Related papers: Modeling Sparse Deviations for Compressed Sensing …
Consider the problem of recovering an unknown signal from undersampled measurements, given the knowledge that the signal has a sparse representation in a specified dictionary $D$. This problem is now understood to be well-posed and…
We consider the general problem of recovering a high-dimensional signal from noisy quantized measurements. Quantization, especially coarse quantization such as 1-bit sign measurements, leads to severe information loss and thus a good prior…
Compressed sensing techniques enable efficient acquisition and recovery of sparse, high-dimensional data signals via low-dimensional projections. In this work, we propose Uncertainty Autoencoders, a learning framework for unsupervised…
In Bora et al. (2017), a mathematical framework was developed for compressed sensing guarantees in the setting where the measurement matrix is Gaussian and the signal structure is the range of a generative neural network (GNN). The problem…
In this article, we review the literature on design and analysis of recursive algorithms for reconstructing a time sequence of sparse signals from compressive measurements. The signals are assumed to be sparse in some transform domain or in…
This paper addresses the reconstruction of an unknown signal vector with sublinear sparsity from generalized linear measurements. Generalized approximate message-passing (GAMP) is proposed via state evolution in the sublinear sparsity…
We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number of…
We demonstrate through numerical simulations with real data the feasibility of using compressive sensing techniques for the acquisition of spectro-polarimetric data. This allows us to combine the measurement and the compression process into…
In the recent years, there has been a significant improvement in the quality of samples produced by (deep) generative models such as variational auto-encoders and generative adversarial networks. However, the representation capabilities of…
Using a low-dimensional parametrization of signals is a generic and powerful way to enhance performance in signal processing and statistical inference. A very popular and widely explored type of dimensionality reduction is sparsity; another…
Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…
Limitations on bandwidth and power consumption impose strict bounds on data rates of diagnostic imaging systems. Consequently, the design of suitable (i.e. task- and data-aware) compression and reconstruction techniques has attracted…
In compressed sensing (CS), sparse signals can be reconstructed from significantly fewer samples than required by the Nyquist-Shannon sampling theorem. While non-sparse signals can be sparsely represented in appropriate transformation…
The problem of multiple sensors simultaneously acquiring measurements of a single object can be found in many applications. In this paper, we present the optimal recovery guarantees for the recovery of compressible signals from multi-sensor…
In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…
We investigate the sparse recovery problem of reconstructing a high-dimensional non-negative sparse vector from lower dimensional linear measurements. While much work has focused on dense measurement matrices, sparse measurement schemes are…
Intensively growing approach in signal processing and acquisition, the Compressive Sensing approach, allows sparse signals to be recovered from small number of randomly acquired signal coefficients. This paper analyses some of the commonly…
Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…
Prototype-driven text generation uses non-parametric models that first choose from a library of sentence "prototypes" and then modify the prototype to generate the output text. While effective, these methods are inefficient at test time as…
Fusion frames are collection of subspaces which provide a redundant representation of signal spaces. They generalize classical frames by replacing frame vectors with frame subspaces. This paper considers the sparse recovery of a signal from…