Implicit Neural Representations (INRs) are continuous function learners for conventional digital signal representations. With the aid of positional embeddings and/or exhaustively fine-tuned activation functions, INRs have surpassed many limitations of traditional discrete representations. However, existing works only find a continuous representation for the digital signal by solely using a single, fixed activation function throughout the INR, and it has not yet been explored to match the INR to the given signal. As current INRs are not matched to the signal being represented by the INR, we hypothesize that this approach could restrict the representation power and generalization capabilities of INRs, limiting their broader applicability. A way to match the INR to the signal being represented is through matching the activation of each layer in the sense of minimizing the mean squared loss. In this paper, we introduce MIRE, a method to find the highly matched activation function for each layer in INR through dictionary learning. To showcase the effectiveness of the proposed method, we utilize a dictionary that includes seven activation atoms: Raised Cosines (RC), Root Raised Cosines (RRC), Prolate Spheroidal Wave Function (PSWF), Sinc, Gabor Wavelet, Gaussian, and Sinusoidal. Experimental results demonstrate that MIRE not only significantly improves INR performance across various tasks, such as image representation, image inpainting, 3D shape representation, novel view synthesis, super-resolution, and reliable edge detection, but also eliminates the need for the previously required exhaustive search for activation parameters, which had to be conducted even before INR training could begin.

Implicit Neural Representations (INRs) provide a continuous mapping between the coordinates of a signal and the corresponding values. As the performance of INRs heavily depends on the choice of nonlinear-activation functions, there has been a significant focus on encoding explicit signals within INRs using diverse activation functions. Despite recent advancements, existing INRs often encounter significant challenges, particularly at fine scales where they often introduce noise-like artifacts over smoother areas compromising the quality of the output. Moreover, they frequently struggle to generalize to unseen coordinates. These drawbacks highlight a critical area for further research and development to enhance the robustness and applicability of INRs across diverse scenarios. To address this challenge, we introduce the Prolate Spheroidal Wave Function-based Implicit Neural Representations (PIN), which exploits the optimal space-frequency domain concentration of Prolate Spheroidal Wave Functions (PSWFs) as the nonlinear mechanism in INRs. Our experimental results reveal that PIN excels not only in representing images and 3D shapes but also significantly outperforms existing methods in various vision tasks that require INR generalization, including image inpainting, novel view synthesis, edge detection, and image denoising.

Abstract. We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a sequence of separable static problems in the mismatch term of the cost function, while the regularization term handles the nonstationary target as a spatio-temporal object. This approach is motivated by the fact that cylindrical shearlets provide (nearly) optimally sparse approximations on an idealized class of functions modeling spatio-temportal data and the numerical observation that they provide highly sparse approximations even for more general spatio-temporal image sequences found in dynamic tomography applications. To formulate our regularization model, we introduce cylindrical shearlet smoothness spaces, which are instrumental for defining suitable embeddings in functional spaces. We prove that the proposed regularization strategy is well-defined, and the minimization problem has a unique solution (for [Formula: see text]). Furthermore, we provide convergence rates (in terms of the symmetric Bregman distance) under deterministic and random noise conditions, within the context of statistical inverse learning. We numerically validate our theoretical results using both simulated and measured dynamic tomography data, showing that our approach leads to an efficient and robust reconstruction strategy.

This work aims to present the VULCAIN mission study to design and characterize a new CubeSat mission for Earth Observation dedicated to volcanoes. The project is supervised by the European Space Agency (ESA) and involves six Italian partners. The project involves the construction of two 12U nanosatellites flying in formation. Each satellite embarks two instruments onboard: a COTS VIS-NIR camera and a multispectral thermal camera with four channels in the 8-12 µm spectral range. The main scientific objectives are to measure the Land Surface Temperature (LST) and to combine VIS-TIR data to enhance the observation on volcanic areas by adding morphological analysis.

Due to a growing interest for imagery with high spatial and spectral resolution, Earth Observation sensors are producing increasing amounts of data. This poses a severe challenge in terms of computational, memory and transmission requirements. In order to overcome these limitations, a fascinating approach is the implementation of a compressive sensing architecture. In this paper, we present an instrumental concept based on the use of a spatial light modulator to implement a super-resolved, compressive demonstrator of an instrument aimed at Earth Observation in the visible and medium infrared spectral regions from geostationary platform.

Hyperspectral imagery (HSI) has emerged as a highly successful sensing modality for a variety of applications ranging from urban mapping to environmental monitoring and precision agriculture. Despite the efforts made by the scientific community, developing reliable algorithms of HSI classification remains a challenging problem, especially for high-resolution HSI data where there is often larger intraclass variability combined with a scarcity of the ground-truth data and class imbalance. In recent years, deep neural networks have emerged as a promising strategy for problems of HSI classification where they have shown remarkable potential for learning joint spectral-spatial features efficiently via backpropagation. In this letter, we propose a deep learning strategy for HSI classification that combines different convolutional neural networks, especially designed to efficiently learn joint spatial-spectral features over multiple scales. Our method achieves an overall classification accuracy of 66.73% on the 2018 IEEE GRSS hyperspectral data set-a high-resolution data set that includes 20 urban land-cover and land-use classes.

Sparse representation based classification has gained popularity with geospatial image analysis in general and hyperspectral image analysis in particular. A central idea with such classification approaches is that a test pixel (spectral reflectance vector) can be sparsely represented in a training dictionary of pixels from all classes - in particular, only training pixels in the dictionary that bear the same class membership of the test pixel will contribute significant coefficients in the sparse representation. The traditional applications of such classifiers to hyperspectral imagery utilize pixel (sample) level information, not spatial contextual information. We propose a sparse representation based classification paradigm that effectively and optimally captures the key geometric properties in hyperspectral images - our classifier that is built on this structured sparse representation then offers very robust classification, including in scenarios where training and test objects have rotational variations (a common occurrence with geospatial images). We validate the proposed approach with benchmark hyperspectral data and present results demonstrating the efficacy of the proposed method.

Hyperspectral imagery has emerged as a popular sensing modality for a variety of applications, and sparsity-based methods were shown to be very effective to deal with challenges coming from high dimensionality in most hyperspectral classification problems. In this paper, we challenge the conventional approach to hyperspectral classification that typically builds sparsity-based classifiers directly on spectral reflectance features or features derived directly from the data. We assert that hyperspectral image (HSI) processing can benefit very significantly by decoupling data into geometrically distinct components since the resulting decoupled components are much more suitable for sparse representation-based classifiers. Specifically, we apply morphological separation to decouple data into texture and cartoon-like components, which are sparsely represented using local discrete cosine bases and multiscale shearlets, respectively. In addition to providing a structured sparse representation, this approach allows us to build classifiers with invariance properties specific to each geometrically distinct component of the data. The experimental results using real-world HSI data sets demonstrate the efficacy of the proposed framework for classifying multichannel imagery under a variety of adverse conditions-in particular, small training sample size, additive noise, and rotational variabilities between training and test samples.

Carbon dioxide (CO2) emissions from industrial sources is one of the main anthropogenic contributors to the greenhouse effect. We investigated the potentiality of satellite hyperspectral sensors, as the Hyperspectral Precursor of the Application Mission (PRISMA) — an optical Earth Observation satellite mission funded by the Italian Space Agency (ASI) — to evaluate significant amounts of CO2concentrations in the lower troposphere. Using synthetic hyperspectra at top of atmosphere, sensitivity analysis to the retrieval of CO2concentrations was performed in the weak (1610 and 1570 nm) and strong (2010 and 2050 nm) absorption bands. Considering the designed spectral and radiometric features of PRISMA, results of the analysis show a relative uncertainty between 3 and 15 % on the retrieval of CO2concentrations between 390 to 5100 ppmv.

This paper presents an improved approach to face recognition, called Regularized Shearlet Network (RSN), which takes advantage of the sparse representation properties of shearlets in biometric applications. One of the novelties of our approach is that directional and anisotropic geometric features are efficiently extracted and used for the recognition step. In addition, our approach includes a module based on regularization theory (RSN) to control the trade-off between the fidelity to the data (gallery) and the smoothness of the solution (probe). In this work, we address the challenging problem of the single training sample per subject (STSS). We compare our new algorithm against different state-of-the-arts method using several facial databases, such as AR, FERET, FRGC, FEI, CK. Our tests show that the RSN approach is very competitive and outperforms several standard face recognition methods.

This paper investigates a new approach for face, gender and race classification, called multi-regularized learning (MRL). This approach combines ideas from the recently proposed algorithms called multi-stage learning (MSL) and multi-task features learning (MTFL). In our approach, we first reduce the dimensionality of the training faces using PCA. Next, for a given a test (probe) face, we use MRL to exploit the relationships among multiple shared stages generated by changing the regularization parameter. Our approach results in convex optimization problem that controls the trade-off between the fidelity to the data (training) and the smoothness of the solution (probe). Our MRL algorithm is compared against different state-of-the-art methods on face recognition (FR), gender classification (GC) and race classification (RC) based on different experimental protocols with AR, LFW, FEI, Lab2 and Indian databases. Results show that our algorithm performs very competitively.

This paper presents an improved approach to face recognition, called Regularized Shear let Network (RSN), that takes advantage of the sparse representation properties of shear lets in biometric applications. The main novelty of our approach is the efficient extraction of geometric features based on the properties of the shear let decomposition, a multiscale directional method which is especially designed to capture directional and anisotropic information in multidimensional data. To further improve the performance of our face recognition algorithm, we include a regularization step to control the trade-off between the fidelity to the data (gallery) and smoothness of the solution (probe). In this work, we focus on the challenging problem of the single training sample per subject (STSS). We compare our new algorithm against different state-of-the-arts method using several facial databases including AR, FERET, FRGC, FEI and CK Our tests show that our RSN algorithm is very competitive and outperforms several state-of-the-art face recognition methods.

This paper presents a novel approach for face recognition (FR) based on a new multiscale directional approach, called Shear let Network (SN), and on a recently emerged machine learning paradigm, called Multi-Task Sparse Learning (MTSL). SN aims to extract anisotropic features from an image in order to efficiently capture the facial geometry (shear face), MTSL is used to exploit the relationships among multiple shared tasks generated by changing the regularization parameter to make the optimization convex. We compare our algorithm, called Sparse Multi-Regularized Shear let Network (SMRSN), against different state-of-the-art methods on different experimental protocols with AR, ORL, LFW, FERET, FRGC v1 and Lab2 databases. Our tests show that the SMRSN approach yields a very competitive performance and outperforms several standard methods of FR.

Wavelets with composite dilations extend the traditional wavelet approach by allowing for the construction of waveforms defined not only at various scales and locations but also according to various orthogonal transformations. The shearlets, which yield optimally sparse representations for a large class of 2D and 3D data is the most widely known example of wavelets with composite dilations. However, many other useful constructions are obtained within this framework. In this paper, we examine the hyperbolic shearlets, a variant of the shearlet construction obtained as a system of well localized waveforms defined at various scales, locations and orientations, where the directionality is controlled by orthogonal transformations producing a sort of shearing along hyperbolic curves. The effectiveness of this new representation is illustrated by applications to image denoising. Our results compare favorably against similar denoising algorithms based on wavelets, curvelets and other sophisticated multiscale representations.

Wavelets with composite dilations provide a general framework for the construction of waveforms defined not only at various scales and locations, as traditional wavelets, but also at various orientations and with different scaling factors in each coordinate. As a result, they are useful to analyze the geometric information that often dominate multidimensional data much more efficiently than traditional wavelets. The shearlet system, for example, is a particular well-known realization of this framework, which provides optimally sparse representations of images with edges. In this paper, we further investigate the constructions derived from this approach to develop critically sampled wavelets with composite dilations for the purpose of image coding. Not only do we show that many nonredundant directional constructions recently introduced in the literature can be derived within this setting, but we also introduce new critically sampled discrete transforms that achieve much better nonlinear approximation rates than traditional discrete wavelet transforms and outperform the other critically sampled multiscale transforms recently proposed.

In this paper, we introduce a digital implementation of the 3-D shearlet transform and illustrate its application to problems of video denoising and enhancement. The shearlet representation is a multiscale pyramid of well-localized waveforms defined at various locations and orientations, which was introduced to overcome the limitations of traditional multiscale systems in dealing with multidimensional data. While the shearlet approach shares the general philosophy of curvelets and surfacelets, it is based on a very different mathematical framework, which is derived from the theory of affine systems and uses shearing matrices rather than rotations. This allows a natural transition from the continuous setting to the digital setting and a more flexible mathematical structure. The 3-D digital shearlet transform algorithm presented in this paper consists in a cascade of a multiscale decomposition and a directional filtering stage. The filters employed in this decomposition are implemented as finite-length filters, and this ensures that the transform is local and numerically efficient. To illustrate its performance, the 3-D discrete shearlet transform is applied to problems of video denoising and enhancement, and compared against other state-of-the-art multiscale techniques, including curvelets and surfacelets.

This paper shows that the continuous shearlet transform, a novel directional multiscale transform recently introduced by the authors and their collaborators, provides a precise geometrical characterization for the boundary curves of very general planar regions. This study is motivated by imaging applications, where such boundary curves represent edges of images. The shearlet approach is able to characterize both locations and orientations of the edge points, including corner points and junctions, where the edge curves exhibit abrupt changes in tangent or curvature. Our results encompass and greatly extend previous results based on the shearlet and curvelet transforms which were limited to very special cases such as polygons and smooth boundary curves with nonvanishing curvature.

We propose a shearlet formulation of the total variation (TV) method for denoising images. Shearlets have been mathematically proven to represent distributed discontinuities such as edges better than traditional wavelets and are a suitable tool for edge characterization. Common approaches in combining wavelet-like representations such as curvelets with TV or diffusion methods aim at reducing Gibbs-type artifacts after obtaining a nearly optimal estimate. We show that it is possible to obtain much better estimates from a shearlet representation by constraining the residual coefficients using a projected adaptive total variation scheme in the shearlet domain. We also analyze the performance of a shearlet-based diffusion method. Numerical examples demonstrate that these schemes are highly effective at denoising complex images and outperform a related method based on the use of the curvelet transform. Furthermore, the shearlet-TV scheme requires far fewer iterations than similar competitors.

It is well known that the wavelet transform provides a very effective framework for analysis of multiscale edges. In this paper, we propose a novel approach based on the shearlet transform: a multiscale directional transform with a greater ability to localize distributed discontinuities such as edges. Indeed, unlike traditional wavelets, shearlets are theoretically optimal in representing images with edges and, in particular, have the ability to fully capture directional and other geometrical features. Numerical examples demonstrate that the shearlet approach is highly effective at detecting both the location and orientation of edges, and outperforms methods based on wavelets as well as other standard methods. Furthermore, the shearlet approach is useful to design simple and effective algorithms for the detection of corners and junctions

Mathematically wavelets are not very effective in representing images containing distributed discontinuities such as edges. This paper deals with a new multiscale directional representation called the shearlet transform that has been shown to represent specific classes of images with edges optimally. Techniques based on this transform for edge detection and analysis are presented. Unlike previously developed directional filter based techniques for edge detection, shearlets provide a theoretical basis for characterizing how edges will behave in such representations. Experiments demonstrate that this novel approach is very competitive for the purpose of edge detection and analysis.