This technology includes a microscopy technique that combines the strengths of multiview imaging (better resolution isotropy, better depth penetration) with resolution-improving structured illumination microscopy (SIM). The proposed microscope uses a sharp line-focused illumination structure to excite and confocally detect sample fluorescence from 3 complementary views. Since resolution along any particular axis is defined by the super-resolved lateral resolution improvement obtained via that axis, axial resolution is improved ~2-fold over the current state of the art (traditional 3D SIM), while introducing less dose and operating at higher speed. Included are additional methods for further improving speed and resolution and reducing phototoxicity. The new computational / optical methods we propose also will provide the basis for powerful machine learning methods that will further improve the performance of the microscope.