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44th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Kaneko, Y. Muramatsu, S. Yasuda, H. Hayasaka, K. Otake, Y. Ono, S. Yukawa, M. Niigata Univ Grad Sch Sci & Tech Niigata Japan Niigata Univ Res Inst Nat Hazard & Disaster Recovery Niigata Japan Niigata Univ Fac Sci Niigata Japan Tokyo Inst Tech Inst Innovat Res Tokyo Japan Niigata Univ Fac Engn Niigata Japan Keio Univ Fac Sci & Tech Keio Japan

ISBN: (纸本)9781479981311

This work proposes convolutional-sparse-coded dynamic mode decomposition (CSC-DMD) by unifying extended dynamic mode decomposition (EDMD) and convolutional sparse coding. EDMD is a data-driven method of analysis used to describe a nonlinear dynamical system with a linear time-evolution equation. Compared with existing EDMD methods, CSC-DMD has the advantage of reflecting the spatial structure of a target. As an example, the proposed method is applied to river bed shape estimation from the water surface observation. This estimation problem is reduced to sparsity aware signal restoration with a hard constraint given by the CSC-DMD prediction, where the algorithm is derived by the primal-dual splitting method. A time series set of water surface and bed shape measured through an experimental river setup is used to train and test the system. From the result, the efficacy of the proposed method is verified.

关键词： Extended dynamic mode decomposition convolutional sparse coding Primal-dual splitting NSOLT

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SPoD-Net: Fast Recovery of Microscopic Images Using Learned ISTA 11

SPoD-Net: Fast Recovery of Microscopic Images Using Learned ...

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11th Asian Conference on Machine Learning (ACML)

作者： Hara, Satoshi Chen, Weichih Washio, Takashi Wazawa, Tetsuichi Nagai, Takeharu Osaka Univ Osaka Japan Natl Taiwan Univ Taipei Taiwan

Recovering high quality images from microscopic observations is an essential technology in biological imaging. Existing recovery methods require solving an optimization problem by using iterative algorithms, which are computationally expensive and time consuming. The focus of this study is to accelerate the image recovery by using deep neural networks (DNNs). In our approach, we first train a certain type of DNN by using some observations from microscopes, so that it can well approximate the image recovery process. The recovery of a new observation is then computed thorough a single forward propagation in the trained DNN. In this study, we specifically focus on observations obtained by SPoD (Super-resolution by Polarization Demodulation), a recently developed microscopic technique, and accelerate the image recovery for SPoD by using DNNs. To this end, we propose SPoD-Net, a specifically tailored DNN for fast recovery of SPoD images. Unlike general DNNs, SPoD-Net can be parameterized using a small number of parameters, which is helpful in two ways: (i) it can be stored in a small memory, and (ii) it can be trained efficiently. We also propose a method to stabilize the training of SPoD-Net. In the experiments with the real SPoD observations, we confirmed the effectiveness of SPoD-Net over existing recovery methods. Specifically, we observed that SPoD-Net could recover images with more than a hundred times faster than the existing method.

关键词： sparse coding convolutional sparse coding learned iterative soft-thresholding algorithm deep neural network

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Improving FISTA's Speed of Convergence via a Novel Inertial Sequence 27

Improving FISTA's Speed of Convergence via a Novel Inertial ...

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27th European Signal Processing Conference (EUSIPCO)

作者： Rodriguez, Paul Pontificia Univ Catolica Peru Elect Dept Lima Peru

ISBN: (纸本)9789082797039

The FISTA (fast iterative shrinkage-thresholding algorithm) is a well-known and fast (theoretical O(k(-2)) rate of convergence) procedure for solving optimization problems composed by the sum of two convex functions, such that one is smooth (differentiable) and the other is possible nonsmooth. FISTA can be understood as a first order method with one important aspect: it uses a suitable extragradient rule, i.e.: the gradient is evaluated at a linear combination of the past two iterates, whose weights, are usually referred to as the inertial sequence. While problem dependent, it has a direct impact on the FISTA's practical computational performance. In this paper we propose a novel inertial sequence;when compared to well-established alternative choices, in the context of convolutional sparse coding and Wavelet-based inpainting, our proposed inertial sequence can reduce the number of FISTA's global iterations (and thus overall computational time) by 30% similar to 50% to attain the same level of reduction in the cost functional.

关键词： FISTA inertial sequence proximal gradient method convolutional sparse coding Wavelet-based inpainting

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Multilayer convolutional sparse Modeling: Pursuit and Dictionary Learning

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2018年第15期66卷 4090-4104页

作者： Sulam, Jeremias Papyan, Vardan Romano, Yaniv Elad, Michael Technion Israel Inst Technol Dept Comp Sci IL-3200003 Haifa Israel Stanford Univ Dept Stat Stanford CA 94305 USA

The recently proposed multilayer convolutional sparse coding (ML-CSC) model, consisting of a cascade of convolutional sparse layers, provides a new interpretation of convolutional neural networks (CNNs). Under this framework, the forward pass in a CNN is equivalent to a pursuit algorithm aiming to estimate the nested sparse representation vectors from a given input signal. Despite having served as a pivotal connection between CNNs and sparse modeling, a deeper understanding of the ML-CSC is still lacking. In this paper, we propose a sound pursuit algorithm for the ML-CSC model by adopting a projection approach. We provide new and improved bounds on the stability of the solution of such pursuit and we analyze different practical alternatives to implement this in practice. We show that the training of the filters is essential to allow for nontrivial signals in the model, and we derive an online algorithm to learn the dictionaries from real data, effectively resulting in cascaded sparse convolutional layers. Last, but not least, we demonstrate the applicability of the ML-CSC model for several applications in an unsupervised setting, providing competitive results. Our work represents a bridge between matrix factorization, sparse dictionary learning, and sparse autoencoders, and we analyze these connections in detail.

关键词： convolutional sparse coding multilayer pursuit convolutional neural networks dictionary learning sparse convolutional filters

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First- and Second-Order Methods for Online convolutional Dictionary Learning

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SIAM JOURNAL ON IMAGING SCIENCES 2018年第2期11卷 1589-1628页

作者： Liu, Jialin Garcia-Cardona, Cristina Wohlbereg, Brendt Yin, Wotao UCLA Dept Math Los Angeles CA 90095 USA Los Alamos Natl Lab CCS Div Los Alamos NM 87545 USA Los Alamos Natl Lab Theoret Div Los Alamos NM 87545 USA

convolutional sparse representations are a form of sparse representation with a structured, translation-invariant dictionary. Most convolutional dictionary learning algorithms to date operate in batch mode, requiring simultaneous access to all training images during the learning process, which results in very high memory usage and severely limits the training data size that can be used. Very recently, however, a number of authors have considered the design of online convolutional dictionary learning algorithms that offer far better scaling of memory and computational cost with training set size than batch methods. This paper extends our prior work, improving a number of aspects of our previous algorithm;proposing an entirely new one, with better performance, that supports the inclusion of a spatial mask for learning from incomplete data;and providing a rigorous theoretical analysis of these methods.

关键词： convolutional sparse coding convolutional dictionary learning online dictionary learning stochastic gradient descent recursive least squares

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convolutional Dictionary Learning: Acceleration and Convergence

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2018年第4期27卷 1697-1712页

作者： Chun, Il Yong Fessler, Jeffrey A. Univ Michigan Dept Elect Engn & Comp Sci Ann Arbor MI 48019 USA

convolutional dictionary learning (CDL or sparsifying CDL) has many applications in image processing and computer vision. There has been growing interest in developing efficient algorithms for CDL, mostly relying on the augmented Lagrangian (AL) method or the variant alternating direction method of multipliers (ADMM). When their parameters are properly tuned, AL methods have shown fast convergence in CDL. However, the parameter tuning process is not trivial due to its data dependence and, in practice, the convergence of AL methods depends on the AL parameters for nonconvex CDL problems. To moderate these problems, this paper proposes a new practically feasible and convergent Block Proximal Gradient method using a Majorizer (BPG-M) for CDL. The BPG-M-based CDL is investigated with different block updating schemes and majorization matrix designs, and further accelerated by incorporating some momentum coefficient formulas and restarting techniques. All of the methods investigated incorporate a boundary artifacts removal (or, more generally, sampling) operator in the learning model. Numerical experiments show that, without needing any parameter tuning process, the proposed BPG-M approach converges more stably to desirable solutions of lower objective values than the existing state-of-the-art ADMM algorithm and its memory-efficient variant do. Compared with the ADMM approaches, the BPG-M method using a multi-block updating scheme is particularly useful in single-threaded CDL algorithm handling large data sets, due to its lower memory requirement and no polynomial computational complexity. Image denoising experiments show that, for relatively strong additive white Gaussian noise, the filters learned by BPG-M-based CDL outperform those trained by the ADMM approach.

关键词： convolutional dictionary learning convolutional sparse coding block proximal gradient method majorization matrix design convergence guarantee

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EFFICIENT SEPARABLE FILTER ESTIMATION USING RANK-1 convolutional DICTIONARY LEARNING 28

EFFICIENT SEPARABLE FILTER ESTIMATION USING RANK-1 CONVOLUTI...

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IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP)

作者： Silva, Gustavo Quesada, Jorge Rodriguez, Paul Pontificia Univ Catolica Peru Elect Engn Dept Lima Peru

ISBN: (纸本)9781538654774

Natively learned separable filters for convolutional sparse coding (CSC) have recently been shown to provide equivalent reconstruction performance to their non-separable counterparts (as opposed to approximated separable filters), while reducing computational cost. Furthermore, multiple approaches to optimize the Dictionary Update stage of convolutional Dictionary Learning (CDL) methods based on the Accelerated Proximal Gradient (APG) framework have recently been proposed. In this paper, we propose a novel separable filter learning method based on the rank-1 decomposition, and test its performance against the existing separable approaches. In adittion, we evaluate how APG-based variations couple with our proposed method in order to improve computational runtime. Our results show that the filters learned through our proposed method match the performance of other natively-learned separable filters, while providing a significant runtime improvement in the learning process through our APG-based implementation.

关键词： Separable Filter learning convolutional sparse Representation convolutional sparse coding

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convolutional Gaussian Mixture Models with Application to Compressive Sensing 20

Convolutional Gaussian Mixture Models with Application to Co...

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IEEE Statistical Signal Processing Workshop (SSP)

作者： Wang, Ren Liao, Xuejun Guo, Jingbo Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China Duke Univ Dept Elect & Comp Engn Durham NC 27708 USA

ISBN: (纸本)9781538615713

Gaussian mixture models (GMM) have been used to statistically represent patches in an image. Extending from small patches to an entire image, we propose a convolutional Gaussian mixture models (convGMM) to model the statistics of an entire image and apply it for compressive sensing (CS). We present the algorithm details for learning a convGMM from training images by maximizing the marginal log-likelihood estimation (MMLE). The learned convGMM is used to perform model-based compressive sensing, using the convGMM as a model of the underlying image. In addition, a key feature of our method is that all of the training and reconstruction process could be fast and efficient calculated in the frequency-domain by 2-dimensional fast Fourier transforms (2d-FFTs). The performance of the convGMM on CS is demonstrated on several image sets.

关键词： Gaussian Mixture Models (GMM) Bayesian compressive sensing convolutional sparse coding expectation maximization (EM)

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SCALABLE convolutional DICTIONARY LEARNING WITH CONSTRAINED RECURRENT sparse AUTO-ENCODERS 28

SCALABLE CONVOLUTIONAL DICTIONARY LEARNING WITH CONSTRAINED ...

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IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP)

作者： Tolooshams, Bahareh Dey, Sourav Ba, Demba Harvard Univ Sch Engn & Appl Sci Cambridge MA 02138 USA Manifold AI Oakland CA USA

ISBN: (纸本)9781538654774

Given a convolutional dictionary underlying a set of observed signals, can a carefully designed auto-encoder recover the dictionary in the presence of noise? We introduce an auto-encoder architecture, termed constrained recurrent sparse auto-encoder (CRsAE), that answers this question in the affirmative. Given an input signal and an approximate dictionary, the encoder finds a sparse approximation using FISTA. The decoder reconstructs the signal by applying the dictionary to the output of the encoder. The encoder and decoder in CRsAE parallel the sparse-coding and dictionary update steps in optimization-based alternating-minimization schemes for dictionary learning. As such, the parameters of the encoder and decoder are not independent, a constraint which we enforce for the first time. We derive the back-propagation algorithm for CRsAE. CRsAE is a framework for blind source separation that, only knowing the number of sources (dictionary elements), and assuming sparsely-many can overlap, is able to separate them. We demonstrate its utility in the context of spike sorting, a source separation problem in computational neuroscience. We demonstrate the ability of CRsAE to recover the underlying dictionary and characterize its sensitivity as a function of SNR.

关键词： Dictionary Learning convolutional sparse coding Auto-encoders Source Separation Spike Sorting

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convolutional sparse REPRESENTATIONS WITH GRADIENT PENALTIES

CONVOLUTIONAL SPARSE REPRESENTATIONS WITH GRADIENT PENALTIES

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IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Wohlberg, Brendt Los Alamos Natl Lab Div Theoret Los Alamos NM 87545 USA

ISBN: (纸本)9781538646588

While convolutional sparse representations enjoy a number of useful properties, they have received limited attention for image reconstruction problems. The present paper compares the performance of block-based and convolutional sparse representations in the removal of Gaussian white noise. The usual formulation of the convolutional sparse coding problem is slightly inferior to the block-based representations in this problem, but the performance of the convolutional form can be boosted beyond that of the block-based form by the inclusion of suitable penalties on the gradients of the coefficient maps.

关键词： convolutional sparse Representations convolutional sparse coding Total Variation

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