Cerebral computed tomography perfusion (CTP) scans are acquired to detect areas of abnormal perfusion in patients with cerebrovascular diseases. These 4D CTP scans consist ofmultiple sequential 3D CT scans over time. Therefore, to reduce radiation exposure to the patient, the amount of x-ray radiation that can be used per sequential scan is limited, which results in a high level of noise. To detect areas of abnormal perfusion, perfusion parameters are derived from the CTP data, such as the cerebral blood flow (CBF). Algorithms to determine perfusion parameters, especially singular value decomposition, are very sensitive to noise. Therefore, noise reduction is an important preprocessing step for CTP analysis. In this paper, we propose a time-intensity profile similarity (TIPS) bilateral filter to reduce noise in 4D CTP scans, while preserving the time-intensity profiles (fourth dimension) that are essential for determining the perfusion parameters. The proposed TIPS bilateral filter is compared to standard Gaussian filtering, and 4D and 3D (applied separately to each sequential scan) bilateral filtering on both phantom and patient data. Results on the phantom data show that the TIPS bilateral filter is best able to approach the ground truth (noise-free phantom), compared to the other filtering methods (lowest root mean square error). An observer study is performed using CBF maps derived from fifteen CTP scans of acute stroke patients filtered with standard Gaussian, 3D, 4D and TIPS bilateral filtering. These CBF maps were blindly presented to two observers that indicated which map they preferred for (1) gray/white matter differentiation, (2) detectability of infarcted area and (3) overall image quality. Based on these results, the TIPS bilateral filter ranked best and its CBF maps were scored to have the best overall image quality in 100% of the cases by both observers. Furthermore, quantitative CBF and cerebral blood volume values in both the phantom and the patient data showed that the TIPS bilateral filter resulted in realistic mean values with a smaller standard deviation than the other evaluated filters and higher contrast-to-noise ratios. Therefore, applying the proposed TIPS bilateral filtering method to 4D CTP data produces higher quality CBF maps than applying the standard Gaussian, 3D bilateral or 4D bilateral filter. Furthermore, the TIPS bilateral filter is computationally faster than both the 3D and 4D bilateral filters.