Scene refocusing beyond extended depth of field for users to observe objects effectively is aimed by researchers in computational photography, microscopic imaging, and so on. Ordinary all-in-focus image reconstruction from a sequence of multi-focus images achieves extended depth of field, where reconstructed images would be captured through a pinhole in the center on the lens. In this paper, we propose a novel method for reconstructing all-in-focus images through shifted pinholes on the lens based on 3D frequency analysis of multi-focus images. Such shifted pinhole images are obtained by a linear combination of multi-focus images with scene-independent 2D filters in the frequency domain. The proposed method enables us to efficiently synthesize dense 4D light field on the lens plane for image-based rendering, especially, robust scene refocusing with arbitrary bokeh. Our novel method using simple linear filters achieves not only reconstruction of all-in-focus images even for shifted pinholes more robustly than the conventional methods depending on scene/focus estimation, but also scene refocusing without suffering from limitation of resolution in comparison with recent approaches using special devices such as lens arrays in computational photography.