Application and Theory of Multimedia Signal Processing Using Machine Learning or Advanced Methods

This Special Issue is a book composed by collecting documents published through peer review on the research of various advanced technologies related to applications and theories of signal processing for multimedia systems using ML or advanced methods. Multimedia signals include image, video, audio, character recognition and optimization of communication channels for networks. The specific contents included in this book are data hiding, encryption, object detection, image classification, and character recognition. Academics and colleagues who are interested in these topics will find it interesting to read

Acceleration Methods for MRI

Acceleration methods are a critical area of research for MRI. Two of the most important acceleration techniques involve parallel imaging and compressed sensing. These advanced signal processing techniques have the potential to drastically reduce scan times and provide radiologists with new information for diagnosing disease. However, many of these new techniques require solving difficult optimization problems, which motivates the development of more advanced algorithms to solve them. In addition, acceleration methods have not reached maturity in some applications, which motivates the development of new models tailored to these applications. This dissertation makes advances in three different areas of accelerations. The first is the development of a new algorithm (called B1-Based, Adaptive Restart, Iterative Soft Thresholding Algorithm or BARISTA), that solves a parallel MRI optimization problem with compressed sensing assumptions. BARISTA is shown to be 2-3 times faster and more robust to parameter selection than current state-of-the-art variable splitting methods. The second contribution is the extension of BARISTA ideas to non-Cartesian trajectories that also leads to a 2-3 times acceleration over previous methods. The third contribution is the development of a new model for functional MRI that enables a 3-4 factor of acceleration of effective temporal resolution in functional MRI scans. Several variations of the new model are proposed, with an ROC curve analysis showing that a combination low-rank/sparsity model giving the best performance in identifying the resting-state motor network.PhDBiomedical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120841/1/mmuckley_1.pd

Compressed Sensing in Resource-Constrained Environments: From Sensing Mechanism Design to Recovery Algorithms

Compressed Sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for reconstruction. It is promising that CS can be utilized in environments where the signal acquisition process is extremely difficult or costly, e.g., a resource-constrained environment like the smartphone platform, or a band-limited environment like visual sensor network (VSNs). There are several challenges to perform sensing due to the characteristic of these platforms, including, for example, needing active user involvement, computational and storage limitations and lower transmission capabilities. This dissertation focuses on the study of CS in resource-constrained environments. First, we try to solve the problem on how to design sensing mechanisms that could better adapt to the resource-limited smartphone platform. We propose the compressed phone sensing (CPS) framework where two challenging issues are studied, the energy drainage issue due to continuous sensing which may impede the normal functionality of the smartphones and the requirement of active user inputs for data collection that may place a high burden on the user. Second, we propose a CS reconstruction algorithm to be used in VSNs for recovery of frames/images. An efficient algorithm, NonLocal Douglas-Rachford (NLDR), is developed. NLDR takes advantage of self-similarity in images using nonlocal means (NL) filtering. We further formulate the nonlocal estimation as the low-rank matrix approximation problem and solve the constrained optimization problem using Douglas-Rachford splitting method. Third, we extend the NLDR algorithm to surveillance video processing in VSNs and propose recursive Low-rank and Sparse estimation through Douglas-Rachford splitting (rLSDR) method for recovery of the video frame into a low-rank background component and sparse component that corresponds to the moving object. The spatial and temporal low-rank features of the video frame, e.g., the nonlocal similar patches within the single video frame and the low-rank background component residing in multiple frames, are successfully exploited

Approximating Spectral Clustering via Sampling: a Review

International audienceSpectral clustering refers to a family of well-known unsupervised learning algorithms. Rather than attempting to cluster points in their native domain, one constructs a (usually sparse) similarity graph and computes the principal eigenvec-tors of its Laplacian. The eigenvectors are then interpreted as transformed points and fed into a k-means clustering algorithm. As a result of this non-linear transformation , it becomes possible to use a simple centroid-based algorithm in order to identify non-convex clusters, something that was otherwise impossible. Unfortunately , what makes spectral clustering so successful is also its Achilles heel: forming a graph and computing its dominant eigenvectors can be computationally prohibitive when dealing with more that a few tens of thousands of points. In this chapter, we review the principal research efforts aiming to reduce this computational cost. We focus on methods that come with a theoretical control on the clustering performance and incorporate some form of sampling in their operation. Such methods abound in the machine learning, numerical linear algebra, and graph signal processing literature and, amongst others, include Nyström-approximation, landmarks, coarsening, coresets, and compressive spectral clustering. We present the approximation guarantees available for each and discuss practical merits and limitations. Surprisingly, despite the breadth of the literature explored, we conclude that there is still a gap between theory and practice: the most scalable methods are only intuitively motivated or loosely controlled, whereas those that come with end-to-end guarantees rely on strong assumptions or enable a limited gain of computation time

Approximating Spectral Clustering via Sampling: a Review

Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of these algorithms' success and their Achilles heel: forming a graph and computing its dominant eigenvectors can indeed be computationally prohibitive when dealing with more that a few tens of thousands of points. In this paper, we review the principal research efforts aiming to reduce this computational cost. We focus on methods that come with a theoretical control on the clustering performance and incorporate some form of sampling in their operation. Such methods abound in the machine learning, numerical linear algebra, and graph signal processing literature and, amongst others, include Nystr\"om-approximation, landmarks, coarsening, coresets, and compressive spectral clustering. We present the approximation guarantees available for each and discuss practical merits and limitations. Surprisingly, despite the breadth of the literature explored, we conclude that there is still a gap between theory and practice: the most scalable methods are only intuitively motivated or loosely controlled, whereas those that come with end-to-end guarantees rely on strong assumptions or enable a limited gain of computation time

Sparse models for positive definite matrices

University of Minnesota Ph.D. dissertation. Febrauary 2015. Major: Electrical Engineering. Advisor: Nikolaos P. Papanikolopoulos. 1 computer file (PDF); ix, 141 pages.Sparse models have proven to be extremely successful in image processing, computer vision and machine learning. However, a majority of the effort has been focused on vector-valued signals. Higher-order signals like matrices are usually vectorized as a pre-processing step, and treated like vectors thereafter for sparse modeling. Symmetric positive definite (SPD) matrices arise in probability and statistics and the many domains built upon them. In computer vision, a certain type of feature descriptor called the region covariance descriptor, used to characterize an object or image region, belongs to this class of matrices. Region covariances are immensely popular in object detection, tracking, and classification. Human detection and recognition, texture classification, face recognition, and action recognition are some of the problems tackled using this powerful class of descriptors. They have also caught on as useful features for speech processing and recognition.Due to the popularity of sparse modeling in the vector domain, it is enticing to apply sparse representation techniques to SPD matrices as well. However, SPD matrices cannot be directly vectorized for sparse modeling, since their implicit structure is lost in the process, and the resulting vectors do not adhere to the positive definite manifold geometry. Therefore, to extend the benefits of sparse modeling to the space of positive definite matrices, we must develop dedicated sparse algorithms that respect the positive definite structure and the geometry of the manifold. The primary goal of this thesis is to develop sparse modeling techniques for symmetric positive definite matrices. First, we propose a novel sparse coding technique for representing SPD matrices using sparse linear combinations of a dictionary of atomic SPD matrices. Next, we present a dictionary learning approach wherein these atoms are themselves learned from the given data, in a task-driven manner. The sparse coding and dictionary learning approaches are then specialized to the case of rank-1 positive semi-definite matrices. A discriminative dictionary learning approach from vector sparse modeling is extended to the scenario of positive definite dictionaries. We present efficient algorithms and implementations, with practical applications in image processing and computer vision for the proposed techniques

Let's Make Block Coordinate Descent Go Fast: Faster Greedy Rules, Message-Passing, Active-Set Complexity, and Superlinear Convergence

Block coordinate descent (BCD) methods are widely-used for large-scale numerical optimization because of their cheap iteration costs, low memory requirements, amenability to parallelization, and ability to exploit problem structure. Three main algorithmic choices influence the performance of BCD methods: the block partitioning strategy, the block selection rule, and the block update rule. In this paper we explore all three of these building blocks and propose variations for each that can lead to significantly faster BCD methods. We (i) propose new greedy block-selection strategies that guarantee more progress per iteration than the Gauss-Southwell rule; (ii) explore practical issues like how to implement the new rules when using "variable" blocks; (iii) explore the use of message-passing to compute matrix or Newton updates efficiently on huge blocks for problems with a sparse dependency between variables; and (iv) consider optimal active manifold identification, which leads to bounds on the "active set complexity" of BCD methods and leads to superlinear convergence for certain problems with sparse solutions (and in some cases finite termination at an optimal solution). We support all of our findings with numerical results for the classic machine learning problems of least squares, logistic regression, multi-class logistic regression, label propagation, and L1-regularization