Representation Learning via Cauchy Convolutional Sparse Coding

In representation learning, Convolutional Sparse Coding (CSC) enables unsupervised learning of features by jointly optimising both an $\ell_2$-norm fidelity term and a sparsity enforcing penalty. This work investigates using a regularisation term derived from an assumed Cauchy prior for the coefficients of the feature maps of a CSC generative model. The sparsity penalty term resulting from this prior is solved via its proximal operator, which is then applied iteratively, element-wise, on the coefficients of the feature maps to optimise the CSC cost function. The performance of the proposed Iterative Cauchy Thresholding (ICT) algorithm in reconstructing natural images is compared against the common choice of $\ell_1$-norm optimised via soft and hard thresholding. ICT outperforms IHT and IST in most of these reconstruction experiments across various datasets, with an average PSNR of up to 11.30 and 7.04 above ISTA and IHT respectively.Comment: 19 pages, 9 figures, journal draf

Representation Learning via Cauchy Convolutional Sparse Coding

In representation learning, Convolutional Sparse Coding (CSC) enables unsupervised learning of features by jointly optimising both an $\ell_2$-norm fidelity term and a sparsity enforcing penalty. This work investigates using a regularisation term derived from an assumed Cauchy prior for the coefficients of the feature maps of a CSC generative model. The sparsity penalty term resulting from this prior is solved via its proximal operator, which is then applied iteratively, element-wise, on the coefficients of the feature maps to optimise the CSC cost function. The performance of the proposed Iterative Cauchy Thresholding (ICT) algorithm in reconstructing natural images is compared against the common choice of $\ell_1$-norm optimised via soft and hard thresholding. ICT outperforms IHT and IST in most of these reconstruction experiments across various datasets, with an average PSNR of up to 11.30 and 7.04 above ISTA and IHT respectively.Comment: 19 pages, 9 figures, journal draf

Clasificación Automática para Animales en Peligro de Extinción de Colombia Usando Redes Neuronales Convolucionales

The extinction of different types of animals is a problem that has been growing over the years, and that, consequently, has caused environmental problems, such as climate change. Genetic diversity (biodiversity) is essential for the development of all species and human beings depend on it in their daily lives. When biodiversity decreases, human life expectancy is reduced, not only from an ecological point of view, but also from a resource point of view, even to be able to have species that are adapted to an ecological niche. This research will expose a computer strategy that over time has achieved great results; convolutional neural networks is a process that has facilitated the monitoring of different kinds of animals in recent years, this, in order to facilitate the process of recognition and counting of animals, focused on agriculture and zoology. For this, an architecture in the field of convolutional neural networks (CNN) will be used, Alexnet, which has references with very high results. In addition, the mathematical programming software Matlab is used for the development of the neural network. Getting of this way a result of accuracy of validation of 97,52%, with the use of a dataset with 3026 images, in where, 80% are used for training and 20% for validation.La extinción de distintos tipos de animales es un problema que ha ido creciendo a lo largo de los años y que, en consecuencia, ha provocado problemas medioambientales, como el cambio climático. La diversidad genética (biodiversidad) es esencial para el desarrollo de todas las especies y los seres humanos dependen de ella en su vida cotidiana. Cuando la biodiversidad disminuye, la esperanza de vida del ser humano se reduce, no sólo desde el punto de vista ecológico, sino también desde el punto de vista de los recursos, incluso para poder tener especies adaptadas a un nicho ecológico. En esta investigación se expondrá una estrategia informática que a lo largo del tiempo ha logrado grandes resultados; las redes neuronales convolucionales es un proceso que ha facilitado el monitoreo de diferentes tipos de animales en los últimos años, esto, con el fin de facilitar el proceso de reconocimiento y conteo de animales, enfocado a la agricultura y la zoología. Para ello, se utilizará una arquitectura en el campo de las redes neuronales convolucionales (CNN), Alexnet, que tiene referencias con resultados muy elevados. Además, se utiliza el software de programación matemática Matlab para el desarrollo de la red neuronal. Obteniendo de esta forma un resultado de precisión de validación del 97,52%, con la utilización de un conjunto de datos con 3026 imágenes, en donde, el 80% se utilizan para el entrenamiento y el 20% para la validación

Convolutional Dictionary Learning: Acceleration and Convergence

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 to the ADMM approaches, the BPG-M method using a multi-block updating scheme is particularly useful in single-threaded CDL algorithm handling large datasets, 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.Comment: 21 pages, 7 figures, submitted to IEEE Transactions on Image Processin