  In this paper, we address the line spectral estimation problem with multiple
measurement corrupted vectors. Such scenarios appear in many practical
applications such as radar, optics, and seismic imaging in which the signal of
interest can be modeled as the sum of a spectrally sparse and a blocksparse
signal known as outlier. Our aim is to demix the two components and for that,
we design a convex problem whose objective function promotes both of the
structures. Using positive trigonometric polynomials (PTP) theory, we
reformulate the dual problem as a semi-definite program (SDP). Our theoretical
results states that for a fixed number of measurements N and constant number of
outliers, up to O(N) spectral lines can be recovered using our SDP problem as
long as a minimum frequency separation condition is satisfied. Our simulation
results also show that increasing the number of samples per measurement
vectors, reduces the minimum required frequency separation for successful
recovery.
