Deep neural networks have achieved impressive performance in problems of object detection and object category classifications. To perform efficiently though, such methods typically require a large number of training samples. Unfortunately, this requirement is highly impractical or impossible in applications such as hyperspectral classification where it is expensive and labor intensive to generate labeled data for training. A few ideas have been proposed in the literature to address this problem such as transfer learning and domain adaptation. In this work, we propose an alternative strategy to reduce the number of network parameters based on Structured Receptive Field Networks (SRFN), a class of convolutional neural networks (CNNs) where each convolutional filter is a linear combination from a predefined dictionary. To better exploit the characteristics of hyperspectral data to be learned, we choose a filter dictionary consisting of directional filters inspired by the theory of shearlets and we train a SRFN by imposing that the convolutional filters form sparse linear combinations in such dictionary. The application of our SRFN to problems of hyperspectral classification shows that this approach achieves very competitive performance as compared to conventional CNNs.
As advances in imaging technologies make more and more data available for biomedical applications, there is an increasing need to develop efficient quantitative algorithms for the analysis and processing of imaging data. In this paper, we introduce an innovative multiscale approach called Directional Ratio which is especially effective to distingush isotropic from anisotropic structures. This task is especially useful in the analysis of images of neurons, the main units of the nervous systems which consist of a main cell body called the soma and many elongated processes called neurites. We analyze the theoretical properties of our method on idealized models of neurons and develop a numerical implementation of this approach for analysis of fluorescent images of cultured neurons. We show that this algorithm is very effective for the detection of somas and the extraction of neurites in images of small circuits of neurons.
In this paper, we present an algorithm for image registration utilizing the shearlet representation. The shearlet framework allows one to collect multi-scale and multi-directional feature information from multidimensional data that can be used to create key feature vectors that are scale, rotation, and shift invariant. These key feature vectors produce a transformation that will align the sensed image to the source image. We demonstrate our registration algorithm on various medical databases.
Region-of-interest (ROI) reconstruction in computed tomography (CT) is a problem receiving increasing attention in the medical imaging community, due to its potential to lower exposure to X-ray radiation and to reduce the scanning time. Since the ROI reconstruction problem requires to deal with truncated projection images, classical CT reconstruction algorithms tend to become very unstable and the solution of this problem requires either ad hoc analytic formulas or more sophisticated numerical schemes. In this paper, we introduce a novel approach for ROI CT reconstruction, formulated as a convex optimization problem with a regularized functional based on shearlets or wavelets. Our numerical implementation consists of an iterative algorithm based on the scaled gradient projection method. As illustrated by numerical tests in the context of fan beam CT, our algorithm is insensitive to the location of the ROI and remains very stable also when the ROI size is rather small.
The automated reconstruction of neuronal morphology is a fundamental task for investigating several problems associated with the nervous system. Revealing the mechanisms of synaptic plasticity, signal transmission, network connectivity and circuit dynamics requires accurate quantitative analyses of digital three-dimensional reconstructions. Yet, while many commercial and non-commercial software packages for neuronal reconstruction are available, these packages typically provide limited quantitative information and require a significant manual intervention. Recent advances in applied harmonic analysis, especially in the area of multiscale representations, offer a variery of techniques and ideas which have the potential to dramatically impact this very active field of scientific investigation. In this paper, we apply such ideas for (i) the derivation of a multiscale directional representation from isotropic filters aimed at detecting tubular structures and (ii) the development of a multiscale quantitative measure capable of distingushing isotropic from anisotropic structures. We showcase the application of these methods for the extraction of geometric features used for the detection of somas and dendritic branches of neurons.
In a recent work, it was shown that the shearlet representation provides a useful formula for the reconstruction of 3D objects from their X-ray projections. One major advantage of this approach is that it yields a near-optimal rate of convergence in estimating piecewise smooth objects from 3D X-ray projections which are corrupted by white Gaussian noise. In this work, we provide numerical demonstrations to illustrate the effectiveness of this method and its performance as compared with other X-ray data restoration algorithms.
This paper introduces a numerical implementation of the 3D shearlet transform, a directional transform which is
derived from the theory of shearlets. The shearlet approach belongs to a class of directional multiscale methods
emerged during the last 10 years to overcome the limitations of traditional multiscale systems, which also include
curvelets and contourlets. Unlike other methods, shearlets are derived from the theory of affine systems, which
allows a very flexible mathematical structure and a natural transition from the continuous to the digital setting.
Following the recent proof of the optimality of the 3D shearlet representation, in this paper we develop an
algorithmic implementation of the 3D shearlet transform that follows closely the spatial-frequency pattern of
the corresponding continuous transform. The performance of the algorithm is illustrated on problems of video
denoising and successfully compared against other state-of-the-art multiscale techniques, including curvelets and
In this work, we present a new approach to image denoising derived from the general framework of wavelets
with composite dilations. This framework extends the traditional wavelet approach by allowing for waveforms
to be defined not only at various scales and locations but also according to various orthogonal transformations
such as shearing transformations. The shearlet representation is, perhaps, the most widely known example of
wavelets with composite dilations. However, many other representations are obtained within this framework,
where directionality properties are controlled by different types of orthogonal matrices, such as the newly defined
hyperbolets. In this paper, we show how to take advantage of different wavelets with composite dilations to
sparsely represent important features such as edges and texture independently, and apply these techniques to
derive improved algorithms for image denoising.
Sparse representations of multidimensional data have gained more and more prominence in recent years, in
response to the need to process large and multi-dimensional data sets arising from a variety of applications in
a timely and effective manner. This is especially important in applications such as remote sensing, satellite
imagery, scientific simulations and electronic surveillance. Directional multiscale systems such as shearlets are
able to provide sparse representations thanks to their ability to approximate anisotropic features much more
efficiently than traditional multiscale representations. In this paper, we show that the shearlet approach is
essentially optimal in representing a large class of 3D containing discontinuities along surfaces. This is the first
nonadaptive approach to achieve provably optimal sparsity properties in the 3D setting.
Many imaging modalities, such as Synthetic Aperture Radar (SAR), can be described mathematically as collecting
data in a Radon transform domain. The process of inverting the Radon transform to form an image can be unstable when the data collected contain noise so that the inversion needs to be regularized in some way. In this work, we develop a method for inverting the Radon transform using a shearlet-based decomposition, which provides a regularization that is nearly optimal for a general class of images. We then show through a variety of examples that this technique performs better than similar competitive methods based on the use of the wavelet and the curvelet transforms.
In this paper we describe a new class of multidimensional
representation systems, called shearlets. They are obtained by
applying the actions of dilation, shear transformation and
translation to a fixed function, and exhibit the geometric and
mathematical properties, e.g., directionality, elongated shapes,
scales, oscillations, recently advocated by many authors for
sparse image processing applications. These systems can be studied
within the framework of a generalized multiresolution analysis.
This approach leads to a recursive algorithm for the
implementation of these systems, that generalizes the classical
Since 1995 GOME-1 is measuring ozone (total column and
profile), nitrogen dioxide and other minor trace gases on-board of ERS-2. An advanced GOME-2 instrument will fly on the METOP satellites. The GOME-2 measurements will provide the input for the ozone data record in the timeframe 2005 to 2020 provided by the EUMETSAT Polar System. The on-ground calibration of the instrument encompasses spectral, absolute radiance and irradiance calibrations as well as polarization, straylight, and slit function characerization. Main results of the first flight model are discussed.
The in-flight radiometric calibration of satellite multispectral sensor for earth and atmospheric observations can be conveniently based on solar diffusers. Theoretically, a knowledge of the spectral bi-directional scatter distribution function (BSDF) of the diffuser panel, and the solar incidence angle is all that is needed to allow the retrieval of the earth albedo in the observed direction. At the request of the ESA, the Centre Spatial de Liege, with the support of Officine Galileo as subcontractor, is currently designing a high-versatility high-accuracy BSDF measurement set-up with application to the calibration of space solar diffusers. This instrument will allow a BSDF measurements uncertainty within 1 percent for any angle in the wavelength range from 200 nm to 2400 nm. Vacuum measurements, polarization analysis capabilities and thermalization of the test sample between 200K and 300K are other unique features of this set-up.
The Interferometric Analysis Computer Code is a program developed to evaluate the performances of Fourier Transform Spectrometers. It has been carried out in the frame of the IASI program. It is a stand-alone code which can use as input the optical system data set up by an optical design software. The interference phenomenon is evaluated using the optical data of both interferometer arms by means of real ray-tracing. The mathematical model used to obtain the output signal is based on the concept that, for a monochromatic source, this signal is quite similar to an ideal sine. This allows to calculate three functions describing the difference between the ideal interferogram and the simulated one. These represent the average level of the output irradiance, the modulation and the phase of the oscillating terms as a function of the Optical Path Difference. These functions are quite smooth and then easily representable by fitting. Therefore in order to have a good representation of them it is sufficient a number of points much smaller than those necessary to represent correctly an interferogram. Then a great advantage in terms of computation time is obtained, especially when many signals have to be added to simulate the effect of a detector covering a quite large field of view. Furthermore, the possibility to input in the optical data files different kinds of manufacturing or assembly errors allows to estimate the sensitivity of the optical components respect to these aspects. This makes possible the calculation of an exhaustive tolerance budget.
The XMM Optical Monitor (XMM/OM) is a co-aligned telescope devoted to make observations of the X-ray sources both in the UV, visible and near-IR spectral bands, simultaneously with the X-ray instrument on the X-ray Multi-Mirror (XMM) satellite. The OM telescope is a Ritchey-Chretien with 300 mm clear aperture, for real time identification of sources up to magnitude mv equals 24. In the design of the telescope, particular care was paid in the selection of the optomechanical architecture and in the thermal and structural analysis, since the adopted optical scheme requires high stability of the structure. The paper highlights the major critical aspects and the criteria followed in the trade-off and design phases.