We propose an algorithm to increase the resolution of multispectral satellite images knowing the panchromatic image at high resolution and the spectral channels at lower resolution. Our algorithm is based on the assumption that, to a large extent, the geometry of the spectral channels is contained in the topographic map of its panchromatic image. This assumption, together with the relation of the panchromatic image to the spectral channels, and the expression of the low-resolution pixel in terms of the high-resolution pixels given by some convolution kernel followed by subsampling, constitute the elements for constructing an energy functional (with several variants) whose minima will give the reconstructed spectral images at higher resolution. We discuss the validity of the above approach and describe our numerical procedure. Finally, some experiments on a set of multispectral satellite images are displayed.

Acquiring good quality images of moving objects by a digital camera remains a valid question, particularly if the velocity of the photographed object is only partially known, it is virtually impossible to tune an optimal exposure time. The same question arises when a solid object is being photographed by a moving camera. This is not only frequent, but even necessary when the camera is embarked on terrestrial vehicle, a plane, or an Earth observation satellite. In the latter cases, the camera velocity is constrained by physical laws. For this reason the recent Raskar and al. flutter shutter and the Durand and al. motion invariant photography methods have generated much interest. This paper proposes a mathematical analysis of moving photography which permits to treat in the same formalism the flutter shutter and the motion invariant photography. A general flutter shutter method is defined and explored, which allows for nonbinary shutter sequences and permits to formalize the question of an optimal flutter shutter code. The first result of this analysis is actually negative, and raises what we call the flutter shutter paradox. We prove that both the flutter shutter and the motion-invariant photography methods cannot increase indefinitely the signal to noise ratio compared to an exposure short enough to avoid motion blur despite the use of a possibly infinite exposure time. Bounds are shown. We also resolve the flutter shutter paradox under the assumption that the relative velocity of object and camera is not a priori known. Then a significant increase of the average SNR can be expected provided there is an a priori knowledge of the probability density for the observed velocities. In this set up we show how to compute analytically an optimal flutter shutter strategy.

The Fourier phase spectrum of an image is well known to contain crucial information about the image geometry, in particular its contours. In this paper, we show that it is also strongly related to the image quality, in particular its sharpness. We propose a way to define the Global Phase Coherence (GPC) of an image, by comparing the likelihood of the image to the likelihood of all possible images sharing the same Fourier power spectrum. The likelihood is measured with the total variation (Rudin-Osher-Fatemi implicit prior), and the numerical estimation is realized by a Monte-Carlo simulation. We show that the obtained GPC measure decreases with blur, noise, and ringing, and thus provides a new interesting sharpness indicator, that can be used for parametric blind deconvolution, as demonstrated by experiments.

The deconvolution of signals is studied with thresholding estimators that decompose signals in an orthonormal basis and threshold the resulting coefficients. A general criterion is established to choose the orthonormal basis in order to minimize the estimation risk. Wavelet bases are highly sub-optimal to restore signals and images blurred by a low-pass filter whose transfer function vanishes at high frequencies. A new orthonormal basis called mirror wavelet basis is constructed to minimize the risk for such deconvolutions. An application to the restoration of satellite images is shown.

This paper presents a study of small baseline stereovision. It is generally admitted that because of the finite resolution of images, getting a good precision in depth from stereovision demands a large angle between the views. In this paper, we show that under simple and feasible hypotheses, small baseline stereovision can be rehabilitated and even favoured. The main hypothesis is that the images should be band limited, in order to achieve sub-pixel precisions in the matching process. This assumption is not satisfied for common stereo pairs. Yet, this becomes realistic for recent spatial or aerian acquisition devices. In this context, block-matching methods, which had become somewhat obsolete for large baseline stereovision, regain their relevance. A multi-scale algorithm dedicated to small baseline stereovision is described along with experiments on small angle stereo pairs at the end of the paper.