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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.…
Minimum Complexity Pursuit
Shirin Jalali, Arian Maleki
The fast growing field of compressed sensing is founded on the fact that if a signal is 'simple' and has some 'structure', then it can be reconstructed accurately with far fewer sa…
Asymptotic Analysis of Complex LASSO via Complex Approximate Message Passing (CAMP)
Arian Maleki, Laura Anitori, Zai Yang +1
Recovering a sparse signal from an undersampled set of random linear measurements is the main problem of interest in compressed sensing. In this paper, we consider the case where b…
Compressed Sensing over -balls: Minimax Mean Square Error
David Donoho, Iain Johnstone, Arian Maleki +1
We consider the compressed sensing problem, where the object $x_0 \in \bR^N$ is to be recovered from incomplete measurements ; here the sensing matrix is an $n \t…