Related papers: Level Set Estimation from Compressive Measurements…
The robust low-rank tensor completion problem addresses the challenge of recovering corrupted high-dimensional tensor data with missing entries, outliers, and sparse noise commonly found in real-world applications. Existing methodologies…
Compressive sensing is used to perform high-dimensional quantum channel estimation with classical light. As an example, we perform a numerical simulation for the case of a three-dimensional classically non-separable state that is propagated…
This paper presents a novel power spectral density estimation technique for band-limited, wide-sense stationary signals from sub-Nyquist sampled data. The technique employs multi-coset sampling and incorporates the advantages of compressed…
Reduced-order models based on level-set methods are widely used tools to qualitatively capture and track the nonlinear dynamics of an interface. The aim of this paper is to develop a physics-informed, data-driven, statistically rigorous…
In this article, we develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of…
Compressive sensing is a technique to sample signals well below the Nyquist rate using linear measurement operators. In this paper we present an algorithm for signal reconstruction given such a set of measurements. This algorithm…
This paper focuses on the development of a space-variant regularization model for solving an under-determined linear inverse problem. The case study is a medical image reconstruction from few-view tomographic noisy data. The primary…
This paper focuses on the estimation of the sample covariance matrix from low-dimensional random projections of data known as compressive measurements. In particular, we present an unbiased estimator to extract the covariance structure from…
As an alternative to the traditional sampling theory, compressed sensing allows acquiring much smaller amount of data, still estimating the spectra of frequency-sparse signals accurately. However, compressed sensing usually requires random…
While Total Variation (TV) excels in noise reduction and edge preservation, its reliance on a scalar regularization parameter limits adaptivity. In this study, we present a Learnable Total Variation (LTV) framework coupling an unrolled TV…
Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…
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.…
Noiseless compressive sensing is a two-steps setting that allows for undersampling a sparse signal and then reconstructing it without loss of information. The LASSO algorithm, based on $\lone$ regularization, provides an efficient and…
Compressed sensing is a signal processing technique that allows for the reconstruction of a signal from a small set of measurements. The key idea behind compressed sensing is that many real-world signals are inherently sparse, meaning that…
The importance of regularization has been well established in image reconstruction -- which is the computational inversion of imaging forward model -- with applications including deconvolution for microscopy, tomographic reconstruction,…
In this paper, a new regularization term is proposed to solve mathematical image problems. By using difference operators in the four directions; horizontal, vertical and two diagonal directions, an estimation of derivative amplitude is…
Identifying anomalies and contamination in datasets is important in a wide variety of settings. In this paper, we describe a new technique for estimating contamination in large, discrete valued datasets. Our approach considers the normal…
Compressed sensing (CS) is on recovery of high dimensional signals from their low dimensional linear measurements under a sparsity prior and digital quantization of the measurement data is inevitable in practical implementation of CS…
We suggest an adaptive sampling rule for obtaining information from noisy signals using wavelet methods. The technique involves increasing the sampling rate when relatively high-frequency terms are incorporated into the wavelet estimator,…
This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method leverages the rapid computation of an accurate…