Image denoising is an important technique of practical significance which serves as a preliminary step for other analyses like image feature extraction, image classification etc. Two novel methods for denoising images are proposed which deal with the case when there is no noise-free training data. The basic method consists of several phases: the first phase involves preprocessing the given noisy data matrix to obtain a good approximation matrix; the second phase involves implementing kernel principal component analysis (KPCA) on the approximation matrix obtained from the first phase. KPCA is one of the useful non-linear techniques applied to image denoising. However, an important problem faced in KPCA is estimating the denoised pre-image. Consequently, we generate a pre-image by solving a regularized regression problem. The second method is an ensemble version of the basic method that provides robustness to noisy instances. Some of the attractive properties of the proposed methods include numerical stability and ease of implementation. Also our methods are based on linear algebra and avoid any nonlinear optimization. Our methods are demonstrated on high-noise cases (for both Gaussian noise and "salt and pepper" noise) for the USPS digits dataset, and they perform better than existing alternatives both in terms of low mean square error and better visual quality of the reconstructed pre-images.