In this paper, a new adaptive variable exponent based total variation image regularization algorithm is proposed. In the proposed algorithm a regularizing term based on variable exponent is used. The model adaptively switches between TV-ROF model and Tikhonov model. At the edges the model behaves like a ROF model preserving edges effectively. In the inner region the model behaves like a Tikhonov model which enables strong smoothing. The weight of the fidelity term is also adaptive. The weight is large at edges and small in the constant flat area. In this paper the performance of proposed adaptive variable exponent based total variation model is compared with TV-ROF model and Tikhonov model. The performance of the proposed model is compared with other classical diffusion algorithms such as perona-malik model and self-snake model. In addition the proposed model is also compared with nonlocal means filter. The performance of the proposed algorithm is validated by denoising rician noise corrupted brain magnetic resonance images as well as denoising salt and pepper noise corrupted standard images.