Dictionary learning for sparsity-driven sar image reconstruction

We consider the problem of synthetic aperture radar (SAR) image formation, where the underlying scene is to be reconstructed from undersampled observed data. Sparsity-based methods for SAR imaging have employed overcomplete dictionaries to represent the magnitude of the complex-valued field sparsely. Selection of an appropriate dictionary with respect to the features of the particular type of underlying scene plays an important role in these methods. In this paper, we develop a new reconstruction method that is based on learning sparsifying dictionaries and using such learned dictionaries in the reconstruction process. Adaptive dictionaries learned from data have the potential to represent the magnitude of complex-valued field more effectively and hence have the potential to widen the applicability of sparsity-based radar imaging. We demonstrate the performance of the proposed method on both synthetic and real SAR images

Sonar Image Speckle Reduction Algorithm Base on Redundant Dictionary

由于水下环境的特殊性，水质对于声波的吸收、散射及混响等因素的存在严重影响了声纳成像效果，尤其是后向散射效应、混响等使得声纳图像中存在强烈的噪声，严重降低了声纳图像的质量，从而给后续的图像处理和应用带来了诸多不利的影响。因此，如何构建出针对水下图像特点的去噪处理算法具有重大的意义。 论文首先分析总结了声纳图像成像影响因素和成像特点，与传统的光学图像相比，声纳图像具有斑点噪声严重、分辨率低、边缘模糊、对比度低等特点。并在其成像机理的基础上得到其斑点噪声的统计分布模型，建立斑点噪声图像的乘性瑞利模型。 然后，根据声纳图像的特点，尝试将基于K-SVD字典学习的去噪方法应用到声纳图像斑点噪声的去除中...Due to the particularity of underwater environment, sonar imaging quality is seriously affected by the absorption, scattering and reverberation, especially the backward scattering and reverberation that make strong noise, seriously degrading the quality of the sonar image, which makes it difficulty to the subsequent image processing and applications. Therefore, how to construct de-noising algorith...学位：工学硕士院系专业：信息科学与技术学院_通信与信息系统学号：2332013115322

Dictionary learning and low-rank sparse matrix decomposition for sparsity driven SAR image reconstruction

Synthetic aperture radar (SAR) is one of the most widely used remote sensing modalities, providing images for a variety of applications including those in defense, environmental science, and weather forecasting. However, conventionally formed SAR imagery from undersampled observed data, arising in several emerging applications and sensing scenarios, suffers from artifacts that might limit effective use of such imagery in remote sensing applications. Recently, sparsity-driven SAR imaging has emerged as an e ective framework to alleviate such problems. Sparsity-based methods for SAR imaging have employed overcomplete dictionaries to represent the magnitude of the complex-valued eld sparsely. Selection of an appropriate dictionary with respect to the features of the particular type of underlying scene plays an important role in these methods. In this thesis, we develop two new sparsity-driven SAR imaging methods that significantly expand the domain of applicability of sparsity-based methods in SAR imaging. Our first contribution involves the development of a new reconstruction method that is based on learning sparsifying dictionaries and using such learned dictionaries in the reconstruction process. Adaptive dictionaries learned from data can represent the magnitude of complex-valued field more effectively and hence have the potential to widen the applicability of sparsity-based radar imaging. Our framework allows the use of both adaptive dictionaries learned offline from a training set and those learned online from the undersampled data used in image formation. We demonstrate the effectiveness of the proposed dictionary learning-based SAR imaging approach as well as the improvements it provides, on both synthetic and real data. The second contribution of this thesis involves the development of a reconstruction method that decomposes the imaged field into a sparse and a low-rank component. Such a decomposition is of interest in image analysis tasks such as segmentation and background subtraction. Conventionally, such operations are performed after SAR image formation. We exploit recent work on sparse and low-rank decomposition of matrices and incorporate such a decomposition into the process of SAR image formation. The outcome is a method that jointly reconstructs a SAR image and decomposes the formed image into its low-rank background and spatially sparse components. We demonstrate the effectiveness of the proposed method on both synthetic and real SAR images

Sparse and Redundant Representations for Inverse Problems and Recognition

Sparse and redundant representation of data enables the description of signals as linear combinations of a few atoms from a dictionary. In this dissertation, we study applications of sparse and redundant representations in inverse problems and object recognition. Furthermore, we propose two novel imaging modalities based on the recently introduced theory of Compressed Sensing (CS). This dissertation consists of four major parts. In the first part of the dissertation, we study a new type of deconvolution algorithm that is based on estimating the image from a shearlet decomposition. Shearlets provide a multi-directional and multi-scale decomposition that has been mathematically shown to represent distributed discontinuities such as edges better than traditional wavelets. We develop a deconvolution algorithm that allows for the approximation inversion operator to be controlled on a multi-scale and multi-directional basis. Furthermore, we develop a method for the automatic determination of the threshold values for the noise shrinkage for each scale and direction without explicit knowledge of the noise variance using a generalized cross validation method. In the second part of the dissertation, we study a reconstruction method that recovers highly undersampled images assumed to have a sparse representation in a gradient domain by using partial measurement samples that are collected in the Fourier domain. Our method makes use of a robust generalized Poisson solver that greatly aids in achieving a significantly improved performance over similar proposed methods. We will demonstrate by experiments that this new technique is more flexible to work with either random or restricted sampling scenarios better than its competitors. In the third part of the dissertation, we introduce a novel Synthetic Aperture Radar (SAR) imaging modality which can provide a high resolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms. We demonstrate that this new imaging scheme, requires no new hardware components and allows the aperture to be compressed. Also, it presents many new applications and advantages which include strong resistance to countermesasures and interception, imaging much wider swaths and reduced on-board storage requirements. The last part of the dissertation deals with object recognition based on learning dictionaries for simultaneous sparse signal approximations and feature extraction. A dictionary is learned for each object class based on given training examples which minimize the representation error with a sparseness constraint. A novel test image is then projected onto the span of the atoms in each learned dictionary. The residual vectors along with the coefficients are then used for recognition. Applications to illumination robust face recognition and automatic target recognition are presented

Applied Harmonic Analysis and Sparse Approximation

Efficiently analyzing functions, in particular multivariate functions, is a key problem in applied mathematics. The area of applied harmonic analysis has a significant impact on this problem by providing methodologies both for theoretical questions and for a wide range of applications in technology and science, such as image processing. Approximation theory, in particular the branch of the theory of sparse approximations, is closely intertwined with this area with a lot of recent exciting developments in the intersection of both. Research topics typically also involve related areas such as convex optimization, probability theory, and Banach space geometry. The workshop was the continuation of a first event in 2012 and intended to bring together world leading experts in these areas, to report on recent developments, and to foster new developments and collaborations

Kernelized Supervised Dictionary Learning

The representation of a signal using a learned dictionary instead of predefined operators, such as wavelets, has led to state-of-the-art results in various applications such as denoising, texture analysis, and face recognition. The area of dictionary learning is closely associated with sparse representation, which means that the signal is represented using few atoms in the dictionary. Despite recent advances in the computation of a dictionary using fast algorithms such as K-SVD, online learning, and cyclic coordinate descent, which make the computation of a dictionary from millions of data samples computationally feasible, the dictionary is mainly computed using unsupervised approaches such as k-means. These approaches learn the dictionary by minimizing the reconstruction error without taking into account the category information, which is not optimal in classification tasks. In this thesis, we propose a supervised dictionary learning (SDL) approach by incorporating information on class labels into the learning of the dictionary. To this end, we propose to learn the dictionary in a space where the dependency between the signals and their corresponding labels is maximized. To maximize this dependency, the recently-introduced Hilbert Schmidt independence criterion (HSIC) is used. The learned dictionary is compact and has closed form; the proposed approach is fast. We show that it outperforms other unsupervised and supervised dictionary learning approaches in the literature on real-world data. Moreover, the proposed SDL approach has as its main advantage that it can be easily kernelized, particularly by incorporating a data-driven kernel such as a compression-based kernel, into the formulation. In this thesis, we propose a novel compression-based (dis)similarity measure. The proposed measure utilizes a 2D MPEG-1 encoder, which takes into consideration the spatial locality and connectivity of pixels in the images. The proposed formulation has been carefully designed based on MPEG encoder functionality. To this end, by design, it solely uses P-frame coding to find the (dis)similarity among patches/images. We show that the proposed measure works properly on both small and large patch sizes on textures. Experimental results show that by incorporating the proposed measure as a kernel into our SDL, it significantly improves the performance of a supervised pixel-based texture classification on Brodatz and outdoor images compared to other compression-based dissimilarity measures, as well as state-of-the-art SDL methods. It also improves the computation speed by about 40% compared to its closest rival. Eventually, we have extended the proposed SDL to multiview learning, where more than one representation is available on a dataset. We propose two different multiview approaches: one fusing the feature sets in the original space and then learning the dictionary and sparse coefficients on the fused set; and the other by learning one dictionary and the corresponding coefficients in each view separately, and then fusing the representations in the space of the dictionaries learned. We will show that the proposed multiview approaches benefit from the complementary information in multiple views, and investigate the relative performance of these approaches in the application of emotion recognition