7 research outputs found
Approximate Primal-Dual Fixed-Point based Langevin Algorithms for Non-smooth Convex Potentials
The Langevin algorithms are frequently used to sample the posterior
distributions in Bayesian inference. In many practical problems, however, the
posterior distributions often consist of non-differentiable components, posing
challenges for the standard Langevin algorithms, as they require to evaluate
the gradient of the energy function in each iteration. To this end, a popular
remedy is to utilize the proximity operator, and as a result one needs to solve
a proximity subproblem in each iteration. The conventional practice is to solve
the subproblems accurately, which can be exceedingly expensive, as the
subproblem needs to be solved in each iteration. We propose an approximate
primal-dual fixed-point algorithm for solving the subproblem, which only seeks
an approximate solution of the subproblem and therefore reduces the
computational cost considerably. We provide theoretical analysis of the
proposed method and also demonstrate its performance with numerical examples
NF-ULA: Normalizing Flow-Based Unadjusted Langevin Algorithm for Imaging Inverse Problems
Bayesian methods for solving inverse problems are a powerful alternative to classical methods since the Bayesian approach offers the ability to quantify the uncertainty in the solution. In recent years, data-driven techniques for solving inverse problems have also been remarkably successful, due to their superior representation ability. In this work, we incorporate data-based models into a class of Langevin-based sampling algorithms for Bayesian inference in imaging inverse problems. In particular, we introduce NF-ULA (Normalizing Flow-based Unadjusted Langevin algorithm), which involves learning a normalizing flow (NF) as the image prior. We use NF to learn the prior because a tractable closed-form expression for the log prior enables the differentiation of it using autograd libraries. Our algorithm only requires a normalizing flow-based generative network, which can be pre-trained independently of the considered inverse problem and the forward operator. We perform theoretical analysis by investigating the well-posedness and non-asymptotic convergence of the resulting NF-ULA algorithm. The efficacy of the proposed NF-ULA algorithm is demonstrated in various image restoration problems such as image deblurring, image inpainting, and limited-angle X-ray computed tomography (CT) reconstruction. NF-ULA is found to perform better than competing methods for severely ill-posed inverse problems
NF-ULA: Langevin Monte Carlo with Normalizing Flow Prior for Imaging Inverse Problems
Bayesian methods for solving inverse problems are a powerful alternative to
classical methods since the Bayesian approach offers the ability to quantify
the uncertainty in the solution. In recent years, data-driven techniques for
solving inverse problems have also been remarkably successful, due to their
superior representation ability. In this work, we incorporate data-based models
into a class of Langevin-based sampling algorithms for Bayesian inference in
imaging inverse problems. In particular, we introduce NF-ULA (Normalizing
Flow-based Unadjusted Langevin algorithm), which involves learning a
normalizing flow (NF) as the image prior. We use NF to learn the prior because
a tractable closed-form expression for the log prior enables the
differentiation of it using autograd libraries. Our algorithm only requires a
normalizing flow-based generative network, which can be pre-trained
independently of the considered inverse problem and the forward operator. We
perform theoretical analysis by investigating the well-posedness and
non-asymptotic convergence of the resulting NF-ULA algorithm. The efficacy of
the proposed NF-ULA algorithm is demonstrated in various image restoration
problems such as image deblurring, image inpainting, and limited-angle X-ray
computed tomography (CT) reconstruction. NF-ULA is found to perform better than
competing methods for severely ill-posed inverse problems
NF-ULA: Normalizing Flow-Based Unadjusted Langevin Algorithm for Imaging Inverse Problems
Bayesian methods for solving inverse problems are a powerful alternative to classical methods since the Bayesian approach offers the ability to quantify the uncertainty in the solution. In recent years, data-driven techniques for solving inverse problems have also been remarkably successful, due to their superior representation ability. In this work, we incorporate data-based models into a class of Langevin-based sampling algorithms for Bayesian inference in imaging inverse problems. In particular, we introduce NF-ULA (Normalizing Flow-based Unadjusted Langevin algorithm), which involves learning a normalizing flow (NF) as the image prior. We use NF to learn the prior because a tractable closed-form expression for the log prior enables the differentiation of it using autograd libraries. Our algorithm only requires a normalizing flow-based generative network, which can be pre-trained independently of the considered inverse problem and the forward operator. We perform theoretical analysis by investigating the well-posedness and non-asymptotic convergence of the resulting NF-ULA algorithm. The efficacy of the proposed NF-ULA algorithm is demonstrated in various image restoration problems such as image deblurring, image inpainting, and limited-angle X-ray computed tomography (CT) reconstruction. NF-ULA is found to perform better than competing methods for severely ill-posed inverse problems
Low-Temperature Solution-Processed Perovskite Solar Cells with High Efficiency and Flexibility
Perovskite compounds have attracted recently great attention in photovoltaic research. The devices are typically fabricated using condensed or mesoporous TiO<sub>2</sub> as the electron transport layer and 2,2′7,7′-tetrakis-(<i>N</i>,<i>N</i>-dip-methoxyÂphenylÂamine)9,9′-spiroÂbiÂfluorene as the hole transport layer. However, the high-temperature processing (450 °C) requirement of the TiO<sub>2</sub> layer could hinder the widespread adoption of the technology. In this report, we adopted a low-temperature processing technique to attain high-efficiency devices in both rigid and flexible substrates, using device structure substrate/ITO/PEDOT:PSS/CH<sub>3</sub>NH<sub>3</sub>PbI<sub>3–<i>x</i></sub>Cl<sub><i>x</i></sub>/PCBM/Al, where PEDOT:PSS and PCBM are used as hole and electron transport layers, respectively. Mixed halide perovskite, CH<sub>3</sub>NH<sub>3</sub>PbI<sub>3–<i>x</i></sub>Cl<sub><i>x</i></sub>, was used due to its long carrier lifetime and good electrical properties. All of these layers are solution-processed under 120 °C. Based on the proposed device structure, power conversion efficiency (PCE) of 11.5% is obtained in rigid substrates (glass/ITO), and a 9.2% PCE is achieved for a polyethylene terephthalate/ITO flexible substrate