On the Performance of Mismatched Data Detection in Large MIMO Systems

We investigate the performance of mismatched data detection in large multiple-input multiple-output (MIMO) systems, where the prior distribution of the transmit signal used in the data detector differs from the true prior. To minimize the performance loss caused by this prior mismatch, we include a tuning stage into our recently-proposed large MIMO approximate message passing (LAMA) algorithm, which allows us to develop mismatched LAMA algorithms with optimal as well as sub-optimal tuning. We show that carefully-selected priors often enable simpler and computationally more efficient algorithms compared to LAMA with the true prior while achieving near-optimal performance. A performance analysis of our algorithms for a Gaussian prior and a uniform prior within a hypercube covering the QAM constellation recovers classical and recent results on linear and non-linear MIMO data detection, respectively.Comment: Will be presented at the 2016 IEEE International Symposium on Information Theor

Suboptimality of Nonlocal Means for Images with Sharp Edges

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. We prove that the mean square risk of an optimally tuned nonlocal means algorithm decays according to $n^{-1}\log^{1/2+\epsilon} n$, for an $n$-pixel image with $\epsilon>0$. This decay rate is an improvement over some of the predecessors of this algorithm, including the linear convolution filter, median filter, and the SUSAN filter, each of which provides a rate of only $n^{-2/3}$. It is also within a logarithmic factor from optimally tuned wavelet thresholding. However, it is still substantially lower than the the optimal minimax rate of $n^{-4/3}$.Comment: 33 pages, 3 figure