MAGMA: Multi-level accelerated gradient mirror descent algorithm for large-scale convex composite minimization

Composite convex optimization models arise in several applications, and are especially prevalent in inverse problems with a sparsity inducing norm and in general convex optimization with simple constraints. The most widely used algorithms for convex composite models are accelerated first order methods, however they can take a large number of iterations to compute an acceptable solution for large-scale problems. In this paper we propose to speed up first order methods by taking advantage of the structure present in many applications and in image processing in particular. Our method is based on multi-level optimization methods and exploits the fact that many applications that give rise to large scale models can be modelled using varying degrees of fidelity. We use Nesterov's acceleration techniques together with the multi-level approach to achieve $\mathcal{O}(1/\sqrt{\epsilon})$ convergence rate, where $\epsilon$ denotes the desired accuracy. The proposed method has a better convergence rate than any other existing multi-level method for convex problems, and in addition has the same rate as accelerated methods, which is known to be optimal for first-order methods. Moreover, as our numerical experiments show, on large-scale face recognition problems our algorithm is several times faster than the state of the art

Single and multiple object tracking using a multi-feature joint sparse representation

In this paper, we propose a tracking algorithm based on a multi-feature joint sparse representation. The templates for the sparse representation can include pixel values, textures, and edges. In the multi-feature joint optimization, noise or occlusion is dealt with using a set of trivial templates. A sparse weight constraint is introduced to dynamically select the relevant templates from the full set of templates. A variance ratio measure is adopted to adaptively adjust the weights of different features. The multi-feature template set is updated adaptively. We further propose an algorithm for tracking multi-objects with occlusion handling based on the multi-feature joint sparse reconstruction. The observation model based on sparse reconstruction automatically focuses on the visible parts of an occluded object by using the information in the trivial templates. The multi-object tracking is simplified into a joint Bayesian inference. The experimental results show the superiority of our algorithm over several state-of-the-art tracking algorithms

Sparse variational regularization for visual motion estimation

The computation of visual motion is a key component in numerous computer vision tasks such as object detection, visual object tracking and activity recognition. Despite exten- sive research effort, efficient handling of motion discontinuities, occlusions and illumina- tion changes still remains elusive in visual motion estimation. The work presented in this thesis utilizes variational methods to handle the aforementioned problems because these methods allow the integration of various mathematical concepts into a single en- ergy minimization framework. This thesis applies the concepts from signal sparsity to the variational regularization for visual motion estimation. The regularization is designed in such a way that it handles motion discontinuities and can detect object occlusions

Sparse motion bases selection for human motion denoising

Human motion denoising is an indispensable step of data preprocessing for many motion data based applications. In this paper, we propose a data-driven based human motion denoising method that sparsely selects the most correlated subset of motion bases for clean motion reconstruction. Meanwhile, it takes the statistic property of two common noises, i.e., Gaussian noise and outliers, into account in deriving the objective functions. In particular, our method firstly divides each human pose into five partitions termed as poselets to gain a much fine-grained pose representation. Then, these poselets are reorganized into multiple overlapped poselet groups using a lagged window moving across the entire motion sequence to preserve the embedded spatial 13temporal motion patterns. Afterward, five compacted and representative motion dictionaries are constructed in parallel by means of fast K-SVD in the training phase; they are used to remove the noise and outliers from noisy motion sequences in the testing phase by solving !131-minimization problems. Extensive experiments show that our method outperforms its competitors. More importantly, compared with other data-driven based method, our method does not need to specifically choose the training data, it can be more easily applied to real-world applications

Dimensionality reduction and sparse representations in computer vision

The proliferation of camera equipped devices, such as netbooks, smartphones and game stations, has led to a significant increase in the production of visual content. This visual information could be used for understanding the environment and offering a natural interface between the users and their surroundings. However, the massive amounts of data and the high computational cost associated with them, encumbers the transfer of sophisticated vision algorithms to real life systems, especially ones that exhibit resource limitations such as restrictions in available memory, processing power and bandwidth. One approach for tackling these issues is to generate compact and descriptive representations of image data by exploiting inherent redundancies. We propose the investigation of dimensionality reduction and sparse representations in order to accomplish this task. In dimensionality reduction, the aim is to reduce the dimensions of the space where image data reside in order to allow resource constrained systems to handle them and, ideally, provide a more insightful description. This goal is achieved by exploiting the inherent redundancies that many classes of images, such as faces under different illumination conditions and objects from different viewpoints, exhibit. We explore the description of natural images by low dimensional non-linear models called image manifolds and investigate the performance of computer vision tasks such as recognition and classification using these low dimensional models. In addition to dimensionality reduction, we study a novel approach in representing images as a sparse linear combination of dictionary examples. We investigate how sparse image representations can be used for a variety of tasks including low level image modeling and higher level semantic information extraction. Using tools from dimensionality reduction and sparse representation, we propose the application of these methods in three hierarchical image layers, namely low-level features, mid-level structures and high-level attributes. Low level features are image descriptors that can be extracted directly from the raw image pixels and include pixel intensities, histograms, and gradients. In the first part of this work, we explore how various techniques in dimensionality reduction, ranging from traditional image compression to the recently proposed Random Projections method, affect the performance of computer vision algorithms such as face detection and face recognition. In addition, we discuss a method that is able to increase the spatial resolution of a single image, without using any training examples, according to the sparse representations framework. In the second part, we explore mid-level structures, including image manifolds and sparse models, produced by abstracting information from low-level features and offer compact modeling of high dimensional data. We propose novel techniques for generating more descriptive image representations and investigate their application in face recognition and object tracking. In the third part of this work, we propose the investigation of a novel framework for representing the semantic contents of images. This framework employs high level semantic attributes that aim to bridge the gap between the visual information of an image and its textual description by utilizing low level features and mid level structures. This innovative paradigm offers revolutionary possibilities including recognizing the category of an object from purely textual information without providing any explicit visual example