An Inverse-Problem Approach to the Estimation of Despeckled and Deconvolved Images From Radio-Frequency Signals in Pulse-Echo Ultrasound

In recent years, there has been notable progress in the development of inverse problems for image reconstruction in pulse-echo ultrasound. Inverse problems are designed to circumvent the restrictions of delay-and-sum, such as limited image resolution and diffraction artifacts, especially when low amount of data are considered. However, the radio-frequency image or tissue reflectivity function that current inverse problems seek to estimate do not possess a structure that can be easily leveraged by a regularizer, in part due to their high dynamic range. The performance of inverse-problem image reconstruction is thus impeded. In contrast, despeckled images exhibit a more exploitable structure. Therefore, we first propose an inverse problem to recover a despeckled image from single-plane-wave radio-frequency echo signals, employing total-variation norm regularization. Then, we introduce an inverse problem to estimate the tissue reflectivity function from radio-frequency echo signals, factoring in the despeckled image obtained by the first problem into a spatially-varying reflectivity prior. We show with simulated, in-vitro, and in-vivo data that the proposed despeckled image estimation technique recovers images almost free of diffraction artifacts and improves contrast with respect to delay-and-sum and non-local means despeckling. Moreover, we show with in-vitro and in-vivo data that the proposed reflectivity estimation method reduces artifacts and improves contrast with respect to a state-of-the-art inverse problem positing a uniform prior. In particular, the proposed techniques could prove beneficial for imaging with ultra-portable transducers, since these devices are likely to be limited in the amount of data they can acquire and transmit.