dictionary learning variables. Dictionary learning is performed directly on the compressed image, and so is tailored to the MRI being considered. In addition, we investigate a total variation penalty term in combination with the dictionary learning model, and show how the denoising property of dictionary learning removes dependence on regularization parameters in the noisy setting. We derive a stochastic optimization algorithm based on Markov Chain Monte Carlo (MCMC) for the Bayesian model, and use the alternating direction method of multipliers (ADMM) for efficiently performing total variation minimization. We present empirical results on several MRI, which show that the proposed regularization framework can improve reconstruction accuracy over other methods.
Compressed sensing MRI is a classic inverse problem in the field of computational imaging, accelerating the MR imaging by measuring less k-space data. The deep neural network models provide the stronger representation ability and faster reconstruction compared with shallow optimization-based methods. However, in the existing deep-based CS-MRI models, the high-level semantic supervision information from massive segmentation-labels in MRI dataset is overlooked. In this paper, we proposed a segmentation-aware deep fusion network called SADFN for compressed sensing MRI. The multilayer feature aggregation (MLFA) method is introduced here to fuse all the features from different layers in the segmentation network. Then, the aggregated feature maps containing semantic information are provided to each layer in the reconstruction network with a feature fusion strategy. This guarantees the reconstruction network is aware of the different regions in the image it reconstructs, simplifying the function mapping. We prove the utility of the cross-layer and cross-task information fusion strategy by comparative study. Extensive experiments on brain segmentation benchmark MRBrainS validated that the proposed SADFN model achieves state-of-the-art accuracy in compressed sensing MRI. This paper provides a novel approach to guide the low-level visual task using the information from mid- or high-level task.
We consider the learning of algorithmic tasks by mere observation of input-output pairs. Rather than studying this as a black-box discrete regression problem with no assumption whatsoever on the input-output mapping, we concentrate on tasks that are amenable to the principle of divide and conquer, and study what are its implications in terms of learning. This principle creates a powerful inductive bias that we leverage with neural architectures that are defined recursively and dynamically, by learning two scale-invariant atomic operations: how to split a given input into smaller sets, and how to merge two partially solved tasks into a larger partial solution. Our model can be trained in weakly supervised environments, namely by just observing input-output pairs, and in even weaker environments, using a non-differentiable reward signal. Moreover, thanks to the dynamic aspect of our architecture, we can incorporate the computational complexity as a regularization term that can be optimized by backpropagation. We demonstrate the flexibility and efficiency of the Divide-and-Conquer Network on several combinatorial and geometric tasks: convex hull, clustering, knapsack and euclidean TSP. Thanks to the dynamic programming nature of our model, we show significant improvements in terms of generalization error and computational complexity.
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