Related papers: Improved success rate and stability for phase retr…
Quadratic programming is a workhorse of modern nonlinear optimization, control, and data science. Although regularized methods offer convergence guarantees under minimal assumptions on the problem data, they can exhibit the slow…
The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier transform, naturally arises in various fields of physics, such as astronomy, radar, speech recognition, quantum mechanics and,…
We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [SIAM J. Sci. Comput.,…
This paper studies an optimization problem on the sum of traces of matrix quadratic forms in $m$ semi-orthogonal matrices, which can be considered as a generalization of the synchronization of rotations. While the problem is nonconvex, the…
Speed-of-sound is a biomechanical property for quantitative tissue differentiation, with great potential as a new ultrasound-based image modality. A conventional ultrasound array transducer can be used together with an acoustic mirror, or…
Achieving high-quality High Dynamic Range (HDR) imaging on resource-constrained edge devices is a critical challenge in computer vision, as its performance directly impacts downstream tasks such as intelligent surveillance and autonomous…
Multidimensional Retiming is one of the most important optimization techniques to improve timing parameters of nested loops. It consists in exploring the iterative and recursive structures of loops to redistribute computation nodes on cycle…
We consider the recovery of sparse signals that share a common support from multiple measurement vectors. The performance of several algorithms developed for this task depends on parameters like dimension of the sparse signal, dimension of…
We introduce and initiate the study of a new model of reductions called the random noise model. In this model, the truth table $T_f$ of the function $f$ is corrupted on a randomly chosen $\delta$-fraction of instances. A randomized…
The machine learning random Fourier feature method for data in high dimension is computationally and theoretically attractive since the optimization is based on a convex standard least squares problem and independent sampling of Fourier…
Low-Rank Adaptation (LoRA) lowers the computational and memory overhead of fine-tuning large models by updating a low-dimensional subspace of the pre-trained weight matrix. Albeit efficient, LoRA exhibits suboptimal convergence and…
Information about microscopic objects with features smaller than the diffraction limit is almost entirely lost in a far-field diffraction image but could be partly recovered with data completition techniques. Any such approach critically…
Phase reconstruction is important in transmission electron microscopy for structural studies. We describe electron Fourier ptychography and its application to phase reconstruction of both radiation-resistant and beam-sensitive materials. We…
In recent years, learning-based methods have achieved significant advancements in multi-exposure image fusion. However, two major stumbling blocks hinder the development, including pixel misalignment and inefficient inference. Reliance on…
Random Fourier features is a widely used, simple, and effective technique for scaling up kernel methods. The existing theoretical analysis of the approach, however, remains focused on specific learning tasks and typically gives pessimistic…
Fourier domain methods are fast algorithms for SAR imaging. They typically involve an interpolation in the frequency domain to re-grid non-uniform data so inverse fast Fourier transforms can be performed. In this paper, we apply a frame…
Two contrasting algorithmic paradigms for constraint satisfaction problems are successive local explorations of neighboring configurations versus producing new configurations using global information about the problem (e.g. approximating…
Goal oriented error estimation and adaptive procedures are essential for the accurate and efficient evaluation of numerical simulations that involve complex domains. By locally improving the approximation quality we can solve expensive…
Phase retrieval is a problem encountered not only in speech and audio processing, but in many other fields such as optics. Iterative algorithms based on non-convex set projections are effective and frequently used for retrieving the phase…
Adaptive Finite Element Method (adaptivity) is known to be an effective numerical tool for some ill-posed problems. The key advantage of the adaptivity is the image improvement with local mesh refinements. A rigorous proof of this property…