Cryogenic electron tomography provides visualization of cellular complexes in situ, allowing a further understanding of cellular function. However, the projection images from this technique present a meager signal-to-noise ratio due to the limited electron dose, and the lack of projections at high tilt angles produces the 'missing-wedge' problem in the Fourier domain. These limitations in the projection data prevent traditional reconstruction techniques from achieving good reconstructions. Multiple strategies have been proposed to deal with the noise and the artifacts arising from the 'missing-wedge’ problem. For example, manually selecting subtomograms of identical structures and averaging them (subtogram averaging), data-driven approaches that intend to perform subtogram averaging automatically, and various methods for denoising tilt-series before reconstruction or denoising the volumes after reconstruction. Most of these approaches are additional pre-processing or post-processing steps independent from the reconstruction method, and the consistency of the resulting tomograms with the original projection data is lost after the modifications. We propose a GPU accelerated optimization-based reconstruction framework using proximal algorithms. Our framework integrates denoising in the reconstruction process by alternating between reconstruction and denoising, relieving the users of the need to select additional denoising algorithms and preserving the consistency between final tomograms and projection data. Thanks to the flexibility provided by proximal algorithms, various available proximal operators can be interchanged for each task, e.g., various algebraic reconstruction methods and denoising techniques. We evaluate our approach qualitatively by comparison with current reconstruction and denoising approaches, showing excellent denoising capabilities and superior visual quality of the reconstructed tomograms. We quantitatively evaluate the methods with a recently proposed synthetic dataset for scanning transmission electron microscopy, achieving superior reconstruction quality for a noisy and angle-limited synthetic dataset.