Related papers: Blind free deconvolution over one-parameter sparse…
This paper provides an analysis of the linearized inverse problem in multifrequency electrical impedance tomography. We consider an isotropic conductivity distribution with a finite number of unknown inclusions with different frequency…
Inverse imaging problems that are ill-posed can be encountered across multiple domains of science and technology, ranging from medical diagnosis to astronomical studies. To reconstruct images from incomplete and distorted data, it is…
Blind super-resolution can be cast as low rank matrix recovery problem by exploiting the inherent simplicity of the signal. In this paper, we develop a simple yet efficient nonconvex method for this problem based on the low rank structure…
Many imaging technologies rely on tomographic reconstruction, which requires solving a multidimensional inverse problem given a finite number of projections. Backprojection is a popular class of algorithm for tomographic reconstruction,…
Blind gain and phase calibration (BGPC) is a bilinear inverse problem involving the determination of unknown gains and phases of the sensing system, and the unknown signal, jointly. BGPC arises in numerous applications, e.g., blind albedo…
This paper considers the sparse eigenvalue problem, which is to extract dominant (largest) sparse eigenvectors with at most $k$ non-zero components. We propose a simple yet effective solution called truncated power method that can…
Restoration of images degraded by spatially varying blurs is an issue of increasing importance in the context of photography, satellite or microscopy imaging. One of the main difficulty to solve this problem comes from the huge dimensions…
We propose a convex and fast signal reconstruction method for block sparsity under arbitrary linear transform with unknown block structure. The proposed method is a generalization of the similar existing method and can reconstruct signals…
We study blind deconvolution of signals defined on the nodes of an undirected graph. Although observations are bilinear functions of both unknowns, namely the forward convolutional filter coefficients and the graph signal input, a filter…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
We derive near optimal performance guarantees for subsampled blind deconvolution. Blind deconvolution is an ill-posed bilinear inverse problem and additional subsampling makes the problem even more challenging. Sparsity and spectral…
We study the problem of identifying the parameters of a linear system from its response to multiple unknown waveforms. We assume that the system response is a scaled superposition of time-delayed and frequency-shifted versions of the…
This paper develops a convex approach for sparse one-dimensional deconvolution that improves upon L1-norm regularization, the standard convex approach. We propose a sparsity-inducing non-separable non-convex bivariate penalty function for…
In its most elementary form, compressed sensing studies the design of decoding algorithms to recover a sufficiently sparse vector or code from a lower dimensional linear measurement vector. Typically it is assumed that the decoder has…
This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…
Ptychography involves a sample being illuminated by a coherent, localised probe of illumination. When the probe interacts with the sample, the light is diffracted and a diffraction pattern is detected. Then the probe or sample is shifted…
Blind deconvolution involves the estimation of a sharp signal or image given only a blurry observation. Because this problem is fundamentally ill-posed, strong priors on both the sharp image and blur kernel are required to regularize the…
In the remote sensing context spectral unmixing is a technique to decompose a mixed pixel into two fundamental representatives: endmembers and abundances. In this paper, a novel architecture is proposed to perform blind unmixing on…
Finding eigenvalue distributions for a number of sparse random matrix ensembles can be reduced to solving nonlinear integral equations of the Hammerstein type. While a systematic mathematical theory of such equations exists, it has not been…
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…