This paper presents an algorithm for reducing speckle noise from optical coherence tomography (OCT) images using an artificial neural network (ANN) algorithm. The noise is modeled using Rayleigh distribution with a noise parameter, sigma, estimated by the ANN. The input to the ANN is a set of intensity and wavelet features computed from the image to be processed, and the output is an estimated sigma value. This is then used along with a numerical method to solve the inverse Rayleigh function to reduce the noise in the image. The algorithm is tested successfully on OCT images of Drosophila larvae. It is demonstrated that the signal-to-noise ratio and the contrast-to-noise ratio of the processed images are increased by the application of the ANN algorithm in comparison with the respective values of the original images.