The Linear Sampling Method and the MUSIC Algorithm

This article gives a short tutorial on the MUSIC algorithm and the linear sampling method of [3], and explains how the latter is an extension of the former. 1 MUSIC MUSIC is an abbreviation for MUltiple SIgnal Classification [10]; we see below why the name is appropriate. 1.1 The basics of MUSIC MUSIC is essentially a method of characterizing the range of a self-adjoint operator. Suppose is a self-adjoint operator with eigenvalues , and 1 corresponding eigenvectors . Suppose the eigenvalues are all zero, so that the vectors span the null space of . Alternatively, could merely be very small, below the noise level of the system represented by ; in this case we say that the vectors span the noise subspace of . We can form the projection onto the noise subspace; this projection is given explicitly by