Navigator Filtering Using Principal Component Analysis

Introduction: The acquisition of Cardiac MR volumes usually requires monitoring diaphragmatic motion to correct for breathing artifacts. In particular navigator echoes and self-respiratory techniques (k0 profiles) can be used to acquire static high-resolution or cine images respectively. However, undesired cardiac motion, field inhomogeneities and high adipose fat signal may reduce the quality of the navigator projections leading to an erroneous and noisy estimation of the respiratory signal. Low pass filter can be used to eliminate the noise [1], but its inherent response delay makes this approach difficult to realize for real time prospective gating [2]. Recently, a methodology for real time navigator processing using Kalman filtering was proposed [3]. However, this approach requires an explicit model for breathing motion obtained from external sensors (e.g. bellows). Moreover, changes of the breathing pattern that differed from the model could lead to an erroneous output. To overcome this problem, we propose a novel approach for filtering the navigator projections rather than the respiratory signal using Principal Component Analysis (PCA). This original method was applied successfully to remove unwanted signals in the projections, and consequently an improved respiratory signal was obtained. Moreover, the proposed approach does not need an explicit model and has a great potential to be implemented in real time. Theory: PCA is an orthogonal linear transform usually used to reduce dimensionality of the data by retaining those characteristics that contributes most to its variance. This process is equivalent to finding the singular value decomposition of a matrix A = USV T and then projecting A into a reduced space defined by only m singular values ̃ A = ̃ U ̃ U A . We proposed to apply this theory for reduction of unwanted signals in the navigator projections. In this case the rows and columns of a matrix A correspond to n pixels and t samples of the navigator projection p respectively: A = [ p 1 v p 2 v p 3 v p 4.......... v p t ]. Once the matrix U is calculated a single projection can then be projected into the reduced space by