Search

We consider deep neural networks with rectifier activations and max-pooling from a signal representation perspective. In this view, such representations mark the transition from using a single linear representation for all signals to utilizing a large collection of affine linear representations that are tailored to particular regions of the signal space. We propose a novel technique to “un-rectify” the nonlinear activations into data-dependent linear equations and constraints, from which we derive explicit expressions for the affine linear operators, their domains and ranges in terms of the network parameters. We show how increasing the depth of the network refines the domain partitioning and derive atomic decompositions for the corresponding affine mappings that process data belonging to the same partitioning region. In each atomic decomposition the connections over all hidden network layers are summarized and interpreted in a single matrix. We apply the decompositions to study the Lipschitz regularity of the networks and give sufficient conditions for network-depth-independent stability of the representation, drawing a connection to compressible weight distributions. Such analyses may facilitate and promote further theoretical insight and exchange from both the signal processing and machine learning communities. [ABSTRACT FROM AUTHOR]

We propose a novel operator-based model called the null space component analysis (NCA) to solve the noisy blind source separation (BSS) problem. Theoretically, we show that the NCA can resolve the rotation ambiguity in the BSS problem. In a set of m linearly independent source signals, the basic principle of the NCA is to associate each signal with a separating operator that includes the signal in its null space and repels other signals from the space. We show that the model can act as a constraint on the source signals in the noisy BSS problem. In contrast to the ICA-based and the sparsity-based approaches, NCA is a deterministic and data-adaptive algorithm that can solve both the under-determined and the over-determined BSS problems. To demonstrate the algorithm׳s efficiency, we process several types of signals, including real-life signals obtained from biomedical systems, and compare the results with those derived by other methods. [ABSTRACT FROM AUTHOR]

Traditional approaches to receiver-driven layered multicast apply coarse-grain layered congestion control, which enables each receiver to adjust its receiving rate to match the available bandwidth. However, this restricts the scalability of fine-grain scalable video coding. In this paper, we present an approach that facilitates bandwidth inference congestion control in a hybrid coarse/fine layered multicast scheme for multimedia delivery. One-way delay trend detection has proven effective in explicitly or implicitly estimating end-to-end available bandwidth. Using a hierarchical layered probing scheme and a delay trend detection method, we have developed a congestion control protocol for fine-grain layered multicast. Combining this protocol with scalable video coding, we present a framework that achieves efficient scalable video streaming over heterogeneous networks. The performance of our hybrid coarse/fine layered multicast scheme is evaluated by network simulations and the video coding efficiency. [ABSTRACT FROM AUTHOR]

Presents information on a study which focused on nonorthogonal wavelet signal estimation algorithm for fractional Brownian motion embedded in white noise. Autocorrelation of fractal wavelet transform and composite singularity; Signal estimation; Simulation results; Conclusions.