SELFNet: Denoising Shear Wave Elastography Using Spatial-temporal Fourier Feature Networks

Ultrasound-based shear wave elastography offers estimation of tissue stiffness through analysis of the propagation of a shear wave induced by a stimulus. Displacement or velocity fields during the process can contain noise as a result of the limited number of acquisitions. With advances in physics-informed deep learning, neural networks can approximate a physics field by minimizing the residuals of governing physics equations.

In this research, we introduce a shear wave elastography Fourier feature network (SELFNet) using spatial-temporal random Fourier features within a physics-informed neural network framework to estimate and denoise particle displacement signals. The network uses a sparse mapping to increase robustness and incorporates the governing equations for regularization while simultaneously learning the mapping of the shear modulus. The method was evaluated in datasets from tissue-mimicking phantom of lesions and ex vivo tissue.

The findings indicate that SELFNet is capable of smoothing out the noise in phantom lesions with different stiffness and sizes, outperforming a reference Gaussian filtering method by 17% in relative ℓ₂ error, 45% in reconstruction root-mean-square error. Furthermore, the ablation study suggested that SELFNet can prevent over-fitting through the Fourier feature mapping module. An ex vivo study confirmed its applicability to different types of tissue.

The implementation of SELFNet shows promise for shear wave elastography with limited acquisitions. In this context, subject to successful translation, it has the potential to be extended to clinical applications, such as the diagnosis of cancer or liver disease.