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Register a new userFRIST - Flipping and Rotation Invariant Sparsifying Transform Learning and Applications
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Added by
Bihan Wen Mr
Publication date
2015
fields
Informatics Engineering
and research's language is
English
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Features based on sparse representation, especially using the synthesis dictionary model, have been heavily exploited in signal processing and computer vision. However, synthesis dictionary learning typically involves NP-hard sparse coding and expensive learning steps. Recently, sparsifying transform learning received interest for its cheap computation and its optimal updates in the alternating algorithms. In this work, we develop a methodology for learning Flipping and Rotation Invariant Sparsifying Transforms, dubbed FRIST, to better represent natural images that contain textures with various geometrical directions. The proposed alternating FRIST learning algorithm involves efficient optimal updates. We provide a convergence guarantee, and demonstrate the empirical convergence behavior of the proposed FRIST learning approach. Preliminary experiments show the promising performance of FRIST learning for sparse image representation, segmentation, denoising, robust inpainting, and compressed sensing-based magnetic resonance image reconstruction.
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Achieving high-quality reconstructions from low-dose computed tomography (LDCT) measurements is of much importance in clinical settings. Model-based image reconstruction methods have been proven to be effective in removing artifacts in LDCT. In this work, we propose an approach to learn a rich two-layer clustering-based sparsifying transform model (MCST2), where image patches and their subsequent feature maps (filter residuals) are clustered into groups with different learned sparsifying filters per group. We investigate a penalized weighted least squares (PWLS) approach for LDCT reconstruction incorporating learned MCST2 priors. Experimental results show the superior performance of the proposed PWLS-MCST2 approach compared to other related recent schemes.
Graph-based representations play a key role in machine learning. The fundamental step in these representations is the association of a graph structure to a dataset. In this paper, we propose a method that aims at finding a block sparse representation of the graph signal leading to a modular graph whose Laplacian matrix admits the found dictionary as its eigenvectors. The role of sparsity here is to induce a band-limited representation or, equivalently, a modular structure of the graph. The proposed strategy is composed of two optimization steps: i) learning an orthonormal sparsifying transform from the data; ii) recovering the Laplacian, and then topology, from the transform. The first step is achieved through an iterative algorithm whose alternating intermediate solutions are expressed in closed form. The second step recovers the Laplacian matrix from the sparsifying transform through a convex optimization method. Numerical results corroborate the effectiveness of the proposed methods over both synthetic data and real brain data, used for inferring the brain functionality network through experiments conducted over patients affected by epilepsy.
The phenomenon of adversarial examples illustrates one of the most basic vulnerabilities of deep neural networks. Among the variety of techniques introduced to surmount this inherent weakness, adversarial training has emerged as the most common and efficient strategy to achieve robustness. Typically, this is achieved by balancing robust and natural objectives. In this work, we aim to achieve better trade-off between robust and natural performances by enforcing a domain-invariant feature representation. We present a new adversarial training method, Domain Invariant Adversarial Learning (DIAL), which learns a feature representation which is both robust and domain invariant. DIAL uses a variant of Domain Adversarial Neural Network (DANN) on the natural domain and its corresponding adversarial domain. In a case where the source domain consists of natural examples and the target domain is the adversarially perturbed examples, our method learns a feature representation constrained not to discriminate between the natural and adversarial examples, and can therefore achieve a more robust representation. Our experiments indicate that our method improves both robustness and natural accuracy, when compared to current state-of-the-art adversarial training methods.
Techniques exploiting the sparsity of images in a transform domain have been effective for various applications in image and video processing. Transform learning methods involve cheap computations and have been demonstrated to perform well in applications such as image denoising and medical image reconstruction. Recently, we proposed methods for online learning of sparsifying transforms from streaming signals, which enjoy good convergence guarantees, and involve lower computational costs than online synthesis dictionary learning. In this work, we apply online transform learning to video denoising. We present a novel framework for online video denoising based on high-dimensional sparsifying transform learning for spatio-temporal patches. The patches are constructed either from corresponding 2D patches in successive frames or using an online block matching technique. The proposed online video denoising requires little memory, and offers efficient processing. Numerical experiments compare the performance to the proposed video denoising scheme but fixing the transform to be 3D DCT, as well as prior schemes such as dictionary learning-based schemes, and the state-of-the-art VBM3D and VBM4D on several video data sets, demonstrating the promising performance of the proposed methods.
In many machine learning tasks it is desirable that a models prediction transforms in an equivariant way under transformations of its input. Convolutional neural networks (CNNs) implement translational equivariance by construction; for other transformations, however, they are compelled to learn the proper mapping. In this work, we develop Steerable Filter CNNs (SFCNNs) which achieve joint equivariance under translations and rotations by design. The proposed architecture employs steerable filters to efficiently compute orientation dependent responses for many orientations without suffering interpolation artifacts from filter rotation. We utilize group convolutions which guarantee an equivariant mapping. In addition, we generalize Hes weight initialization scheme to filters which are defined as a linear combination of a system of atomic filters. Numerical experiments show a substantial enhancement of the sample complexity with a growing number of sampled filter orientations and confirm that the network generalizes learned patterns over orientations. The proposed approach achieves state-of-the-art on the rotated MNIST benchmark and on the ISBI 2012 2D EM segmentation challenge.
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