Saïd Ladjal

Toward Optimal Destriping of MODIS Data Using a Unidirectional Variational Model

Images acquired by the Moderate Resolution Imaging Spectroradiometer (MODIS) aboard Terra and Aqua exhibit strong detector striping. This artifact is common to most pushbroom scanners and affects both visual interpretation and radiometric integrity of remotely sensed data. A considerable effort has been made to remove stripe noise and reduce its impact on high-level products. Despite the variety of destriping algorithms proposed in the literature, complete removal of stripes without signal distortion is yet to be overcome. In this paper, we tackle the striping issue from a variational angle. Basic statistical assumptions used in previous techniques are replaced by a much realistic geometrical consideration on the striping unidirectional variations. The resulting algorithm is tested on Aqua and Terra MODIS data contaminated with severe stripes and is shown to provide optimal qualitative and quantitative results.

EXEMPLAR-BASED INPAINTING FROM A VARIATIONAL POINT OF VIEW

Among all methods for reconstructing missing regions in a digital image, the so-called exemplar-based algorithms are very efficient and often produce striking results. They are based on the simple idea—initially used for texture synthesis—that the unknown part of an image can be reconstructed by simply pasting samples extracted from the known part. Beyond heuristic considerations, there have been very few contributions in the literature to explain from a mathematical point of view the performances of these purely algorithmic and discrete methods. More precisely, a recent paper by Levina and Bickel [Ann. Statist., 34 (2006), pp. 1751–1773] provides a theoretical explanation of their ability to recover very well the texture, but nothing equivalent has been done so far for the recovery of geometry. Our purpose in this paper is twofold: (1) to propose well-posed variational models in the continuous domain that can be naturally associated to exemplar-based algorithms; (2) to investigate their ability to recons...

Dequantizing image orientation

We address the problem of computing a local orientation map in a digital image. We show that standard image gray level quantization causes a strong bias in the repartition of orientations, hindering any accurate geometric analysis of the image. In continuation, a simple dequantization algorithm is proposed, which maintains all of the image information and transforms the quantization noise in a nearby Gaussian white noise (we actually prove that only Gaussian noise can maintain isotropy of orientations). Mathematical arguments are used to show that this results in the restoration of a high quality image isotropy. In contrast with other classical methods, it turns out that this property can be obtained without smoothing the image or increasing the signal-to-noise ratio (SNR). As an application, it is shown in the experimental section that, thanks to this dequantization of orientations, such geometric algorithms as the detection of nonlocal alignments can be performed efficiently. We also point out similar improvements of orientation quality when our dequantization method is applied to aliased images.

Resolution- Independent Characteristic Scale Dedicated to Satellite Images

We study the problem of finding the characteristic scale of a given satellite image. This feature is defined so that it does not depend on the spatial resolution of the image. This is a different problem than achieving scale invariance, as often studied in the literature. Our approach is based on the use of a linear scale space and the total variation (TV). The critical scale is defined as the one at which the normalized TV reaches its maximum. It is shown experimentally, both on synthetic and real data, that the computed characteristic scale is resolution independent.

Robust Multi-image Processing with Optimal Sparse Regularization

Sparse modeling can be used to characterize outlier type noise. Thanks to sparse recovery theory, it was shown that 1-norm super-resolution is robust to outliers if enough images are captured. Moreover, sparse modeling of signals is a way to overcome ill-posedness of under-determined problems. This naturally leads to this question: does an added sparsity assumption on the signal improve the robustness to outliers of the 1-norm super-resolution, and if yes, how strong should this assumption be? In this article, we review and extend results of the literature to the robustness to outliers of overdetermined signal recovery problems under sparse regularization, with a convex variational formulation. We then apply them to general random matrices, and show how the regularization parameter acts on the robustness to outliers. Finally, we show that in the case of multi-image processing, the structure of the support of signal and noise must be studied precisely. We show that the sparsity assumption improves robustness if outliers do not overlap with signal jumps, and determine how the regularization parameter can be chosen.

Characteristic Scale in Satellite Images

We study the problem of finding the characteristic scale of a given satellite image. We want to define this feature so that it does not depend on the spatial resolution of the image. Our approach is based on the use of a linear scale space and the total variation. The critical scale is defined as the one at which the normalized total variation is maximum

Outlier Removal Power of the L1-Norm Super-Resolution

Super-resolution combines several low resolution images having different sampling into a high resolution image. L1-norm data fit minimization has been proposed to solve this problem in a robust way. The outlier rejection capability of this methods has been shown experimentally for super-resolution. However, existing approaches add a regularization term to perform the minimization while it may not be necessary. In this paper, we recall the link between robustness to outliers and the sparse recovery framework. We use a slightly weaker Null Space Property to characterize this capability. Then, we apply these results to super resolution and show both theoretically and experimentally that we can quantify the robustness to outliers with respect to the number of images.

A variational approach for the destriping of modis data

The Moderate Resolution Imaging Spectrometer (MODIS) monitors the earth in 36 spectral bands using a cross-track double-sided continuously rotating scan mirror. The imperfect calibration of the linear arrays of detectors and additional random noise in the internal calibration system induce detector-to-detector stripes, mirror side stripes and noisy stripes visible in most emissive bands. This artefact affects seriously the visual quality and radiometric integrity of measured data. Several approaches including fourier filtering [1,2], wavelet analysis [3,4] and statistical techniques such as moment matching or histogram matching have been used to reduce striping on MODIS Data [5,6,7]. Despite an extensive and diverse destriping litterature, most techniques display residual stripes if not strong distortion from the original image. In this paper, we introduce a robust destriping methodology based on a variational approach.

Extrapolation of Wavelet Features for the Indexing of Satellite Images with Different Resolutions

In this paper, we propose a new scheme to extrapolate wavelet features with respect to the resolution. By explicitly taking into account the acquisition process of satellite images, we compute how wavelet features behave when the resolution changes. This approach is validated by classifying satellite images with different resolutions.