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Tomography has made a revolutionary impact on diverse fields, ranging from macro-/mesoscopic scale studies in biology, radiology, plasma physics to the characterization of 3D atomic structure in material science. The fundamental of tomography is to reconstruct a 3D object from a set of 2D projections. To solve the tomography problem, many algorithms have been developed. Among them are methods using transformation technique such as computed tomography (CT) based on Radon transform and Generalized Fourier iterative reconstruction (GENFIRE) based on Fourier slice theorem (FST), and direct methods such as Simultaneous Iterative Reconstruction Technique (SIRT) and Simultaneous Algebraic Reconstruction Technique (SART) using gradient descent and algebra technique. In this paper, we propose a hybrid gradient descent to solve the tomography problem by combining Fourier slice theorem and calculus of variations. By using simulated and experimental data, we show that the state-of-art RESIRE can produce more superior results than previous methods; the reconstructed objects have higher quality and smaller relative errors. More importantly, RESIRE can deal with partially blocked projections rigorously where only part of projection information are provided while other methods fail. We anticipate RESIRE will not only improve the reconstruction quality in all existing tomographic applications, but also expand tomography method to a broad class of functional thin films. We expect RESIRE to find a broad applications across diverse disciplines.