We consider the problem of image denoising with unknown noise distribution. We propose a hybrid approach where model-based space-variant total variation (TV) regularization is used for denoising with hyperparameters estimated locally using a Convolutional Neural Network (CNN) with a simple and light architecture. The special choice of the weighted TV prior allows for the use of a limited learning set, while the use of the proposed CNN approach allows for local parameter estimation independently of the type of noise in the data. The obtained results show that the proposed hybrid approach takes benefit from both the prior information encoded in the choice of the regularization model and the versatility of the CNN-based parameter estimation approach.