In recent work, we obtained finite sample guarantees for the problem of Principal Component Analysis (PCA) in nonisotropic and data-dependent noise. In this work, we study an important special case of this: the problem of PCA in sparse data-dependent noise with the noise depending linearly on the signal (true data) at each time. This special case occurs in many practical applications. Two examples that we describe include (a) PCA with missing data and (b) the subspace update step of an online algorithm for dynamic robust PCA called ReProCS. The full version is [1].