This paper proposes a novel denoising and edge detection algorithms for image using least squares support vector machine (LS-SVM) with Gaussian radial basis functions (RBF) kernel. The new filter, called least squares support vector machine filter (LS-SVMF) for image denoising, is based on the general concept of binary filters and machine learning theory. Using the LS-SVM, a set of the new gradient operators and the corresponding second derivative operators are obtained. Computer experiments are carried out for denoising and extracting edge information from real images. The results obtained for the applications show that the proposed algorithms outperform many other existing methods in the image denoising task and the traditional edge detectors. The proposed algorithms can be successfully applied for the processing of images corrupted with impulsive noise while maintaining the visual quality and a low reconstruction error.