Noise Reduction in Real-Time Phase Velocity Images via the Karhunen-Loeve Transform

Introduction: Clinical applications such as exercise stress cardiac MRI require the use of accelerated scan techniques to minimize acquisition time while maintaining image quality. In this context, maintaining sufficient signal-to-noise ratio (SNR) is crucial in order to preserve clinically relevant information. While the combination of echo planar readout and parallel reconstruction successfully reduces acquisition time and enables real-time phase-velocity imaging, these techniques increase image noise, potentially reducing their usefulness. Temporal averaging can only be practically applied with ECG synchronization and respiratory suspension or respiratory-gating, but these are often not possible in real-time stress imaging applications. Spatial averaging is another common noise reduction strategy, but can significantly affect image resolution and smooth out relevant image features. Therefore, we investigated the use of an automated post-processing technique for reduction of noise that does not adversely affect relevant information, such as peak velocity, in real-time phase velocity imaging. The Karhunev-Loeve Transform (KLT) (1) is an adaptive unitary linear transform that applied retrospectively to an image sequence results in a set of eigenimages with the signal energy concentrated within a discrete subset of eigenimages and the remaining eigenimages consisting only of noise. Such a transform is optimal in the least-squares sense and exploits data redundancy found in cardiac cine and velocity images. Filtering of real-time cine images may be carried out by zero-filling noise-only eigenimages in the KLT domain and inverting the transform. Determination of noise-only eigenimages is carried out by performing a search over subsets of eigenvalues in the KLT domain. For frames containing purely independent and identically distributed noise, the corresponding eigenvalues in the KLT domain fit the Marcenko-Pastur distribution (2), and examination of the statistical goodness-of-fit between eigenvalue subsets from the data matrix and the theoretical distribution allow the determination of the largest subset containing noise-only eigenimages. KLT filtering by zero-filling this subset results in an SNR gain determined by the cutoff level of the number of eigenimages identified as containing only noise. KLT filtering may be regarded as a form of smart adaptive weighted averaging that may be applied automatically to real-time velocity images. The automated application of KLT filtering bears advantages over temporal averaging, which without breath-hold and ECG-synchronization requires registration post-acquisition to produce meaningful results. Additionally, KLT filtering provides advantages over spatial averaging which, while robust to varied levels of noise, tends to significantly affect clinically relevant features. We apply KLT filtering to real-time phase velocity images in the presence of added noise and demonstrate that the KLT filtering process achieves a significant SNR gain without affecting peak velocity measurements. We then compare our results with those obtained using spatial averaging.