While sparsity-promoting priors have shown effectiveness in promoting piecewise constant solutions in linear inverse problems, they may have limitations in capturing the true conductivity structure in practical EIT applications. One potential limitation is the assumption of sparsity itself, which may not always align with the actual conductivity distribution in real-world scenarios. In cases where the conductivity varies smoothly or exhibits complex patterns that are not inherently sparse, the sparsity-promoting prior may introduce biases or inaccuracies in the reconstruction.
Additionally, the sparsity-promoting prior may struggle to capture fine details or subtle variations in the conductivity distribution, especially in regions where the conductivity changes gradually or exhibits intricate patterns. This limitation can impact the ability of the Bayesian framework to accurately recover the true conductivity structure, leading to potential reconstruction errors or loss of important information in the imaging process.
Furthermore, the effectiveness of the sparsity-promoting prior heavily relies on the choice of hyperparameters, such as the regularization strength and the shape of the prior distribution. Suboptimal selection of these hyperparameters can result in subpar reconstructions and hinder the framework's ability to capture the complexity of the conductivity distribution.