This paper describes performance bounds for compressed sensing in the presence of Poisson noise and shows that, for sparse or compressible signals, they are within a log factor of known lower bounds on the risk. The signal-independent and bounded noise models used in the literature to analyze the performance of compressed sensing do not accurately model the effects of Poisson noise. However, Po...

We investigate the problem of robust joint transmitter and receiver power allocation for uplink multiuser multi-input multi-output (MIMO) transmissions. The channel model is assumed to have Rayleigh flat fading. The objective of power allocation is to minimize the maximum MSE among all users each of which has limited transmit power. We investigate robust joint transmitter and receiver power all...

We develop a linear time algorithm algorithm for the following problem: given an ordered sequence of n real weights w1, w2, . . . , wn, construct a binary tree on n leaves labeled with those weights when read from left to right so that the maximum value of wi plus depth of the i-th leftmost leaf is minimized. This improves the previously known O(n logn) time solutions [2,11,13]. We also give a ...

We study the convergence of regularized Newton methods applied to nonlinear operator equations in Hilbert spaces if the data are perturbed by random noise. It is shown that the expected square error is bounded by a constant times the minimax rates of the corresponding linearized problem if the stopping index is chosen using a-priori knowledge of the smoothness of the solution. For unknown smoot...

The theme of this paper is the application of linear analysis to simplify and extend convex analysis. The central problem treated is the standard convex program -minimize a convex function subject to inequality constraints on other convex functions. The present approach uses the support planes of the constraint region to transform the convex program into an equivalent linear program. Then the d...

We study the nonparametric covariance estimation of a stationary Gaussian field X observed on a regular lattice. In the time series setting, some procedures like AIC are proved to achieve optimal model selection among autoregressive models. However, there exists no such equivalent results of adaptivity in a spatial setting. By considering collections of Gaussian Markov random fields (GMRF) as a...

This paper is concerned with adaptive kernel estimation of the Lévy density N(x) for bounded-variation pure-jump Lévy processes. The sample path is observed at n discrete instants in the ”high frequency” context (∆ = ∆(n) tends to zero while n∆ tends to infinity). We construct a collection of kernel estimators of the function g(x) = xN(x) and propose a method of local adaptive selection of the ...

This paper states that for financial markets with continuous filtrations, the minimax local martingale measure defined by Frittelli is equivalent to the objective measure for nondecreasing but not strictly increasing utility functions if it exists, provided the dual utility function satisfies some boundedness assumptions for the relative risk aversion, and there exists an equivalent local marti...

We review and extend the main topological minimax theorems based on connectedness that have been developed over the years since the pioneering paper of Wu (1959). It is shown in particular that the topological minimax theorems of Geraghty and Lin (1984) are essentially a rediscovery of much earlier results of Tuy (1974), while the latter can be derived from a minimax theorem recently developed ...

In this paper we consider non parametric finite translation mixtures. We prove that all the parameters of the model are identifiable as soon as the matrix that defines the joint distribution of two consecutive latent variables is non singular and the translation parameters are distinct. Under this assumption, we provide a consistent estimator of the number of populations, of the translation par...