Related papers: Robust 1-Bit Compressed Sensing via Hinge Loss Min…
Consider estimating a structured signal $\mathbf{x}_0$ from linear, underdetermined and noisy measurements $\mathbf{y}=\mathbf{A}\mathbf{x}_0+\mathbf{z}$, via solving a variant of the lasso algorithm: $\hat{\mathbf{x}}=\arg\min_\mathbf{x}\{…
Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…
This paper describes recursive algorithms for state estimation of linear dynamical systems when measurements are noisy with unknown bias and/or outliers. For situations with noisy and biased measurements, algorithms are proposed that…
The purpose of this thesis is to develop new theories on high-dimensional structured signal recovery under a rather weak assumption on the measurements that only a finite number of moments exists. High-dimensional recovery has been one of…
This paper concerns the problem of recovering an unknown but structured signal $x \in R^n$ from $m$ quadratic measurements of the form $y_r=|<a_r,x>|^2$ for $r=1,2,...,m$. We focus on the under-determined setting where the number of…
We prove new results about the robustness of well-known convex noise-blind optimization formulations for the reconstruction of low-rank matrices from underdetermined linear measurements. Our results are applicable for symmetric rank-one…
The theory of Compressed Sensing, the emerging sampling paradigm 'that goes against the common wisdom', asserts that 'one can recover signals in Rn from far fewer samples or measurements, if the signal has a sparse representation in some…
Unlike compressive sensing where the measurement outputs are assumed to be real-valued and have infinite precision, in "one-bit compressive sensing", measurements are quantized to one bit, their signs. In this work, we show how to recover…
This paper determines to within a single measurement the minimum number of measurements required to successfully reconstruct a signal drawn from a Gaussian mixture model in the low-noise regime. The method is to develop upper and lower…
We propose a new method, {\it binary fused compressive sensing} (BFCS), to recover sparse piece-wise smooth signals from 1-bit compressive measurements. The proposed algorithm is a modification of the previous {\it binary iterative hard…
We give the first computationally tractable and almost optimal solution to the problem of one-bit compressed sensing, showing how to accurately recover an s-sparse vector x in R^n from the signs of O(s log^2(n/s)) random linear measurements…
Sign information is the key to overcoming the inevitable saturation error in compressive sensing systems, which causes information loss and results in bias. For sparse signal recovery from saturation, we propose to use a linear loss to…
This paper considers the linear inverse problem where we wish to estimate a structured signal $x$ from its corrupted observations. When the problem is ill-posed, it is natural to make use of a convex function $f(\cdot)$ that exploits the…
Robust statistical inference often faces a severe computational-statistical gap when dealing with complex parameter spaces. We investigate minimax signal detection in the Gaussian sequence model under strong $\epsilon$-contamination, where…
We consider the problem of sparse signal reconstruction from noisy one-bit compressed measurements when the receiver has access to side-information (SI). We assume that compressed measurements are corrupted by additive white Gaussian noise…
Van Rooyen et al. introduced a notion of convex loss functions being robust to random classification noise, and established that the "unhinged" loss function is robust in this sense. In this note we study the accuracy of binary classifiers…
We propose to reduce the original well-posed problem of compressive sensing to weighted-MAX-SAT. Compressive sensing is a novel randomized data acquisition approach that linearly samples sparse or compressible signals at a rate much below…
Random and structured noise both affect seismic data, hiding the reflections of interest (primaries) that carry meaningful geophysical interpretation. When the structured noise is composed of multiple reflections, its adaptive cancellation…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
Traditional sampling theories consider the problem of reconstructing an unknown signal $x$ from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that $x$ lies in a known subspace.…