Dynamic computed tomography (CT) angiography of the abdomen provides perfusion information and characteristics of the tissues present in the abdomen. This information could potentially help characterize liver metastases. However, radiation dose has to be relatively low for the patient, causing the images to have very high noise content. Denoising methods are needed to increase image quality. The purpose of this study was to investigate the performance, limitations, and behavior of a new 4D filtering method, called the 4D Similarity Filter (4DSF), to reduce image noise in temporal CT data. The 4DSF averages voxels with similar time-intensity curves (TICs). Each phase is filtered individually using the information of all phases except for the one being filtered. This approach minimizes the bias toward the noise initially present in this phase. Since the 4DSF does not base similarity on spatial proximity, loss of spatial resolution is avoided. The 4DSF was evaluated on a 12-phase liver dynamic CT angiography acquisition of 52 digital anthropomorphic phantoms, each containing one hypervascular 1cm lesion with a small necrotic core. The metrics used for evaluation were noise reduction, lesion contrast-to-noise ratio (CNR), CT number accuracy using peak-time and peak-intensity of the TICs, and resolution loss. The results were compared to those obtained by the time-intensity profile similarity (TIPS) filter, which uses the whole TIC for determining similarity, and the combination 4DSF followed by TIPS filter (4DSF + TIPS). The 4DSF alone resulted in a median noise reduction by a factor of 6.8, which is lower than that obtained by the TIPS filter at 8.1, and 4DSF + TIPS at 12.2. The 4DSF increased the median CNR from 0. 44 to 1.85, which is less than the TIPS filter at 2.59 and 4DSF + TIPS at 3.12. However, the peak-intensity accuracy in the TICs was superior for the 4DSF, with a median intensity decrease of -34 HU compared to -88 and -50 HU for the hepatic artery when using the TIPS filter and 4DSF + TIPS, respectively. The median peak-time accuracy was inferior for the 4DSF filter and 4DSF + TIPS, with a time shift of -1 phases for the portal vein TIC compared to no shift in time when using the TIPS. The analysis of the full-width-at-half-maximum (FWHM) of a small artery showed significantly less spatial resolution loss for the 4DSF at 3.2 pixels, compared to the TIPS filter at 4.3 pixels, and 3.4 pixels for the 4DSF + TIPS. The 4DSF can reduce noise with almost no resolution loss, making the filter very suitable for denoising 4D CT data for detection tasks, even in very low dose, i.e., very high noise level, situations. In combination with the TIPS filter, the noise reduction can be increased even further.