Blind compressive sensing dynamic MRI.
Blind compressive sensing dynamic MRI.
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DOI：
10.1109/tmi.2013.2255133
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发表时间：
2013-06
影响因子：
10.6
通讯作者：
Jacob M
中科院分区：
文献类型：
--
作者：
Lingala SG;Jacob M
我们提出了一种新的盲压缩感知（BCS）框架工作，以恢复动态磁共振图像欠采样测量。该方案将动态信号建模为从大型字典中选择的时间基函数的稀疏线性组合。与传统的压缩感知算法相比，BCS算法能够同时估计出字典和稀疏系数。除了系数的稀疏性之外，BCS方案与当前低秩方法的关键区别在于字典基函数的非正交性质。由于BCS模型的自由度的数量小于低秩方法，它提供了在高加速度下的改进的重建。我们制定的重建作为一个约束优化问题，目标函数是一个数据的一致性和稀疏性促进系数的先验的线性组合。使用Frobenius范数字典约束来避免尺度歧义。我们引入了一个简单而有效的优化最小化算法，它将原准则分解为三个简单的子问题。使用交替最小化策略，其中我们循环通过三个简单的问题的最小化。该算法被认为是相当快的方法，交替稀疏编码和字典估计，以及K-SVD字典学习方案的扩展。与大多数字典学习算法中假设的100范数和列范数约束相比，使用101罚和Frobenius范数字典约束能够衰减不重要的基函数;这是特别重要的，因为可以可靠估计的基函数的数量受到可用测量的限制。我们还观察到，该计划是更强大的局部极小值相比，K-SVD方法，它依赖于贪婪稀疏编码。我们的相变实验表明，BCS方案提供了更好的恢复率比经典的基于傅立叶的CS计划，而只是稍微差于字典感知设置。由于额外估计字典的开销很低，因此该方法在动态MRI应用中非常有用，其中信号在已知字典中并不稀疏。我们证明了BCS计划在加速对比度增强的动态数据的效用。我们观察到上级的重建性能与BCS计划相比，现有的低秩和压缩感知计划。
We propose a novel blind compressive sensing (BCS) frame work to recover dynamic magnetic resonance images from undersampled measurements. This scheme models the dynamic signal as a sparse linear combination of temporal basis functions, chosen from a large dictionary. In contrast to classical compressed sensing, the BCS scheme simultaneously estimates the dictionary and the sparse coefficients from the undersampled measurements. Apart from the sparsity of the coefficients, the key difference of the BCS scheme with current low rank methods is the non-orthogonal nature of the dictionary basis functions. Since the number of degrees of freedom of the BCS model is smaller than that of the low-rank methods, it provides improved reconstructions at high acceleration rates. We formulate the reconstruction as a constrained optimization problem; the objective function is the linear combination of a data consistency term and sparsity promoting ℓ1 prior of the coefficients. The Frobenius norm dictionary constraint is used to avoid scale ambiguity. We introduce a simple and efficient majorize-minimize algorithm, which decouples the original criterion into three simpler sub problems. An alternating minimization strategy is used, where we cycle through the minimization of three simpler problems. This algorithm is seen to be considerably faster than approaches that alternates between sparse coding and dictionary estimation, as well as the extension of K-SVD dictionary learning scheme. The use of the ℓ1 penalty and Frobenius norm dictionary constraint enables the attenuation of insignificant basis functions compared to the ℓ0 norm and column norm constraint assumed in most dictionary learning algorithms; this is especially important since the number of basis functions that can be reliably estimated is restricted by the available measurements. We also observe that the proposed scheme is more robust to local minima compared to K-SVD method, which relies on greedy sparse coding. Our phase transition experiments demonstrate that the BCS scheme provides much better recovery rates than classical Fourier-based CS schemes, while being only marginally worse than the dictionary aware setting. Since the overhead in additionally estimating the dictionary is low, this method can be very useful in dynamic MRI applications, where the signal is not sparse in known dictionaries. We demonstrate the utility of the BCS scheme in accelerating contrast enhanced dynamic data. We observe superior reconstruction performance with the BCS scheme in comparison to existing low rank and compressed sensing schemes.