Depth (disparity) estimation from a light field (a set of dense multi-view images) is currently attracting much research interest. This paper focuses on how to handle a noisy light field for disparity estimation, because if left as it is, the noise deteriorates the accuracy of estimated disparity maps. Several researchers have worked on this problem, e.g., by introducing disparity cues that are robust to noise. However, it is not easy to break the trade-off between the accuracy and computational speed. To tackle this trade-off, we have integrated a fast denoising scheme in a fast disparity estimation framework that works in the epipolar plane image (EPI) domain. Specifically, we found that a simple 1-D slanted filter is very effective for reducing noise while preserving the underlying structure in an EPI. Moreover, this simple filtering does not require elaborate parameter configurations in accordance with the target noise level. Experimental results including real-world inputs show that our method can achieve good accuracy with much less computational time compared to some state-of-the-art methods.