Deconvolution is a computational method used to reduce out-of-focus fluorescence in three-dimensional (3D) microscope images. It can be applied in principle to any type of microscope image but has most often been used to improve images from conventional fluorescence microscopes. Compared to other forms of 3D light microscopy, like confocal microscopy, the advantage of deconvolution microscopy i...

The localization of sound sources with delay-and-sum (DAS) beamforming is limited by a poor spatial resolution-particularly at low frequencies. Various methods based on deconvolution are examined to improve the resolution of the beamforming map, which can be modeled by a convolution of the unknown acoustic source distribution and the beamformer's response to a point source, i.e., point-spread f...

In this work, we propose a novel prior term for the regularization of blind deblurring methods. The proposed method introduces machine learning techniques into the blind deconvolution process. The proposed technique has sound mathematical foundations and is generic to many inverse problems. We demonstrate the usage of this regularizer within Bayesian blind deconvolution framework, and also inte...

This paper studies the issue of optimal deconvolution density estimation using wavelets. We explore the asymptotic properties of estimators based on thresholding of estimated wavelet coe cients. Minimax rates of convergence under the integrated square loss are studied over Besov classes B pq of functions for both ordinary smooth and supersmooth convolution kernels. The minimax rates of converge...

In this paper, we study three interconnected inverse problems in shift invariant spaces: 1) the convolution/deconvolution problem; 2) the uniformly sampled convolution and the reconstruction problem; 3) the sampled convolution followed by sampling on irregular grid and the reconstruction problem. In all three cases, we study both the stable reconstruction as well as ill-posed reconstruction pro...

Deconvolution is usually regarded as one of the ill-posed problems in applied mathematics if no constraints on the unknowns are assumed. In this paper, we discuss the idea of welldefined statistical models being a counterpart of the notion of well-posedness. We show that constraints on the unknowns such as positivity and sparsity can go a long way towards overcoming the ill-posedness in deconvo...

This paper is devoted to blind deconvolution and blind separation problems. Blind deconvolution is the identiication of a point spread function and an input signal from an observation of their convolution. Blind source separation is the recovery of a vector of input signals from a vector of observed signals, which are mixed by a linear (unknown) operator. We show that both problems are paradigm...

Random matrix and free probability theory have many fruitful applications in many research areas, such as digital communication, mathematical finance and nuclear physics. In particular, the concept of free deconvolution can be used to obtain the eigenvalue distributions of involved functionals of random matrices. Historically, free deconvolution has been applied in the asymptotic setting, i.e.,...

We present an approach to determine suucient conditions for the global convergence of iterative blind deconvolution algorithms using nite impulse response (FIR) deconvolution lters. The novel technique, which incorporates Lyapunov's direct method, is general, exible and can be easily adapted to analyze the behaviour of many types of nonlinear iterative signal processing algorithms. Speciically,...

We propose a total variation based model for simultaneous image inpainting and blind deconvolution. We demonstrate that the tasks are inherently coupled together and that solving them individually will lead to poor results. The main advantages of our model are that (i) boundary conditions for deconvolution required near the interface between observed and occluded regions are naturally generated...