Most signal processing problems involve the challenging task of multidimensional probability density function (PDF) estimation. In this paper, we propose a solution to this problem by using a family of rotation-based iterative Gaussianization (RBIG) transforms. The general framework consists of the sequential application of a univariate marginal Gaussianization transform followed by an orthonormal transform. The proposed procedure looks for differentiable transforms to a known PDF so that the unknown PDF can be estimated at any point of the original domain. In particular, we aim at a zero-mean unit-covariance Gaussian for convenience. RBIG is formally similar to classical iterative projection pursuit algorithms. However, we show that, unlike in PP methods, the particular class of rotations used has no special qualitative relevance in this context, since looking for interestingness is not a critical issue for PDF estimation. The key difference is that our approach focuses on the univariate part (marginal Gaussianization) of the problem rather than on the multivariate part (rotation). This difference implies that one may select the most convenient rotation suited to each practical application. The differentiability, invertibility, and convergence of RBIG are theoretically and experimentally analyzed. Relation to other methods, such as radial Gaussianization, one-class support vector domain description, and deep neural networks is also pointed out. The practical performance of RBIG is successfully illustrated in a number of multidimensional problems such as image synthesis, classification, denoising, and multi-information estimation.

We develop a framework for rendering photographic images by directly optimizing their perceptual similarity to the original visual scene. Specifically, over the set of all images that can be rendered on a given display, we minimize the normalized Laplacian pyramid distance (NLPD), a measure of perceptual dissimilarity that is derived from a simple model of the early stages of the human visual system. When rendering images acquired with a higher dynamic range than that of the display, we find that the optimization boosts the contrast of low-contrast features without introducing significant artifacts, yielding results of comparable visual quality to current state-of-the-art methods, but without manual intervention or parameter adjustment. We also demonstrate the effectiveness of the framework for a variety of other display constraints, including limitations on minimum luminance (black point), mean luminance (as a proxy for energy consumption), and quantized luminance levels (halftoning). We show that the method may generally be used to enhance details and contrast, and, in particular, can be used on images degraded by optical scattering (e.g., fog). Finally, we demonstrate the necessity of each of the NLPD components—an initial power function, a multiscale transform, and local contrast gain control—in achieving these results and we show that NLPD is competitive with the current state-of-the-art image quality metrics.

Mechanisms of human color vision are characterized by two phenomenological aspects: the system is nonlinear and adaptive to changing environments. Conventional attempts to derive these features from statistics use separate arguments for each aspect. The few statistical explanations that do consider both phenomena simultaneously follow parametric formulations based on empirical models. Therefore, it may be argued that the behavior does not come directly from the color statistics but from the convenient functional form adopted. In addition, many times the whole statistical analysis is based on simplified databases that disregard relevant physical effects in the input signal, as, for instance, by assuming flat Lambertian surfaces. In this work, we address the simultaneous statistical explanation of the nonlinear behavior of achromatic and chromatic mechanisms in a fixed adaptation state and the change of such behavior (i.e., adaptation) under the change of observation conditions. Both phenomena emerge directly from the samples through a single data-driven method: the sequential principal curves analysis (SPCA) with local metric. SPCA is a new manifold learning technique to derive a set of sensors adapted to the manifold using different optimality criteria. Here sequential refers to the fact that sensors (curvilinear dimensions) are designed one after the other, and not to the particular (eventually iterative) method to draw a single principal curve. Moreover, in order to reproduce the empirical adaptation reported under D65 and A illuminations, a new database of colorimetrically calibrated images of natural objects under these illuminants was gathered, thus overcoming the limitations of available databases. The results obtained by applying SPCA show that the psychophysical behavior on color discrimination thresholds, discount of the illuminant, and corresponding pairs in asymmetric color matching emerge directly from realistic data regularities, assuming no a priori functional form. These results provide stronger evidence for the hypothesis of a statistically driven organization of color sensors. Moreover, the obtained results suggest that the nonuniform resolution of color sensors at this low abstraction level may be guided by an error-minimization strategy rather than by an information-maximization goal.

The number of Earth observation satellites carrying optical sensors with similar characteristics is constantly growing. Despite their similarities and the potential synergies among them, derived satellite products are often developed for each sensor independently. Differences in retrieved radiances lead to significant drops in accuracy, which hampers knowledge and information sharing across sensors. This is particularly harmful for machine learning algorithms, since gathering new ground truth data to train models for each sensor is costly and requires experienced manpower. In this work, we propose a domain adaptation transformation to reduce the statistical differences between images of two satellite sensors in order to boost the performance of transfer learning models. The proposed methodology is based on the Cycle Consistent Generative Adversarial Domain Adaptation (CyCADA) framework that trains the transformation model in an unpaired manner. In particular, Landsat-8 and Proba-V satellites, which present different but compatible spatio-spectral characteristics, are used to illustrate the method. The obtained transformation significantly reduces differences between the image datasets while preserving the spatial and spectral information of adapted images, which is hence useful for any general purpose cross-sensor application. In addition, the training of the proposed adversarial domain adaptation model can be modified to improve the performance in a specific remote sensing application, such as cloud detection, by including a dedicated term in the cost function. Results show that, when the proposed transformation is applied, cloud detection models trained in Landsat-8 data increase cloud detection accuracy in Proba-V.

Two key hurdles to the adoption of Machine Learning (ML) techniques in hyperspectral data compression are computational complexity and scalability for large numbers of bands. These are due to the limited computing capacity available in remote sensing platforms and the high computational cost of compression algorithms for hyperspectral data, especially when the number of bands is large. To address these issues, a channel clusterisation strategy is proposed, which reduces the computational demands of learned compression methods for real scenarios and is scalable for different sources of data with varying numbers of bands. The proposed method is compatible with an embedded implementation for state-of-the-art on board hardware, a first for a ML hyperspectral data compression method. In terms of coding performance, our proposal surpasses established lossy methods such as JPEG 2000 preceded by a spectral Karhunen-Loève Transform (KLT), in clusters of 3 to 7 bands, achieving a PSNR improvement of, on average, 9 dB for AVIRIS and 3 dB for Hyperion images.