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We consider nonparametric measurement error density deconvolution subject to heteroscedastic measurement errors as well as symmetry about zero and shape constraints, in particular unimodality. The problem is motivated by applications where…
Deconvolution is a statistical inverse problem to estimate the distribution of a random variable based on its noisy observations. Despite the extensive studies on the topic, deconvolution with unknown noise distribution remains as a…
This work considers recovery of signals that are sparse over two bases. For instance, a signal might be sparse in both time and frequency, or a matrix can be low rank and sparse simultaneously. To facilitate recovery, we consider minimizing…
A number of ill-posed inverse problems in signal processing, like blind deconvolution, matrix factorization, dictionary learning and blind source separation share the common characteristic of being bilinear inverse problems (BIPs), i.e. the…
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…
Existing reduced-dimension beam-Doppler space-time adaptive processing (RD-BD-STAP) algorithms are confined to the beam-Doppler cells used for adaptation, which often leads to some performance degradation. In this work, a novel…
Joint sparsity has attracted considerable attention in recent years in many fields including sparse signal recovery in compressed sensing (CS), statistics, and machine learning. Traditional convex models suffer from the suboptimal…
We consider the paradigm of unsupervised anomaly detection, which involves the identification of anomalies within a dataset in the absence of labeled examples. Though distance-based methods are top-performing for unsupervised anomaly…
Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…
Consistency learning is a central strategy to tackle unlabeled data in semi-supervised medical image segmentation (SSMIS), which enforces the model to produce consistent predictions under the perturbation. However, most current approaches…
The miniaturization of optics through the use of two-dimensional metalenses has enabled novel applications in imaging. To date, single-lens imaging remains the most common configuration, in part due to the limited focusing efficiency of…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
We introduce a novel learning-based method to reconstruct the high-quality geometry and complex, spatially-varying BRDF of an arbitrary object from a sparse set of only six images captured by wide-baseline cameras under collocated point…
We study the recovery of sparse vectors from subsampled random convolutions via $\ell_1$-minimization. We consider the setup in which both the subsampling locations as well as the generating vector are chosen at random. For a subgaussian…
In this paper, we focus on the nonlinear least squares: $\mbox{min}_{\mathbf{x} \in \mathbb{H}^d}\| |A\mathbf{x}|-\mathbf{b}\|$ where $A\in \mathbb{H}^{m\times d}$, $\mathbf{b} \in \mathbb{R}^m$ with $\mathbb{H} \in \{\mathbb{R},\mathbb{C}…
Gravitational-wave searches for the merger of compact binaries use matched-filtering as the method of detecting signals and estimating parameters. Such searches construct a fine mesh of filters covering a signal parameter space at high…
Binary embedding is the problem of mapping points from a high-dimensional space to a Hamming cube in lower dimension while preserving pairwise distances. An efficient way to accomplish this is to make use of fast embedding techniques…
Typical blur from camera shake often deviates from the standard uniform convolutional script, in part because of problematic rotations which create greater blurring away from some unknown center point. Consequently, successful blind…
Bayesian neural networks (BNNs) offer uncertainty quantification but come with the downside of substantially increased training and inference costs. Sparse BNNs have been investigated for efficient inference, typically by either slowly…
We provide the first convergence guarantee for full black-box variational inference (BBVI), also known as Monte Carlo variational inference. While preliminary investigations worked on simplified versions of BBVI (e.g., bounded domain,…