The aim of this paper is to present an image compression method using feedforward backpropagation neural networks. Medical imaging is an efficient source for better diagnosis of the disease and also helps in assessing the severity of the disease. But due to the increasing size of the medical images, transferring and storage of images require huge bandwidth and storage space. Therefore, it is essential to derive an effective compression algorithm, which have minimal loss, time complexity, and increased reduction in size. With the concept of Neural Network, data compression can be achieved by producing an internal data representation. The training algorithm and development architecture gives less distortion and considerable compression ratio and also keeps up the capability of hypothesizing and is becoming important. The performance metrics of three algorithms, Levenberg Marquardt algorithm, Resilient backpropagation algorithm, and Gradient Decent algorithm have been computed on Magnetic Resonance Imaging (MRI) images and it is observed that Levenberg Marquardt algorithm is more accurate when compared to the other two algorithms.