We study the design of a coding mask for pulse-echo ultrasound imaging. We are interested in the scenario of a single receiving transducer with an aberrating layer, or ‘mask,’ in front of the transducer's receive surface, with a separate co-located transmit transducer. The mask encodes spatial measurements into a single output signal, containing more information about a reflector's position than a transducer without a mask. The amount of information in such measurements is dependent on the mask geometry, which we propose to optimize using an image reconstruction mean square error (MSE) criterion. We approximate the physics involved to define a linear measurement model, which we use to find an expression for the image error covariance matrix. By discretizing the mask surface and defining a discrete number of mask thickness levels per point on its surface, we show how finding the best mask can be posed as a variation of a sensor selection problem. We propose a convex relaxation in combination with randomized rounding, as well as a greedy optimization algorithm to solve this problem. We show empirically that both algorithms come close to the global optimum. Our simulations further show that the optimized masks have better a MSE than nearly all randomly shaped masks. We observe that an optimized mask amplifies echoes coming from within the region of interest (ROI), and strongly reduces the correlation between echoes of pixels within the ROI.
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- Coded aperture
- compressed sensing
- experimental design
- sparse sensing
- ultrasound imaging