Learning-based Reconstruction of FRI Signals

Finite Rate of Innovation (FRI) sampling theory enables reconstruction of classes of continuous non-bandlimited signals that have a small number of free parameters from their low-rate discrete samples. This task is often translated into a spectral estimation problem that is solved using methods involving estimating signal subspaces, which tend to break down at a certain peak signal-to-noise ratio (PSNR). To avoid this breakdown, we consider alternative approaches that make use of information from labelled data. We propose two model-based learning methods, including deep unfolding the denoising process in spectral estimation, and constructing an encoder-decoder deep neural network that models the acquisition process. Simulation results of both learning algorithms indicate significant improvements of the breakdown PSNR over classical subspace-based methods. While the deep unfolded network achieves similar performance as the classical FRI techniques and outperforms the encoder-decoder network in the low noise regimes, the latter allows to reconstruct the FRI signal even when the sampling kernel is unknown. We also achieve competitive results in detecting pulses from in vivo calcium imaging data in terms of true positive and false positive rate while providing more precise estimations.

A Fast Automatic Method for Deconvoluting Macro X-ray Fluorescence Data Collected from Easel Paintings

Macro X-ray Fluorescence (MA-XRF) scanning is increasingly widely used by researchers in heritage science to analyse easel paintings as one of a suite of non-invasive imaging techniques. The task of processing the resulting MA-XRF datacube generated in order to produce individual chemical element maps is called MA-XRF deconvolution. While there are several existing methods that have been proposed for MA-XRF deconvolution, they require a degree of manual intervention from the user that can affect the final results. The state-of-the-art AFRID approach can automatically deconvolute the datacube without user input, but it has a long processing time and does not exploit spatial dependency. In this paper, we propose two versions of a fast automatic deconvolution (FAD) method for MA-XRF datacubes collected from easel paintings with ADMM (alternating direction method of multipliers) and FISTA (fast iterative shrinkage-thresholding algorithm). The proposed FAD method not only automatically analyses the datacube and produces element distribution maps of high-quality with spatial dependency considered, but also significantly reduces the running time. The results generated on the MA-XRF datacubes collected from two easel paintings from the National Gallery, London, verify the performance of the proposed FAD method.

DURRNet: Deep Unfolded Single Image Reflection Removal Network

Single image reflection removal problem aims to divide a reflection-contaminated image into a transmission image and a reflection image. It is a canonical blind source separation problem and is highly ill-posed. In this paper, we present a novel deep architecture called deep unfolded single image reflection removal network (DURRNet) which makes an attempt to combine the best features from model-based and learning-based paradigms and therefore leads to a more interpretable deep architecture. Specifically, we first propose a model-based optimization with transform-based exclusion prior and then design an iterative algorithm with simple closed-form solutions for solving each sub-problems. With the deep unrolling technique, we build the DURRNet with ProxNets to model natural image priors and ProxInvNets which are constructed with invertible networks to impose the exclusion prior. Comprehensive experimental results on commonly used datasets demonstrate that the proposed DURRNet achieves state-of-the-art results both visually and quantitatively.

Mixed X-Ray Image Separation for Artworks with Concealed Designs

In this paper, we focus on X-ray images of paintings with concealed sub-surface designs (e.g., deriving from reuse of the painting support or revision of a composition by the artist), which include contributions from both the surface painting and the concealed features. In particular, we propose a self-supervised deep learning-based image separation approach that can be applied to the X-ray images from such paintings to separate them into two hypothetical X-ray images. One of these reconstructed images is related to the X-ray image of the concealed painting, while the second one contains only information related to the X-ray of the visible painting. The proposed separation network consists of two components: the analysis and the synthesis sub-networks. The analysis sub-network is based on learned coupled iterative shrinkage thresholding algorithms (LCISTA) designed using algorithm unrolling techniques, and the synthesis sub-network consists of several linear mappings. The learning algorithm operates in a totally self-supervised fashion without requiring a sample set that contains both the mixed X-ray images and the separated ones. The proposed method is demonstrated on a real painting with concealed content, Do\~na Isabel de Porcel by Francisco de Goya, to show its effectiveness.

WINNet: Wavelet-inspired Invertible Network for Image Denoising

Image denoising aims to restore a clean image from an observed noisy image. The model-based image denoising approaches can achieve good generalization ability over different noise levels and are with high interpretability. Learning-based approaches are able to achieve better results, but usually with weaker generalization ability and interpretability. In this paper, we propose a wavelet-inspired invertible network (WINNet) to combine the merits of the wavelet-based approaches and learningbased approaches. The proposed WINNet consists of K-scale of lifting inspired invertible neural networks (LINNs) and sparsity-driven denoising networks together with a noise estimation network. The network architecture of LINNs is inspired by the lifting scheme in wavelets. LINNs are used to learn a non-linear redundant transform with perfect reconstruction property to facilitate noise removal. The denoising network implements a sparse coding process for denoising. The noise estimation network estimates the noise level from the input image which will be used to adaptively adjust the soft-thresholds in LINNs. The forward transform of LINNs produce a redundant multi-scale representation for denoising. The denoised image is reconstructed using the inverse transform of LINNs with the denoised detail channels and the original coarse channel. The simulation results show that the proposed WINNet method is highly interpretable and has strong generalization ability to unseen noise levels. It also achieves competitive results in the non-blind/blind image denoising and in image deblurring.

Video Summarization through Reinforcement Learning with a 3D Spatio-Temporal U-Net

Intelligent video summarization algorithms allow to quickly convey the most relevant information in videos through the identification of the most essential and explanatory content while removing redundant video frames. In this paper, we introduce the 3DST-UNet-RL framework for video summarization. A 3D spatio-temporal U-Net is used to efficiently encode spatio-temporal information of the input videos for downstream reinforcement learning (RL). An RL agent learns from spatio-temporal latent scores and predicts actions for keeping or rejecting a video frame in a video summary. We investigate if real/inflated 3D spatio-temporal CNN features are better suited to learn representations from videos than commonly used 2D image features. Our framework can operate in both, a fully unsupervised mode and a supervised training mode. We analyse the impact of prescribed summary lengths and show experimental evidence for the effectiveness of 3DST-UNet-RL on two commonly used general video summarization benchmarks. We also applied our method on a medical video summarization task. The proposed video summarization method has the potential to save storage costs of ultrasound screening videos as well as to increase efficiency when browsing patient video data during retrospective analysis or audit without loosing essential information

LINN: Lifting Inspired Invertible Neural Network for Image Denoising

In this paper, we propose an invertible neural network for image denoising (DnINN) inspired by the transform-based denoising framework. The proposed DnINN consists of an invertible neural network called LINN whose architecture is inspired by the lifting scheme in wavelet theory and a sparsity-driven denoising network which is used to remove noise from the transform coefficients. The denoising operation is performed with a single soft-thresholding operation or with a learned iterative shrinkage thresholding network. The forward pass of LINN produces an over-complete representation which is more suitable for denoising. The denoised image is reconstructed using the backward pass of LINN using the output of the denoising network. The simulation results show that the proposed DnINN method achieves results comparable to the DnCNN method while only requiring 1/4 of learnable parameters.

Meta-learning for Multi-variable Non-convex Optimization Problems: Iterating Non-optimums Makes Optimum Possible

In this paper, we aim to address the problem of solving a non-convex optimization problem over an intersection of multiple variable sets. This kind of problems is typically solved by using an alternating minimization (AM) strategy which splits the overall problem into a set of sub-problems corresponding to each variable, and then iteratively performs minimization over each sub-problem using a fixed updating rule. However, due to the intrinsic non-convexity of the overall problem, the optimization can usually be trapped into bad local minimum even when each sub-problem can be globally optimized at each iteration. To tackle this problem, we propose a meta-learning based Global Scope Optimization (GSO) method. It adaptively generates optimizers for sub-problems via meta-learners and constantly updates these meta-learners with respect to the global loss information of the overall problem. Therefore, the sub-problems are optimized with the objective of minimizing the global loss specifically. We evaluate the proposed model on a number of simulations, including solving bi-linear inverse problems: matrix completion, and non-linear problems: Gaussian mixture models. The experimental results show that our proposed approach outperforms AM-based methods in standard settings, and is able to achieve effective optimization in some challenging cases while other methods would typically fail.

Learning Deep Analysis Dictionaries -- Part II: Convolutional Dictionaries

In this paper, we introduce a Deep Convolutional Analysis Dictionary Model (DeepCAM) by learning convolutional dictionaries instead of unstructured dictionaries as in the case of deep analysis dictionary model introduced in the companion paper. Convolutional dictionaries are more suitable for processing high-dimensional signals like for example images and have only a small number of free parameters. By exploiting the properties of a convolutional dictionary, we present an efficient convolutional analysis dictionary learning approach. A L-layer DeepCAM consists of L layers of convolutional analysis dictionary and element-wise soft-thresholding pairs and a single layer of convolutional synthesis dictionary. Similar to DeepAM, each convolutional analysis dictionary is composed of a convolutional Information Preserving Analysis Dictionary (IPAD) and a convolutional Clustering Analysis Dictionary (CAD). The IPAD and the CAD are learned using variations of the proposed learning algorithm. We demonstrate that DeepCAM is an effective multilayer convolutional model and, on single image super-resolution, achieves performance comparable with other methods while also showing good generalization capabilities.

Learning Deep Analysis Dictionaries -- Part I: Unstructured Dictionaries

Inspired by the recent success of Deep Neural Networks and the recent efforts to develop multi-layer dictionary models, we propose a Deep Analysis dictionary Model (DeepAM) which is optimized to address a specific regression task known as single image super-resolution. Contrary to other multi-layer dictionary models, our architecture contains L layers of analysis dictionary and soft-thresholding operators to gradually extract high-level features and a layer of synthesis dictionary which is designed to optimize the regression task at hand. In our approach, each analysis dictionary is partitioned into two sub-dictionaries: an Information Preserving Analysis Dictionary (IPAD) and a Clustering Analysis Dictionary (CAD). The IPAD together with the corresponding soft-thresholds is designed to pass the key information from the previous layer to the next layer, while the CAD together with the corresponding soft-thresholding operator is designed to produce a sparse feature representation of its input data that facilitates discrimination of key features. Simulation results show that the proposed deep analysis dictionary model achieves comparable performance with a Deep Neural Network which has the same structure and is optimized using back-propagation.