Learning Multiscale Convolutional Dictionaries for Image Reconstruction

  title={Learning Multiscale Convolutional Dictionaries for Image Reconstruction},
  author={Tianlin Liu and Anadi Chaman and David Belius and Ivan Dokmani'c},
  journal={IEEE Transactions on Computational Imaging},
Convolutional neural networks (CNNs) have been tremendously successful in solving imaging inverse problems. To understand their success, an effective strategy is to construct simpler and mathematically more tractable convolutional sparse coding (CSC) models that share essential ingredients with CNNs. Existing CSC methods, however, underperform leading CNNs in challenging inverse problems. We hypothesize that the performance gap may be attributed in part to how they process images at different… 

Conditional Injective Flows for Bayesian Imaging

C-Trumpets are proposed—conditional injective flows specifically designed for imaging problems, which greatly diminish these challenges of ill-posedness, nonlinearity, model mismatch, and noise and enable fast approximation of point estimates like MMSE or MAP as well as physically-meaningful uncertainty quantiflcation.

FunkNN: Neural Interpolation for Functional Generation

FunkNN is a new convolutional network which learns how to reconstruct continuous images at arbitrary coordinates and can be applied to any image dataset and becomes a functional generator which can act as a prior in continuous ill-posed inverse problems.

Sinogram upsampling using Primal-Dual UNet for undersampled CT and radial MRI reconstruction

The proposed Primal-Dual UNet improves the overall image quality, but also improves the image quality for the regions-of-interest: liver, kidneys, and spleen; as well as generalises better than the baselines in presence of a needle.

Deep Injective Prior for Inverse Scattering

A new data-driven framework for inverse scattering based on deep generative models that outperforms the traditional iterative methods especially for strong scatterers while having comparable reconstruction quality to state-of-the-art deep learning methods like U-Net.

Enhanced artificial intelligence-based diagnosis using CBCT with internal denoising: Clinical validation for discrimination of fungal ball, sinusitis, and normal cases in the maxillary sinus

An AI-based computer-aided diagnosis method using CBCT with a denoising module is proposed, implemented before diagnosis to reconstruct the internal ground-truth full-dose scan corresponding to an input CBCT image and thereby improve the diagnostic performance.



When to Use Convolutional Neural Networks for Inverse Problems

This work argues that for some types of inverse problems the CNN approximation breaks down leading to poor performance, and argues that the CSC approach should be used instead and validate this argument with empirical evidence.

Convolutional Neural Networks Analyzed via Convolutional Sparse Coding

This work proposes a novel multi-layer model, ML-CSC, in which signals are assumed to emerge from a cascade of CSC layers, and presents an alternative to the forward pass, which is connected to deconvolutional, recurrent and residual networks, and has better theoretical guarantees.

Denoising Prior Driven Deep Neural Network for Image Restoration

A convolutional neural network (CNN) based denoiser that can exploit the multi-scale redundancies of natural images is proposed, which not only exploits the powerful denoising ability of DNNs, but also leverages the prior of the observation model.

Deep Laplacian Pyramid Networks for Fast and Accurate Super-Resolution

This paper proposes the Laplacian Pyramid Super-Resolution Network (LapSRN) to progressively reconstruct the sub-band residuals of high-resolution images and generates multi-scale predictions in one feed-forward pass through the progressive reconstruction, thereby facilitates resource-aware applications.

Understanding Geometry of Encoder-Decoder CNNs

A unified mathematical framework shows that encoder-decoder CNN architecture is closely related to nonlinear basis representation using combinatorial convolution frames, whose expressibility increases exponentially with the network depth, and the importance of skipped connection in terms of expressibility, and optimization landscape.

Variations on the Convolutional Sparse Coding Model

This work expands the range of formulations for the CSC model by proposing two convex alternatives that merge global norms with local penalties and constraints and derivation of efficient and provably converging algorithms to solve these new sparse coding formulations.

Removing Rain from Single Images via a Deep Detail Network

A deep detail network is proposed to directly reduce the mapping range from input to output, which makes the learning process easier and significantly outperforms state-of-the-art methods on both synthetic and real-world images in terms of both qualitative and quantitative measures.

Convolutional Kernel Networks

This paper proposes a new type of convolutional neural network (CNN) whose invariance is encoded by a reproducing kernel, and bridges a gap between the neural network literature and kernels, which are natural tools to model invariance.

Learning Deep Analysis Dictionaries for Image Super-Resolution

Simulation results show that the proposed deep analysis dictionary model achieves better performance compared to a deep neural network that has the same structure and is optimized using back-propagation when training datasets are small.

Image super-resolution by learning weighted convolutional sparse coding

An end-to-end trainable unfolding network which leverages both DL- and prior-based methods and presents a SISR model by learning weighted convolutional sparse coding, in which the channel attention is resorted to learn the weight.