Ultrasonic imaging serves as a pivotal tool in mitigating overdiagnosis of breast cancer in women, owing to its high sensitivity, low false-positive rate, and ability to reduce unnecessary biopsies. Nevertheless, these images are impaired by speckle noise, which appears as granular interference obscuring tissue boundaries and diminishing image contrast. This noise impedes subsequent image processing tasks such as edge detection, segmentation, feature extraction, and classification. Existing strategies for speckle noise reduction in ultrasonic images either compromise on effectiveness or demand substantial processing time, presenting challenges in preserving fine edge details. Addressing these issues, we propose an innovative hybrid deep learning model, FCNN-IDOA, which synergizes a Fundamental Convolutional Neural Network (FCNN) with an optimization algorithm. Our FCNN model is built upon the framework of GoogLeNet, enhanced with fifteen additional layers to augment its expressiveness. Subsequently, an Improved Dragonfly Optimization Algorithm (IDOA) is deployed to optimize FCNN's parameters, thereby improving the computational efficiency of the model. The suggested model has demonstrated superior performance, outstripping previous models in terms of accuracy. During experimental validation, the model achieved an average t(s) value of 84.764421, a PSNR value of 66, an MSE value of 54.9143, an RMSE value of 0.491631, and a final t(s) value of 83.759067. The results indicate that this novel model significantly outperforms the BC models, rendering it a promising solution for speckle noise reduction in breast cancer ultrasound images.