Many inverse problems require to minimize a criterion being the sum of a non necessarily smooth function and a Lipschitz differentiable function. Such an optimization problem can be solved with the forward-backward al...
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ISBN:
(纸本)9781479928934
Many inverse problems require to minimize a criterion being the sum of a non necessarily smooth function and a Lipschitz differentiable function. Such an optimization problem can be solved with the forward-backward algorithm which can be accelerated thanks to the use of variable metrics derived from the Majorize-Minimize principle. The convergence of this approach is guaranteed provided that the criterion satisfies some additional technical conditions. Combining this method with an alternating minimization strategy will be shown to allow us to address a broad class of optimization problems involving large-size signals. An application example to a nonconvex spectral unmixing problem will be presented.
We propose a forward-backward splitting algorithm based on Bregman distances for composite minimization problems in general reflexive Banach spaces. The convergence is established using the notion of variable quasi-Br...
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We propose a forward-backward splitting algorithm based on Bregman distances for composite minimization problems in general reflexive Banach spaces. The convergence is established using the notion of variable quasi-Bregman monotone sequences. Various examples are discussed, including some in Euclidean spaces, where new algorithms are obtained.
The forward-backward algorithm is commonly used to train neural network acoustic models when optimizing a sequence objective like MMI and sMBR. Recent work on lattice-free MMI training of neural network acoustic model...
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ISBN:
(纸本)9781510848764
The forward-backward algorithm is commonly used to train neural network acoustic models when optimizing a sequence objective like MMI and sMBR. Recent work on lattice-free MMI training of neural network acoustic models shows that the forward-backward algorithm can be computed efficiently in the probability domain as a series of sparse matrix multiplications using GPUs. In this paper. we present a more efficient way of computing forward-backward using a dense matrix multiplication approach. We do this by exploiting the block-diagonal structure of the n-gram state transition matrix;instead of multiplying large sparse matrices, the proposed method involves a series of smaller dense matrix multiplications, which can be computed in parallel. Efficient implementation can be easily achieved by leveraging on the optimized matrix multiplication routines provided by standard libraries, such as NumPy and TensorFlow. Runtime benchmarks show that the dense multiplication method is consistently faster than the sparse multiplication method (on both CPUs and GPUs), when applied to a 4-gram phone language model. This is still the case even when the sparse multiplication method uses a more compact finite state model representation by excluding unseen n-grams.
We investigate the convergence analysis of the following general inexact algorithm for approximating a zero of the sum of a cocoercive operator A and maximal monotone operators B with D(B)⊂H: xn+1=αnf(xn)+γnxn+δn(I...
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Electrical Impedance Tomography (EIT) is known to be a nonlinear and ill-posed inverse problem. Conventional penalty-based regularization methods rely on the linearized model of the nonlinear forward operator. However...
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ISBN:
(纸本)9783030869700;9783030869694
Electrical Impedance Tomography (EIT) is known to be a nonlinear and ill-posed inverse problem. Conventional penalty-based regularization methods rely on the linearized model of the nonlinear forward operator. However, the linearized problem is only a rough approximation of the real situation, where the measurements can further contain unavoidable noise. The proposed reconstruction variational framework allows to turn the complete nonlinear ill-posed EIT problem into a sequence of regularized linear least squares optimization problems via a forward-backward splitting strategy, thus converting the ill-posed problem to a well-posed one. The framework can easily integrate suitable penalties to enforce smooth or piecewise-constant conductivity reconstructions depending on prior information. Numerical experiments validate the effectiveness and feasibility of the proposed approach.
We develop a probabilistic approach to construction of a viscosity solution of the Cauchy problem for a system of quasilinear parabolic equations with respect to a vector function u(t, x) ∈ Rd1, x ∈ Rd. Our approach...
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Probe-storage devices employ large arrays of probes to write/read data in parallel in some storage medium, and combine ultra-high density, low access times, and low power consumption. A particular probe-storage techni...
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Probe-storage devices employ large arrays of probes to write/read data in parallel in some storage medium, and combine ultra-high density, low access times, and low power consumption. A particular probe-storage technique utilizes thermomechanical means to store and retrieve information in thin polymer films. In this paper, a system-level channel model for the thermomechanical probe-storage channel is presented. Each of the components of the proposed model is derived by extensive characterization of experimentally obtained readback signals from probe recording tests. Moreover, detection techniques that are actually utilized in a probe-storage prototype implementation are described, followed by coding techniques for added reliability in the presence of particles or other impurities of the storage medium. In addition to low-complexity coding constructs, a concatenated coding scheme with an outer LDPC and inner modulation code is considered, in order to establish a benchmark for overall system performance. A novel methodology for joint decoding of outer LDPC and inner (d,k) modulation codes is developed. Furthermore, an optimal soft decoder for the modulation code is proposed, based on a modification of the decoder metrics to accurately account for the probe storage channel output statistics. Experimental results are used throughout the paper to validate the channel model and identify its relevant parameters, as well as to verify the system performance obtained by simulations.
In this paper, we present several confidence measures for large vocabulary continuous speech recognition. We propose to estimate the confidence of a hypothesized word directly as its posterior probability, given all a...
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In this paper, we present several confidence measures for large vocabulary continuous speech recognition. We propose to estimate the confidence of a hypothesized word directly as its posterior probability, given all acoustic observations of the utterance. These probabilities are computed on word graphs using a forward-backward algorithm. We also study the estimation of posterior probabilities on N-best lists instead of word graphs and compare both algorithms in detail. In addition, we compare the posterior probabilities with two alternative confidence measures, i.e., the acoustic stability and the hypothesis density. We present experimental results on five different corpora: the Dutch ARISE 1k evaluation corpus, the German Verbmobil '98 7k evaluation corpus, the English North American Business '94 20k and 64k development corpora, and the English Broadcast News '96 65k evaluation corpus, We show that the posterior probabilities computed on word graphs outperform all other confidence measures. The relative reduction in confidence error rate ranges between 19% and 35% compared to the baseline confidence error rate.
Models that combine Markovian states with implicit geometric state occupancy distributions and semi-Markovian states with explicit state occupancy distributions, are investigated. This type of model retains the flexib...
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Models that combine Markovian states with implicit geometric state occupancy distributions and semi-Markovian states with explicit state occupancy distributions, are investigated. This type of model retains the flexibility of hidden semi-Markov chains for the modeling of short or medium size homogeneous zones along sequences but also enables the modeling of long zones with Markovian states. The forward-backward algorithm, which in particular enables to implement efficiently the E-step of the EM algorithm, and the Viterbi algorithm for the restoration of the most likely state sequence are derived. It is also shown that macro-states, i.e. series-parallel networks of states with common observation distribution, are not a valid alternative to semi-Markovian states but may be useful at a more macroscopic level to combine Markovian states with semi-Markovian states. This statistical modeling approach is illustrated by the analysis of branching and flowering patterns in plants. (c) 2004 Elsevier B.V. All rights reserved.
Fixed point iterations play a central role in the design and the analysis of a large number of optimization algorithms. We study a new iterative scheme in which the update is obtained by applying a composition of quas...
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Fixed point iterations play a central role in the design and the analysis of a large number of optimization algorithms. We study a new iterative scheme in which the update is obtained by applying a composition of quasi-nonexpansive operators to a point in the affine hull of the orbit generated up to the current iterate. This investigation unifies several algorithmic constructs, including Mann's mean value method, inertial methods, and multilayer memoryless methods. It also provides a framework for the development of new algorithms, such as those we propose for solving monotone inclusion and minimization problems.
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