论文标题
可变密度傅立叶采样图像的彩色混叠模型传递的近似消息传递
Approximate Message Passing with a Colored Aliasing Model for Variable Density Fourier Sampled Images
论文作者
论文摘要
大概消息传递（AMP）算法有效地重建了已用大i.i.d进行采样的信号。下高斯传感矩阵。 AMP的核心是其“状态进化”，它保证了当前估计和地面真理（“混叠”）之间的差异在每种迭代中都遵循可以完全表征标量的高斯分布。但是，当采样具有非均匀光谱密度的信号的傅立叶系数（例如在磁共振成像（MRI）中）时，混叠为本质上是颜色的，AMP的标量状态进化不再准确，并且算法遇到的算法会逆转问题。作为响应，我们提出了可变密度近似消息传递（VDAMP）算法，该算法使用小波域来对彩色的混叠进行建模。我们提供了VDAMP遵守“有色状态演化”的经验证据，在该证据中，该混叠遵守一个高斯分布，可以用每个小波s子带一个标量来表征一个高斯分布。国家进化的一个好处是，可以有效地实施Stein的无偏风险估计（确定），从而产生具有无自由参数的子带依赖性阈值的算法。我们从经验上评估了VDAMP对快速迭代收缩阈值（FISTA）的三种变化的有效性，并发现它平均比下一个最快的方法差的迭代率少了10倍，并且与可比的于点相似。
The Approximate Message Passing (AMP) algorithm efficiently reconstructs signals which have been sampled with large i.i.d. sub-Gaussian sensing matrices. Central to AMP is its "state evolution", which guarantees that the difference between the current estimate and ground truth (the "aliasing") at every iteration obeys a Gaussian distribution that can be fully characterized by a scalar. However, when Fourier coefficients of a signal with non-uniform spectral density are sampled, such as in Magnetic Resonance Imaging (MRI), the aliasing is intrinsically colored, AMP's scalar state evolution is no longer accurate and the algorithm encounters convergence problems. In response, we propose the Variable Density Approximate Message Passing (VDAMP) algorithm, which uses the wavelet domain to model the colored aliasing. We present empirical evidence that VDAMP obeys a "colored state evolution", where the aliasing obeys a Gaussian distribution that can be fully characterized with one scalar per wavelet subband. A benefit of state evolution is that Stein's Unbiased Risk Estimate (SURE) can be effectively implemented, yielding an algorithm with subband-dependent thresholding that has no free parameters. We empirically evaluate the effectiveness of VDAMP on three variations of Fast Iterative Shrinkage-Thresholding (FISTA) and find that it converges in around 10 times fewer iterations on average than the next-fastest method, and to a comparable mean-squared-error.
