Related papers: Multi-Dimensional Unlimited Sampling and Robust Re…
In this work, we introduce a novel stochastic second-order method, within the framework of a non-monotone trust-region approach, for solving the unconstrained, nonlinear, and non-convex optimization problems arising in the training of deep…
In the undersampled phase retrieval problem, the goal is to recover an $N$-dimensional complex signal $\mathbf{x}$ from only $M<N$ noisy intensity measurements without phase information. This problem has drawn a lot of attention to reduce…
Suppose that we observe noisy linear measurements of an unknown signal that can be modeled as the sum of two component signals, each of which arises from a nonlinear sub-manifold of a high dimensional ambient space. We introduce SPIN, a…
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…
Folded sampling replaces clipping in analog-to-digital converters by reducing samples modulo a threshold, thereby avoiding saturation artifacts. We study the reconstruction of bandlimited functions from folded samples and show that, for…
Spatial sampling is traditionally studied in a static setting where static sensors scattered around space take measurements of the spatial field at their locations. In this paper we study the emerging paradigm of sampling and reconstructing…
Noise robust compressive sensing algorithm is considered. This algorithm allows an efficient signal reconstruction in the presence of different types of noise due to the possibility to change minimization norm. For instance, the commonly…
Hyperspectral (HS) unmixing is the process of decomposing an HS image into material-specific spectra (endmembers) and their spatial distributions (abundance maps). Existing unmixing methods have two limitations with respect to noise…
We present a new Unbiased Minimal Variance (UMV) estimator for the purpose of reconstructing the large--scale structure of the universe from noisy, sparse and incomplete data. Similar to the Wiener Filter (WF), the UMV estimator is derived…
Estimation of third-order statistics relies on the availability of a huge amount of data records, which can pose severe challenges on the data collecting hardware in terms of considerable storage costs, overwhelming energy consumption, and…
This paper studies the problem of recovering a signal from one-bit compressed sensing measurements under a manifold model; that is, assuming that the signal lies on or near a manifold of low intrinsic dimension. We provide a convex recovery…
We present a scalable low dimensional manifold model for the reconstruction of noisy and incomplete hyperspectral images. The model is based on the observation that the spatial-spectral blocks of a hyperspectral image typically lie close to…
Multidimensional Scaling (MDS) is a classical technique for embedding data in low dimensions, still in widespread use today. Originally introduced in the 1950's, MDS was not designed with high-dimensional data in mind; while it remains…
Compressed sensing is a technique for recovering a high-dimensional signal from lower-dimensional data, whose components represent partial information about the signal, utilizing prior knowledge on the sparsity of the signal. For further…
Analog to digital converters (ADCs) act as a bridge between the analog and digital domains. Two important attributes of any ADC are sampling rate and its dynamic range. For bandlimited signals, the sampling should be above the Nyquist rate.…
Deep neural networks have proven to be highly effective when large amounts of data with clean labels are available. However, their performance degrades when training data contains noisy labels, leading to poor generalization on the test…
The realisation of sensing modalities based on the principles of compressed sensing is often hindered by discrepancies between the mathematical model of its sensing operator, which is necessary during signal recovery, and its actual…
We consider the \textit{phase retrieval} problem of recovering a sparse signal $\mathbf{x}$ in $\mathbb{R}^d$ from intensity-only measurements in dimension $d \geq 2$. Phase retrieval can be equivalently formulated as the problem of…
Compressed sensing has shown that it is possible to reconstruct sparse high dimensional signals from few linear measurements. In many cases, the solution can be obtained by solving an L1-minimization problem, and this method is accurate…
Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common methods the signal is recovered in the sparse domain. A method for the reconstruction of sparse signal which reconstructs the…