The field of inverse problems and imaging is rapidly advancing, with a focus on developing innovative methods for solving complex problems. One of the key directions is the use of deep learning techniques, which have shown great promise in improving the accuracy and efficiency of inverse problem solutions. Another important area of research is the development of new regularization techniques, which can help to improve the stability and robustness of inverse problem solutions.
Notable papers in this area include the proposal of a universal median lattice-based algorithm for multivariate L2-approximation, which eliminates the need for prior information on smoothness and weights. Additionally, a self-supervised learning method has been proposed for phase retrieval, which overcomes the limitation of requiring fully sampled data.
The use of unsupervised learning methods, such as the unsupervised unfolded rPCA (U2-rPCA) method, has also shown great potential in high-sensitivity clutter filtering for ultrasound microvascular imaging. Furthermore, the development of new data selection methods, such as those using randomized numerical linear algebra, has improved the efficiency and accuracy of inverse problem solutions.
Overall, the field of inverse problems and imaging is rapidly evolving, with a focus on developing innovative methods for solving complex problems. These advances have the potential to improve the accuracy and efficiency of inverse problem solutions, and to enable new applications in a variety of fields.