The paper considers the sparse filtering problem under arbitrary norm-bounded exogenous disturbances. We propose a simple and universal observer-based approach to its solution, based on the LMI technique and the method of invariant ellipsoids; it allows the use of a reduced number of system outputs. From a technical point of view of application, we reduce the original problem to semi-definite programming, which is easily solved numerically. The proposed simple approach is easy to implement and can be equally extended to systems in continuous and discrete time.