Tensor regularized total variation for denoising of third harmonic generation images of brain tumors

Abstract

Third harmonic generation (THG) microscopy shows great potential for instant pathology of brain tissue during surgery. However, the rich morphologies contained and the noise associated makes image restoration, necessary for quantification of the THG images, challenging. Anisotropic diffusion filtering (ADF) has been recently applied to restore THG images of normal brain, but ADF is hard-to-code, time-consuming and only reconstructs salient edges. This work overcomes these drawbacks by expressing ADF as a tensor regularized total variation model, which uses the Huber penalty and the L₁ norm for tensor regularization and fidelity measurement, respectively. The diffusion tensor is constructed from the structure tensor of ADF yet the tensor decomposition is performed only in the non-flat areas. The resulting model is solved by an efficient and easy-to-code primal-dual algorithm. Tests on THG brain tumor images show that the proposed model has comparable denoising performance as ADF while it much better restores weak edges and it is up to 60% more time efficient.

Keywords: anisotropic diffusion; convex optimization; tensor regularization; third harmonic generation; weak edges.