• Publications
  • Influence
Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems
TLDR
This paper proposes gradient projection algorithms for the bound-constrained quadratic programming (BCQP) formulation of these problems and test variants of this approach that select the line search parameters in different ways, including techniques based on the Barzilai-Borwein method. Expand
Wavelet-based statistical signal processing using hidden Markov models
TLDR
A new framework for statistical signal processing based on wavelet-domain hidden Markov models (HMMs) that concisely models the statistical dependencies and non-Gaussian statistics encountered in real-world signals is developed. Expand
Sparse Reconstruction by Separable Approximation
TLDR
This work proposes iterative methods in which each step is obtained by solving an optimization subproblem involving a quadratic term with diagonal Hessian plus the original sparsity-inducing regularizer, and proves convergence of the proposed iterative algorithm to a minimum of the objective function. Expand
An EM algorithm for wavelet-based image restoration
TLDR
An expectation-maximization (EM) algorithm for image restoration (deconvolution) based on a penalized likelihood formulated in the wavelet domain is introduced, and it is shown that under mild conditions the algorithm converges to a globally optimal restoration. Expand
Online identification and tracking of subspaces from highly incomplete information
TLDR
This work presents GROUSE (Grassmanian Rank-One Update Subspace Estimation), an efficient online algorithm for tracking subspaces from highly incomplete observations that performs exceptionally well in practice both in tracking subspace and as an online algorithms for matrix completion. Expand
Compressed Channel Sensing: A New Approach to Estimating Sparse Multipath Channels
TLDR
The notion of multipath sparsity is formalized and a new approach to estimating sparse multipath channels is presented that is based on some of the recent advances in the theory of compressed sensing, which can potentially achieve a target reconstruction error using far less energy and latency and bandwidth than that dictated by the traditional least-squares-based training methods. Expand
lil' UCB : An Optimal Exploration Algorithm for Multi-Armed Bandits
TLDR
It is proved that the UCB procedure for identifying the arm with the largest mean in a multi-armed bandit game in the fixed confidence setting using a small number of total samples is optimal up to constants and also shows through simulations that it provides superior performance with respect to the state-of-the-art. Expand
Transduction with Matrix Completion: Three Birds with One Stone
TLDR
This work poses transductive classification as a matrix completion problem by assuming the underlying matrix has a low rank, and solves the resulting nuclear norm minimization problem with a modified fixed-point continuation method that is guaranteed to find the global optimum. Expand
Wavelet-based Rician noise removal for magnetic resonance imaging
  • R. Nowak
  • Mathematics, Medicine
  • IEEE Trans. Image Process.
  • 1 October 1999
TLDR
A novel wavelet-domain filter that adapts to variations in both the signal and the noise is presented, which is especially problematic in low signal-to-noise ratio (SNR) regimes. Expand
Minimax Bounds for Active Learning
  • R. Castro, R. Nowak
  • Mathematics, Computer Science
  • IEEE Transactions on Information Theory
  • 1 May 2008
TLDR
The achievable rates of classification error convergence for broad classes of distributions characterized by decision boundary regularity and noise conditions are studied using minimax analysis techniques to indicate the conditions under which one can expect significant gains through active learning. Expand
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