Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userNeural Proximal Gradient Descent for Compressive Imaging
109
0
0.0
(
0
)
Added by
Morteza Mardani
Publication date
2018
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Recovering high-resolution images from limited sensory data typically leads to a serious ill-posed inverse problem, demanding inversion algorithms that effectively capture the prior information. Learning a good inverse mapping from training data faces severe challenges, including: (i) scarcity of training data; (ii) need for plausible reconstructions that are physically feasible; (iii) need for fast reconstruction, especially in real-time applications. We develop a successful system solving all these challenges, using as basic architecture the recurrent application of proximal gradient algorithm. We learn a proximal map that works well with real images based on residual networks. Contraction of the resulting map is analyzed, and incoherence conditions are investigated that drive the convergence of the iterates. Extensive experiments are carried out under different settings: (a) reconstructing abdominal MRI of pediatric patients from highly undersampled Fourier-space data and (b) superresolving natural face images. Our key findings include: 1. a recurrent ResNet with a single residual block unrolled from an iterative algorithm yields an effective proximal which accurately reveals MR image details. 2. Our architecture significantly outperforms conventional non-recurrent deep ResNets by 2dB SNR; it is also trained much more rapidly. 3. It outperforms state-of-the-art compressed-sensing Wavelet-based methods by 4dB SNR, with 100x speedups in reconstruction time.
rate research
Read More
Recovering an underlying image from under-sampled measurements, Compressive Sensing Imaging (CSI) is a challenging problem and has many practical applications. Recently, deep neural networks have been applied to this problem with promising results, owing to its implicitly learned prior to alleviate the ill-poseness of CSI. However, existing neural network approaches require separate models for each imaging parameter like sampling ratios, leading to training difficulties and overfitting to specific settings. In this paper, we present a dynamic proximal unrolling network (dubbed DPUNet), which can handle a variety of measurement matrices via one single model without retraining. Specifically, DPUNet can exploit both embedded physical model via gradient descent and imposing image prior with learned dynamic proximal mapping leading to joint reconstruction. A key component of DPUNet is a dynamic proximal mapping module, whose parameters can be dynamically adjusted at inference stage and make it adapt to any given imaging setting. Experimental results demonstrate that the proposed DPUNet can effectively handle multiple CSI modalities under varying sampling ratios and noise levels with only one model, and outperform the state-of-the-art approaches.
The classical problem of phase retrieval arises in various signal acquisition systems. Due to the ill-posed nature of the problem, the solution requires assumptions on the structure of the signal. In the last several years, sparsity and support-based priors have been leveraged successfully to solve this problem. In this work, we propose replacing the sparsity/support priors with generative priors and propose two algorithms to solve the phase retrieval problem. Our proposed algorithms combine the ideas from AltMin approach for non-convex sparse phase retrieval and projected gradient descent approach for solving linear inverse problems using generative priors. We empirically show that the performance of our method with projected gradient descent is superior to the existing approach for solving phase retrieval under generative priors. We support our method with an analysis of sample complexity with Gaussian measurements.
Compressing large Neural Networks (NN) by quantizing the parameters, while maintaining the performance is highly desirable due to reduced memory and time complexity. In this work, we cast NN quantization as a discrete labelling problem, and by examining relaxations, we design an efficient iterative optimization procedure that involves stochastic gradient descent followed by a projection. We prove that our simple projected gradient descent approach is, in fact, equivalent to a proximal version of the well-known mean-field method. These findings would allow the decades-old and theoretically grounded research on MRF optimization to be used to design better network quantization schemes. Our experiments on standard classification datasets (MNIST, CIFAR10/100, TinyImageNet) with convolutional and residual architectures show that our algorithm obtains fully-quantized networks with accuracies very close to the floating-point reference networks.
Natural gradient descent has proven effective at mitigating the effects of pathological curvature in neural network optimization, but little is known theoretically about its convergence properties, especially for emph{nonlinear} networks. In this work, we analyze for the first time the speed of convergence of natural gradient descent on nonlinear neural networks with squared-error loss. We identify two conditions which guarantee efficient convergence from random initializations: (1) the Jacobian matrix (of networks output for all training cases with respect to the parameters) has full row rank, and (2) the Jacobian matrix is stable for small perturbations around the initialization. For two-layer ReLU neural networks, we prove that these two conditions do in fact hold throughout the training, under the assumptions of nondegenerate inputs and overparameterization. We further extend our analysis to more general loss functions. Lastly, we show that K-FAC, an approximate natural gradient descent method, also converges to global minima under the same assumptions, and we give a bound on the rate of this convergence.
Particle-based approximate Bayesian inference approaches such as Stein Variational Gradient Descent (SVGD) combine the flexibility and convergence guarantees of sampling methods with the computational benefits of variational inference. In practice, SVGD relies on the choice of an appropriate kernel function, which impacts its ability to model the target distribution -- a challenging problem with only heuristic solutions. We propose Neural Variational Gradient Descent (NVGD), which is based on parameterizing the witness function of the Stein discrepancy by a deep neural network whose parameters are learned in parallel to the inference, mitigating the necessity to make any kernel choices whatsoever. We empirically evaluate our method on popular synthetic inference problems, real-world Bayesian linear regression, and Bayesian neural network inference.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
