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We consider the problem of estimating the covariance matrix and the transition matrix of vector autoregressive (VAR) processes from partial measurements. This model encompasses settings where there are limitations in the data acquisition of the underlying measurement systems so that data is lost or corrupted by noise. An estimator for the covariance matrix of the observations is first presented.

We consider the problem of estimating the covariance matrix and the transition matrix of vector autoregressive (VAR) processes from partial measurements. This model encompasses settings where there are limitations in the data acquisition of the underlying measurement systems so that data is lost or corrupted by noise. An estimator for the covariance matrix of the observations is first presented.

In this paper, we propose a new emission strategy in the context of plane wave imaging. Plane wave imaging indeed implies compounding in order to preserve a good image quality. Such compounding is usually obtained using multiple, successive emissions, which in turn yields a decrease of the frame rate. As opposed to this approach, our method is based on the simultaneous emission of several coded plane waves. This allows the reconstruction of all the images corresponding to the different plane waves, by using an inverse problem approach.