This paper deals with the estimation of the inner-diameter of the Carotid Artery (CA). Arteries pulsate as blood is pumped through them by the heart. Plaque depositions along the inner wall makes the arteries rigid and obstructs the flow of blood. This increases the risk of a heart attack. The dynamics of the inner-diameter of the CA is a good indicator of this risk. An ultrasound transducer is placed on the neck of a subject and a sequence of ultrasound pulses are sent. The echoes due to the CA and other anatomical structures in the vicinity are recorded. Considering each ultrasound pulse as an input and its corresponding echo (reflections from the CA and other structures) as the output, the propagation path is modeled as a FIR filter with a sparse impulse response. Reconstruction of the echo signal, for each pulse, from the estimated impulse response significantly reduces the measurement noise. This enables the development of algorithms for accurate detection of the walls of CA and tracking of its inner-diameter dynamics. Results suggest repeatable and reliable measurements of the inner-diameter of the CA. Further more, as only the reconstructed echo signals are used, it is enough to retain the non zero filter coefficients and its corresponding indices. This leads to a large reduction in the size of the data that needs to be stored for a subject. © 2015 IEEE.