Speckles are introduced in the ultrasound data due to constructive and destructive interference of the probing signals that are used for capturing the characteristics of the tissue being imaged. There are a plethora of models discussed in the literature to improve the contrast and resolution of the ultrasound images by despeckling them. There is a class of models that assumes that the noise is multiplicative in its original form, and transforming the model to a log domain makes it an additive one. Nevertheless, such a transformation duly oversimplifies the scenario and does not capture the inherent properties of the data-correlated nature of speckles. Therefore, it results in poor reconstruction. This problem is addressed to a considerable extent in the subsequent works by adopting various models to address the data-correlated nature of the noise and its distributions. This work introduces a weberized non-local total bounded variational model based on the noise distribution built on the Retinex theory. This perceptually inspired model apparently restores and improves the contrast of the images without compromising much on the details inherently present in the data. The numerical implementation of the model is carried out using the Bregman formulation to improve the convergence rate and reduce the parameter sensitivity. The experimental results are highlighted and compared to demonstrate the efficiency of the model.