One of the affordable and least harmful modalities used to efficiently detect and diagnose the kidney diseases is the Ultrasound scans. The main drawback of the ultrasound images is the presence of speckle noise that reduces the efficiency of image processing and hinders the interpretation. This paper proposes a novel technique named Local Binary Pattern based Discrete Topological Derivative and its variants to address speckle noise reduction problem in 2D ultrasound kidney images. In typical Discrete Topological Derivative, the execution time is higher and as a result an optimizer is incorporated based on local pattern and gradient tolerance value resulting in 20 times reduction in execution time with improved results. The experimentation is carried out on 100 clinical 2D ultrasound images and moreover, proposed methods are compared with the competing Discrete Topological Derivative and some commonly used speckle noise removal filters. The results are promising and thereby confirms that the proposed Local Binary Pattern based Discrete Topological Derivative can produce a better speckle noise reduction that enables the doctors to detect and diagnose kidney diseases in 2D ultrasound images with lesser strain.