Sparse Representation Based Classification for Face Recognition by k-LiMapS Algorithm

In this paper, we present a new approach for face recognition that is robust against both poorly defined and poorly aligned training and testing data even with few training samples. Working in the conventional feature space yielded by the Fisher\u2019s Linear Discriminant analysis, it uses a recent algorithm for sparse representation, namely k -LiMapS, as general classification criterion. Such a technique performs a local \u21130 pseudo-norm minimization by iterating suitable parametric nonlinear mappings. Thanks to its particular search strategy, it is very fast and able to discriminate among separated classes lying in the low-dimension Fisherspace. Experiments are carried out on the FRGC version 2.0 database showing good classification capability even when compared with the state-of-the-art \u21131 norm-based sparse representation classifier (SRC)

Forward Primal-Dual Half-Forward Algorithm for Splitting Four Operators

In this article, we propose a splitting algorithm to find zeros of the sum of four maximally monotone operators in real Hilbert spaces. In particular, we consider a Lipschitzian operator, a cocoercive operator, and a linear composite term. In the case when the Lipschitzian operator is absent, our method reduces to the Condat-V\~u algorithm. On the other hand, when the linear composite term is absent, the algorithm reduces to the Forward-Backward-Half-Forward algorithm (FBHF). Additionally, in each case, the set of step-sizes that guarantee the weak convergence of those methods are recovered. Therefore, our algorithm can be seen as a generalization of Condat-V\~u and FBHF. Moreover, we propose extensions and applications of our method in multivariate monotone inclusions and saddle point problems. Finally, we present a numerical experiment in image deblurring problems

The Geometry of Monotone Operator Splitting Methods

We propose a geometric framework to describe and analyze a wide array of operator splitting methods for solving monotone inclusion problems. The initial inclusion problem, which typically involves several operators combined through monotonicity-preserving operations, is seldom solvable in its original form. We embed it in an auxiliary space, where it is associated with a surrogate monotone inclusion problem with a more tractable structure and which allows for easy recovery of solutions to the initial problem. The surrogate problem is solved by successive projections onto half-spaces containing its solution set. The outer approximation half-spaces are constructed by using the individual operators present in the model separately. This geometric framework is shown to encompass traditional methods as well as state-of-the-art asynchronous block-iterative algorithms, and its flexible structure provides a pattern to design new ones

Orthogonal procrustes analysis for dictionary learning in sparse linear representation

In the sparse representation model, the design of overcomplete dictionaries plays a key role for the effectiveness and applicability in different domains. Recent research has produced several dictionary learning approaches, being proven that dictionaries learnt by data examples significantly outperform structured ones, e.g. wavelet transforms. In this context, learning consists in adapting the dictionary atoms to a set of training signals in order to promote a sparse representation that minimizes the reconstruction error. Finding the best fitting dictionary remains a very difficult task, leaving the question still open. A well-established heuristic method for tackling this problem is an iterative alternating scheme, adopted for instance in the well-known K-SVD algorithm. Essentially, it consists in repeating two stages; the former promotes sparse coding of the training set and the latter adapts the dictionary to reduce the error. In this paper we present R-SVD, a new method that, while maintaining the alternating scheme, adopts the Orthogonal Procrustes analysis to update the dictionary atoms suitably arranged into groups. Comparative experiments on synthetic data prove the effectiveness of R-SVD with respect to well known dictionary learning algorithms such as K-SVD, ILS-DLA and the online method OSDL. Moreover, experiments on natural data such as ECG compression, EEG sparse representation, and image modeling confirm R-SVD's robustness and wide applicability

Robust single-sample face recognition by sparsity-driven sub-dictionary learning using deep features

Face recognition using a single reference image per subject is challenging, above all when referring to a large gallery of subjects. Furthermore, the problem hardness seriously increases when the images are acquired in unconstrained conditions. In this paper we address the challenging Single Sample Per Person (SSPP) problem considering large datasets of images acquired in the wild, thus possibly featuring illumination, pose, face expression, partial occlusions, and low-resolution hurdles. The proposed technique alternates a sparse dictionary learning technique based on the method of optimal direction and the iterative \u2113 0 -norm minimization algorithm called k-LIMAPS. It works on robust deep-learned features, provided that the image variability is extended by standard augmentation techniques. Experiments show the effectiveness of our method against the hardness introduced above: first, we report extensive experiments on the unconstrained LFW dataset when referring to large galleries up to 1680 subjects; second, we present experiments on very low-resolution test images up to 8 7 8 pixels; third, tests on the AR dataset are analyzed against specific disguises such as partial occlusions, facial expressions, and illumination problems. In all the three scenarios our method outperforms the state-of-the-art approaches adopting similar configurations

High-rate compression of ECG signals by an accuracy-driven sparsity model relying on natural basis

Long duration recordings of ECG signals require high compression ratios, in particular when storing on portable devices. Most of the ECG compression methods in literature are based on wavelet transform while only few of them rely on sparsity promotion models. In this paper we propose a novel ECG signal compression framework based on sparse representation using a set of ECG segments as natural basis. This approach exploits the signal regularity, i.e. the repetition of common patterns, in order to achieve high compression ratio (CR). We apply k-LiMapS as fine-tuned sparsity solver algorithm guaranteeing the required signal reconstruction quality PRDN (Normalized Percentage Root-mean-square Difference). Extensive experiments have been conducted on all the 48 records of MIT-BIH Arrhythmia Database and on some 24 hour records from the Long-Term ST Database. Direct comparisons of our method with several state-of-the-art ECG compression methods (namely ARLE, Rajoub's, SPIHT, TRE) prove its effectiveness. Our method achieves average performances that are two-three times higher than those obtained by the other assessed methods. In particular the compression ratio gap between our method and the others increases with growing PRDN

Data driven regularization models of non-linear ill-posed inverse problems in imaging

Imaging technologies are widely used in application fields such as natural sciences, engineering, medicine, and life sciences. A broad class of imaging problems reduces to solve ill-posed inverse problems (IPs). Traditional strategies to solve these ill-posed IPs rely on variational regularization methods, which are based on minimization of suitable energies, and make use of knowledge about the image formation model (forward operator) and prior knowledge on the solution, but lack in incorporating knowledge directly from data. On the other hand, the more recent learned approaches can easily learn the intricate statistics of images depending on a large set of data, but do not have a systematic method for incorporating prior knowledge about the image formation model. The main purpose of this thesis is to discuss data-driven image reconstruction methods which combine the benefits of these two different reconstruction strategies for the solution of highly nonlinear ill-posed inverse problems. Mathematical formulation and numerical approaches for image IPs, including linear as well as strongly nonlinear problems are described. More specifically we address the Electrical impedance Tomography (EIT) reconstruction problem by unrolling the regularized Gauss-Newton method and integrating the regularization learned by a data-adaptive neural network. Furthermore we investigate the solution of non-linear ill-posed IPs introducing a deep-PnP framework that integrates the graph convolutional denoiser into the proximal Gauss-Newton method with a practical application to the EIT, a recently introduced promising imaging technique. Efficient algorithms are then applied to the solution of the limited electrods problem in EIT, combining compressive sensing techniques and deep learning strategies. Finally, a transformer-based neural network architecture is adapted to restore the noisy solution of the Computed Tomography problem recovered using the filtered back-projection method

Generating and auto-tuning parallel stencil codes

In this thesis, we present a software framework, Patus, which generates high performance stencil codes for different types of hardware platforms, including current multicore CPU and graphics processing unit architectures. The ultimate goals of the framework are productivity, portability (of both the code and performance), and achieving a high performance on the target platform. A stencil computation updates every grid point in a structured grid based on the values of its neighboring points. This class of computations occurs frequently in scientific and general purpose computing (e.g., in partial differential equation solvers or in image processing), justifying the focus on this kind of computation. The proposed key ingredients to achieve the goals of productivity, portability, and performance are domain specific languages (DSLs) and the auto-tuning methodology. The Patus stencil specification DSL allows the programmer to express a stencil computation in a concise way independently of hardware architecture-specific details. Thus, it increases the programmer productivity by disburdening her or him of low level programming model issues and of manually applying hardware platform-specific code optimization techniques. The use of domain specific languages also implies code reusability: once implemented, the same stencil specification can be reused on different hardware platforms, i.e., the specification code is portable across hardware architectures. Constructing the language to be geared towards a special purpose makes it amenable to more aggressive optimizations and therefore to potentially higher performance. Auto-tuning provides performance and performance portability by automated adaptation of implementation-specific parameters to the characteristics of the hardware on which the code will run. By automating the process of parameter tuning — which essentially amounts to solving an integer programming problem in which the objective function is the number representing the code's performance as a function of the parameter configuration, — the system can also be used more productively than if the programmer had to fine-tune the code manually. We show performance results for a variety of stencils, for which Patus was used to generate the corresponding implementations. The selection includes stencils taken from two real-world applications: a simulation of the temperature within the human body during hyperthermia cancer treatment and a seismic application. These examples demonstrate the framework's flexibility and ability to produce high performance code