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Sparse Stochastic Processes and Discretization of Linear Inverse Problems
Emrah Bostan, Ulugbek S. Kamilov, Masih Nilchian +1
We present a novel statistically-based discretization paradigm and derive a class of maximum a posteriori (MAP) estimators for solving ill-conditioned linear inverse problems. We a…
Bayesian Estimation for Continuous-Time Sparse Stochastic Processes
Arash Amini, Ulugbek S. Kamilov, Emrah Bostan +1
We consider continuous-time sparse stochastic processes from which we have only a finite number of noisy/noiseless samples. Our goal is to estimate the noiseless samples (denoising…
Operator-Like Wavelet Bases of
Ildar Khalidov, Michael Unser, John Paul Ward
The connection between derivative operators and wavelets is well known. Here we generalize the concept by constructing multiresolution approximations and wavelet basis functions th…
Hessian Schatten-Norm Regularization for Linear Inverse Problems
Stamatios Lefkimmiatis, John Paul Ward, Michael Unser
We introduce a novel family of invariant, convex, and non-quadratic functionals that we employ to derive regularized solutions of ill-posed linear inverse imaging problems. The pro…
Approximate Message Passing with Consistent Parameter Estimation and Applications to Sparse Learning
Ulugbek S. Kamilov, Sundeep Rangan, Alyson K. Fletcher +1
We consider the estimation of an i.i.d. (possibly non-Gaussian) vector $\xbf \in \R^n$ from measurements $\ybf \in \R^m$ obtained by a general cascade model consisting of a known l…