Four-dimensional dynamic computed tomography (4D-dCT) plays an important role in radiation treatment planning, delivery, and verification for lung cancer management, in addition to heart studies. 4D-dCT acquires multiple repeated measurements from the same patient. Therefore, the radiation dose during a 4D-dCT procedure is much higher than a routine 3D CT study. Low-dose scans for 4D-dCT is needed. In this work, a new reconstruction strategy is proposed to address the noise problem associated with low-dose dynamic CT scans. It first applies the Karhunen-Loève (KL) transform to the neighboring phases of 4D-dCT noise sinogram to consider the data correlation along the time dimension. In the KL domain, the independent 3D principal components are arranged according to their signal-to-noise ratios (which are reflected by their eigenvalues). It then adapts the filtered backprojection (FBP) algorithm to reconstruct each principal component in the KL domain, where the filter's cutoff frequency is adaptive to the eigenvalue of the corresponding KL component. Finally, the 4D-dCT image is obtained by inverse KL transform. A patient study was performed to demonstrate the effectiveness of the proposed strategy with comparison to a direct FBP reconstruction which does not consider the correlation or employ the KL transform. The gain of the KL-domain adaptive FBP reconstruction was measured quantitatively by noise-resolution tradeoff study.