Compressive Imaging using Approximate Message Passing and a Markov-Tree Prior

We propose a novel algorithm for compressive imaging that exploits both the sparsity and persistence across scales found in the 2D wavelet transform coefficients of natural images. Like other recent works, we model wavelet structure using a hidden Markov tree (HMT) but, unlike other works, ours is based on loopy belief propagation (LBP). For LBP, we adopt a recently proposed "turbo" message passing schedule that alternates between exploitation of HMT structure and exploitation of compressive-measurement structure. For the latter, we leverage Donoho, Maleki, and Montanari's recently proposed approximate message passing (AMP) algorithm. Experiments with a large image database suggest that, relative to existing schemes, our turbo LBP approach yields state-of-the-art reconstruction performance with substantial reduction in complexity

VisIRR: Interactive Visual Information Retrieval and Recommendation for Large-scale Document Data

Research areas: Machine learning, Data mining, Information visualization, Visual analytics, Text visualization.We present a visual analytics system called VisIRR, which is an interactive visual information retrieval and recommendation system for document discovery. VisIRR effectively combines both paradigms of passive pull through a query processes for retrieval and active push that recommends the items of potential interest based on the user preferences. Equipped with efficient dynamic query interfaces for a large corpus of document data, VisIRR visualizes the retrieved documents in a scatter plot form with their overall topic clusters. At the same time, based on interactive personalized preference feedback on documents, VisIRR provides recommended documents reaching out to the entire corpus beyond the retrieved sets. Such recommended documents are represented in the same scatter space of the retrieved documents so that users can perform integrated analyses of both retrieved and recommended documents seamlessly. We describe the state-of-the-art computational methods that make these integrated and informative representations as well as real time interaction possible. We illustrate the way the system works by using detailed usage scenarios. In addition, we present a preliminary user study that evaluates the effectiveness of the system

Compressive Imaging using Approximate Message Passing and a

Abstract—We propose a novel algorithm for compressive imaging that exploits both the sparsity and persistence across scales found in the 2D wavelet transform coefficients of natural images. Like other recent works, we model wavelet structure using a hidden Markov tree (HMT) but, unlike other works, ours is based on loopy belief propagation (LBP). For LBP, we adopt a recently proposed “turbo ” message passing schedule that alternates between exploitation of HMT structure and exploitation of compressive-measurement structure. For the latter, we leverage Donoho, Maleki, and Montanari’s recently proposed approximate message passing (AMP) algorithm. Experiments on a large image database show that our turbo LBP approach maintains state-ofthe-art reconstruction performance at half the complexity. 1 I

On Approximate Message Passing for Reconstruction of Non-Uniformly Sparse Signals

Abstract—This paper considers the reconstruction of nonuniformly sparse signals from noisy linear observations. By nonuniformly sparse, we mean that the signal coefficients can be partitioned into subsets that differ in the rate at which the coefficients tend to be active (i.e., nonzero). Inspired by recent work of Donoho, Maleki, and Montanari, we design a minimaxoptimal approximate message passing (AMP) algorithm and we analyze it using a state evolution (SE) formalism that applies in the limit of very large problem dimensions. For the noiseless case, the SE formalism implies a phase transition curve (PTC) that bisects the admissible region of the sparsity-undersampling plane into two sub-regions: one where perfect recovery is very likely, and one where it is very unlikely. The PTC depends on the ratios of the activity rates and the relative sizes of the coefficient subsets. For the noisy case, we show that the same PTC also bisects the admissible region of the sparsity-undersampling plane into two sub-regions: one where the noise sensitivity remains finite and characterizable, and one where it becomes infinite (as the problem dimensions increase). Furthermore, we derive the formal mean-squared error (MSE) for (sparsity,undersampling) pairs in the region below the PTC. Numerical results suggest that the MSE predicted by the SE formalism closely matches the empirical MSE throughout the admissible region of the sparsityundersampling plane, so long as the dimensions of the problem are adequately large. 1 I