Joint optimization of coding mask and scan positions for compressive single sensor imaging

We study the optimal design of an aperture coding mask, and the optimal sensing positions of a single ultrasound sensor with a scanning configuration. In previous works, we have shown that 3D ultrasound imaging is possible using a randomly shaped coding mask with randomly chosen sensing positions. Here we propose an optimization algorithm for the joint design of the coding mask and the sensing positions. We first define a linear measurement model and parameterize it with respect to the mask shape. To optimize the shape of the mask, we use a greedy descent algorithm to minimize the imaging MSE, assuming a Wiener estimate is used for image reconstruction. To optimize the sensing positions, we pre-define a set of such sensing positions by gridding the measurement plane, and regard each sensing position as a virtual sensor candidate. We then use a greedy sensor selection algorithm to find a good selection of sensing positions. To jointly optimize for both the mask and the sensing positions, we alternatingly optimize between them, keeping either the mask shape or the sensing positions fixed. Using simulations we show that the joint optimization results in better imaging performance than optimizing for the mask or the sensing positions alone, or using a completely random design.