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Consistent Parameter Estimation for LASSO and Approximate Message Passing
Ali Mousavi, Arian Maleki, Richard G. Baraniuk
We consider the problem of recovering a vector from random and noisy linear observations , where is the measurement matrix and is no…
Path Thresholding: Asymptotically Tuning-Free High-Dimensional Sparse Regression
Divyanshu Vats, Richard G. Baraniuk
In this paper, we address the challenging problem of selecting tuning parameters for high-dimensional sparse regression. We propose a simple and computationally efficient method, c…
Swapping Variables for High-Dimensional Sparse Regression with Correlated Measurements
Divyanshu Vats, Richard G. Baraniuk
We consider the high-dimensional sparse linear regression problem of accurately estimating a sparse vector using a small number of linear measurements that are contaminated by nois…
Asymptotic Analysis of LASSOs Solution Path with Implications for Approximate Message Passing
Ali Mousavi, Arian Maleki, Richard G. Baraniuk
This paper concerns the performance of the LASSO (also knows as basis pursuit denoising) for recovering sparse signals from undersampled, randomized, noisy measurements. We conside…
Anisotropic Nonlocal Means Denoising
Arian Maleki, Manjari Narayan, Richard G. Baraniuk
It has recently been proved that the popular nonlocal means (NLM) denoising algorithm does not optimally denoise images with sharp edges. Its weakness lies in the isotropic nature…
Suboptimality of Nonlocal Means for Images with Sharp Edges
Arian Maleki, Manjari Narayan, Richard G. Baraniuk
We conduct an asymptotic risk analysis of the nonlocal means image denoising algorithm for the Horizon class of images that are piecewise constant with a sharp edge discontinuity.…