Related papers: Designing optimal dual frames for $\ell^p-$average…
This paper provides novel results for the recovery of signals from undersampled measurements based on analysis $\ell_1$-minimization, when the analysis operator is given by a frame. We both provide so-called uniform and nonuniform recovery…
In recent investigations, the problem of detecting edges given non-uniform Fourier data was reformulated as a sparse signal recovery problem with an l1-regularized least squares cost function. This result can also be derived by employing a…
We consider the problem of recovering fusion frame sparse signals from incomplete measurements. These signals are composed of a small number of nonzero blocks taken from a family of subspaces. First, we show that, by using a-priori…
In this paper we introduce and study the concept of optimal and surely optimal dual martingales in the context of dual valuation of Bermudan options, and outline the development of new algorithms in this context. We provide a…
Electron ptychography provides new opportunities to resolve atomic structures with deep sub-angstrom spatial resolution and studying electron-beam sensitive materials with high dose efficiency. In practice, obtaining accurate ptychography…
Reverberation may severely degrade the quality of speech signals recorded using microphones in a room. For compact microphone arrays, the choice of the reference microphone for multi-microphone dereverberation typically does not have a…
Electron microscopy has shown to be a very powerful tool to map the chemical nature of samples at various scales down to atomic resolution. However, many samples can not be analyzed with an acceptable signal-to-noise ratio because of the…
Matrix completion has been well studied under the uniform sampling model and the trace-norm regularized methods perform well both theoretically and numerically in such a setting. However, the uniform sampling model is unrealistic for a…
Compressed Sensing (CS) significantly speeds up Magnetic Resonance Image (MRI) processing and achieves accurate MRI reconstruction from under-sampled k-space data. According to the current research, there are still several problems with…
In the context of compressed sensing (CS), this paper considers the problem of reconstructing sparse signals with the aid of other given correlated sources as multiple side information. To address this problem, we theoretically study a…
The requirement of high spectrum efficiency puts forward higher requirements on frame synchronization (FS) in wireless communication systems. Meanwhile, a large number of nonlinear devices or blocks will inevitably cause nonlinear…
Fluoroscopic imaging that captures X-ray images at video framerates is advantageous for guiding catheter insertions by vascular surgeons and interventional radiologists. Visualizing the dynamical movements non-invasively allows complex…
Extended ambiguity performance (EAP), which includes all grating lobes and side peaks, indicates the maximum detectable region without undesired peaks for target parameter estimation and is critical to radar sensor design. Driven by EAP…
The decomposition or approximation of a linear operator on a matrix space as a sum of Kronecker products plays an important role in matrix equations and low-rank modeling. The approximation problem in Frobenius norm admits a well-known…
We consider the notion of finite dimensional reconstructions systems (RS's), which includes the fusion frames as projective RS's. We study erasures, some geometrical properties of these spaces, the spectral picture of the set of all dual…
Tensor-based discrete density estimation requires flexible modeling and proper divergence criteria to enable effective learning; however, traditional approaches using $\alpha$-divergence face analytical challenges due to the $\alpha$-power…
Given a function f defined on a bidimensional bounded domain and a positive integer N, we study the properties of the triangulation that minimizes the distance between f and its interpolation on the associated finite element space, over all…
We propose an image restoration algorithm that can control the perceptual quality and/or the mean square error (MSE) of any pre-trained model, trading one over the other at test time. Our algorithm is few-shot: Given about a dozen images…
In this paper, we study the problem of compressed sensing using binary measurement matrices and $\ell_1$-norm minimization (basis pursuit) as the recovery algorithm. We derive new upper and lower bounds on the number of measurements to…
A class of linear parabolic equations is considered. We derive a framework for the a posteriori error analysis of time discretisations by Richardson extrapolation of arbitrary order combined with finite element discretisations in space. We…