  The Singular Value Decomposition is a matrix decomposition technique widely
used in the analysis of multivariate data, such as complex space-time images
obtained in both physical and biological systems. In this paper, we examine the
distribution of Singular Values of low rank matrices corrupted by additive
noise. Past studies have been limited to uniform uncorrelated noise. Using
diagrammatic and saddle point integration techniques, we extend these results
to heterogeneous and correlated noise sources. We also provide perturbative
estimates of error bars on the reconstructed low rank matrix obtained by
truncating a Singular Value Decomposition.
