Advances in Inverse Problems and Imaging

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.

Sources

In silico Deep Learning Protocols for Label-Free Super-Resolution Microscopy: A Comparative Study of Network Architectures and SNR Dependence

An Adaptive CUR Algorithm and its Application to Reduced-Order Modeling of Random PDEs

Mixed-Derivative Total Variation

Universal $L_2$-approximation using median lattice algorithms

On the Performance of Amplitude-Based Models for Low-Rank Matrix Recovery

Self-supervised learning for phase retrieval

Unsupervised Unfolded rPCA (U2-rPCA): Deep Interpretable Clutter Filtering for Ultrasound Microvascular Imaging

Equivariant Splitting: Self-supervised learning from incomplete data

Data selection: at the interface of PDE-based inverse problem and randomized linear algebra

NPN: Non-Linear Projections of the Null-Space for Imaging Inverse Problems

Learning Regularization Functionals for Inverse Problems: A Comparative Study

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