We present an image reconstruction approach that incorporates regularization by multiplying the data-fidelity term by a total variation functional. Usually, regularization is carried out in an additive manner, with a regularization parameter balancing out the two terms. Such a parameter often needs to be tuned for each dataset through extensive numerical experimentation. Our approach does not require such a parameter. We applied the method to in-vivo data acquired using a low-field MR scanner. Our results show that the method successfully denoises low-field MR images.