Related papers: Analyzing the structure of multidimensional compre…
In NMR spectroscopy, undersampling in the indirect dimensions causes reconstruction artifacts whose size can be bounded using the so-called {\it coherence}. In experiments with multiple indirect dimensions, new undersampling approaches were…
Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…
Sparsity is a ubiquitous feature of many real world signals such as natural images and neural spiking activities. Conventional compressed sensing utilizes sparsity to recover low dimensional signal structures in high ambient dimensions…
Demixing is the problem of identifying multiple structured signals from a superimposed, undersampled, and noisy observation. This work analyzes a general framework, based on convex optimization, for solving demixing problems. When the…
Compressed sensing is a theory which guarantees the exact recovery of sparse signals from a small number of linear projections. The sampling schemes suggested by current compressed sensing theories are often of little practical relevance…
This paper is concerned with the problem of reconstructing an infinite-dimensional signal from a limited number of linear measurements. In particular, we show that for binary measurements (modelled with Walsh functions and Hadamard…
Coherent superpositions are one of the hallmarks of quantum mechanics and are vital for any quantum mechanical device to outperform the classically achievable. Generically, superpositions are verified in interference experiments, but…
Imaging by aperture synthesis from interferometric data is a well-known, but is a strong ill-posed inverse problem. Strong and faint radio sources can be imaged unambiguously using time and frequency integration to gather more Fourier…
Engineered infrastructure systems pose inverse problems in which hidden states, unknown parameters, and subsystem couplings must be inferred from sparse and noisy measurements. These problems are difficult because physical subsystems are…
Sensor selection refers to the problem of intelligently selecting a small subset of a collection of available sensors to reduce the sensing cost while preserving signal acquisition performance. The majority of sensor selection algorithms…
In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the…
The pre-existing literature on phenomena at the mesoscopic scale is concerned among other things with phase coherent transport. Phase coherent transport dominates at very low temperatures. With increase in temperature, as the system size…
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…
We advocate a compressed sensing strategy that consists of multiplying the signal of interest by a wide bandwidth modulation before projection onto randomly selected vectors of an orthonormal basis. Firstly, in a digital setting with random…
Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform…
We establish large sample approximations for an arbitray number of bilinear forms of the sample variance-covariance matrix of a high-dimensional vector time series using $ \ell_1$-bounded and small $\ell_2$-bounded weighting vectors.…
Artificial quantum systems with synthetic dimensions enable exploring novel quantum phenomena difficult to create in conventional materials. These synthetic degrees of freedom increase the system's dimensionality without altering its…
The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…
Diffusion models have emerged as powerful generative priors for solving inverse imaging problems. However, their practical deployment is hindered by the substantial computational cost of slow, multi-step sampling. Although Consistency…
In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…