This paper presents an analysis of the multiresolution form of singular value decomposition SVD (MR-SVD) and generalizes the analysis into a random multiresolution form of singular value decomposition (R-MR-SVD) with an intrinsic randomness. The core idea behind the proposed transform is to introduce randomness in the computing process based on parameters without which one can neither decompose nor reconstruct the data correctly. The proposed transform inherits the excellent properties of MR-SVD along with its own unique features, which can be useful in many research areas. Image encryption, lossy image compression, and face recognition are the primary applications used to illustrate the practical usage of the proposed transform. © 2014 Elsevier Inc. All rights reserved.