A simple, universal approach to solving the sparse filtering problem - problem using a reduced number of outputs - with arbitrary bounded exogenous disturbances by employing an observer is presented. The approach is based on the invariant ellipsoid method and the technique of linear matrix inequalities. An application of this concept has made it possible to reduce the original problem to a semidefinite programming problem that is easy to solve numerically. The approach is distinguished by its simplicity and ease of implementation and covers both continuous- and discrete-time statements of the problem. The efficiency of the procedure proposed is demonstrated by a test example.