Multiscale analyses can be provided by application wavelet transforms. For image processing purposes, we applied algorithms which imply a quasi isotropic vision. For a uniform noisy image, a wavelet coefficient W has a probability density function (PDF) p(W) which depends on the noise statistic. The PDF was determined for many statistical noises: Gauss, Poission, Rayleigh, exponential. For CCD observations, the Anscombe transform was generalized to a mixed Gasus+Poisson noise. From the discrete wavelet transform a set of significant wavelet coefficients (SSWC)is obtained. Many applications have been derived like denoising and deconvolution. Our main application is the decomposition of the image into objects, i.e the vision. At each scale an image labelling is performed in the SSWC. An interscale graph linking the fields of significant pixels is then obtained. The objects are identified using this graph. The wavelet coefficients of the tree related to a given object allow one to reconstruct its image by a classical inverse method. This vision model has been applied to astronomical images, improving the analysis of complex structures.

We present a novel method for joint estimation of the degradation and restoration of photon-limited images. Our method will be demonstrated on confocal microscope images, since confocal microscopy is an important tool in many academic (fundamental biology, . . . ) and industrial (material science, pharmaceutical industry, . . . ) applications. However, the observed images are usually degraded, which hinders analysis and interpretation of the images. Degradation in this kind of images is due to two sources: first, we have blurring due to the bandlimited nature of the optical system; second, Poisson noise contaminates the observations due to the discrete nature of the photon detection process. The proposed method iterates noise reduction and blur estimation using the steerable pyramid transform (which is a variant of the wavelet transform) and deconvolution in the signal domain. These steps are applied in two phases, a training phase and a restoration phase. In the first phase, these three steps are iterated until the blur estimation converges. The second phase is the actual restoration phase. During the iterations the blur estimation serves as a sharpness measure for the restored image, and is used to controls the number of iterations. So, our integrated method provides a completely automatic algorithm where no prior information about the image degradation is required. Our integrated technique was compared with other common restoration techniques for these kind of images, and provided the best restoration results, with least artifacts.

Due to its functional capabilities, gamma imaging is an interesting tool for medical diagnosis. Recent developments lead to improved intrinsic resolution. However this gain is impaired by the poor activity detected and the Poissonian feature of gamma ray emission. High resolution gamma images are grainy. This is a real nuisance for detecting cold nodules in an emitting organ. A specific translation wavelet filter which takes into account the Poissonian feature of noise, has been developed in order to improve the diagnostic capabilities of radioisotopic high resolution images. Monte Carlo simulations of a hot thyroid phantom in which cold spheres, 3-7 mm in diameter, could be included were performed. The loss of activity induced by cold nodules was determined on filtered images by using catchment basins determination. On the original images, only 5-7 mm cold spheres were clearly visible. On filtered images, 3 and 4 mm spheres were put in prominent. The limit of the developed filter is approximately the detection of 3 mm spherical cold nodule in acquisition and activity conditions which mimic a thyroid examination. Furthermore, no disturbing artifacts are generated. It is therefore a powerful tool for detecting small cold nodules in a gamma emitting medium.

This paper deals with the rational wavelet transform apply to a wavelet shrinkage problem. The rational multiresolution analysis (MRA) allows a better adaptation of the scale factor to the signal components than the dyadic one. The theory of the rational MRA is reviewed and a pyramidal algorithm for the computation of the fast orthogonal wavelet transform is proposed. Both, the analysis and the synthesis parts of the process are detailed. Moreover, using filters defined in Fourier domain, the implementation of the proposed algorithm is extended to this space. To illustrate the potential of rational analysis for signal processing, a wavelet shrinkage application is presented.

There is a considerable amount of literature about image denoising using wavelet-based methods. Some new ideas where also reported using fractal methods. In this paper we propose a hybrid wavelet-fractal denoising method. Using a non-subsampled overcomplete wavelet transform we present the image as a collection of translation invariant copies in different frequency subbands. Within this multiple representation we do a fractal coding which tries to approximate a noise free image. The inverse wavelet transform of the fractal collage leads to the denoised image. Our results are comparable to some of the most efficient known denoising methods.

We develop a sequential wavelet domain and temporal filtering scheme, with jointly optimized parameters, which results in high-quality video denoising over a large range of noise levels. In this scheme, spatial filtering is performed by a spatially adaptive Bayesian wavelet shrinkage in a redundant wavelet representation. In the next filtering stage, a motion detector controls selective, recursive averaging of pixel intensities over time. The results demonstrate that the proposed filter outperforms recent single-resolution representatives as well as some recent motion-compensated wavelet based video filters. We also analyze important practical issues for possible industrial applications. In particular, we investigate the performance degradations that result from making the wavelet domain filtering part less complex, by removing the redundancy of the representation and/or by replacing a sophisticated spatially adaptive shrinkage method by soft-thresholding.

Multiscale statistical signal and image models resulted in major advances in many signal processing disciplines. This paper focuses on Bayesian image denoising. We discuss two important problems in specifying priors for image wavelet coefficients. The first problem is the characterization of the marginal subband statistics. Different existing models include highly kurtotic heavy-tailed distributions, Gaussian scale mixture models and weighted sums of two different distributions. We discuss the choice of a particular prior and give some new insights in this problem. The second problem that we address is statistical modelling of inter- and intrascale dependencies between image wavelet coefficients. Here we discuss the use of Hidden Markov Tree models, which are efficient in capturing inter-scale dependencies, as well as the use of Markov Random Field models, which are more efficient when it comes to spatial (intrascale) correlations. Apart from these relatively complex models, we review within a new unifying framework a class of low-complexity locally adaptive methods, which encounter the coefficient dependencies via local spatial activity indicators.

This article presents a visual browsing content-based indexing and retrieval (CBIR) system for large image databases applied to a paleontology database. The studied system offers a hierarchical organization of feature vectors into signature vectors leading to a research tree so that users can explore the database visually. To build the tree, our technique consists in transforming the images using multiresolution analysis in order to extract features at multiple scales. Then a hierarchical signature vector for each scale is built using extracted features. An automatic classification of the obtained signatures is performed using the k-means algorithm. The images are grouped into clusters and for each cluster a model image is computed. This model image is inserted into a research tree proposed to users to browse the database visually. The process is reiterated and each cluster is split into sub-clusters with one model image per cluster, giving the nodes of the tree. The multiresolution approach combined with the organized signature vectors offers a coarse-to-fine research during the retrieval process (i.e. during the progression in the research tree).

The starting point for this paper is the well known equivalence between convolution filtering with a rescaled Gaussian and the solution of the heat equation. In the first sections we analyze the equivalence between multiscale convolution filtering, linear smoothing methods based on continuous wavelet transforms and the solutions of linear diffusion equations. I.e. we determine a wavelet ψ, resp. a convolution filter φ, which is associated with a given linear diffusion equation u_t = Pu and vice versa. This approach has an extension to non-linear smoothing techniques. The main result of this paper is the derivation of a differential equation, whose solution is equivalent to non-linear multi-scale smoothing based on soft shrinkage methods applied to Fourier or continuous wavelet transforms.

We discuss a wavelet based treatment of variational problems arising in the context of image processing, inspired by papers of Vese-Osher and Osher-Sole-Vese, in particular, we introduce a special class of variational functionals, that induce a decomposition of images in oscillating and cartoon components. Cartoons are often modeled by BV functions. In the setting of Vese et.el. and Osher et.al. the incorporation of BV penalty terms leads to PDE schemes that are numerically intensive. We propose to embed the problem in a wavelet framework. This provides us with elegant and numerically efficient schemes even though a basic requirement, the involvement of the space BV , has to be softened slightly. We show results on test images of our wavelet algorithm with a B¹₁ (L₁) penalty term, and we compare them with the BV restorations of Osher-Sole-Vese.

Compactly supported wavelets have several properties that are useful for representing solutions of PDEs. The orthogonality, compact support and exact representation of polynomials of a fixed degree allow the efficient and stable calculation in regions with strong gradients or oscillations. The general method is a straightforward adaptation of the Galerkin procedure with a wavelet basis. Boundary conditions are imposed by a capacitance matrix method. Among the equations solved by these methods are the Burgers equation, the equations of Gas dynamics, the Euler and Navier-Stokes equations for an incompressible fluid in two dimensions with boundary conditions, the Schrodinger equation in two dimensions with singular particle potentials, the heat equation in two dimensions with boundary conditions and a discontinuous coefficient of diffusion, and the wave equation in two dimensions with a discontinuous sound speed (layered media). We present examples of the wavelet-Galerkin method applied to: the calculation of shocks for the Burgers equation, the calculation of the vortex dynamics for the Euler and Navier-Stokes equations, and calculations of solutions for the heat and wave equations in layered media.

In this paper, we are interested in designing lifting schemes adapted to the statistics of the wavelet coefficients of multiband images for compression applications. More precisely, nonseparable vector lifting schemes are used in order to capture simultaneously the spatial and the spectral redundancies. The underlying operators are then computed in order to minimize the entropy of the resulting multiresolution representation. To this respect, we have developed a new iterative block-based classification algorithm. Simulation tests carried out on remotely sensed multispectral images indicate that a substantial gain in terms of bit-rate is achieved by the proposed adaptive coding method w.r.t the non-adaptive one.

Recently, two new international image and video coding standards have been released: the wavelet-based JPEG2000 standard designed basically for compressing still images, and H.264/AVC, the newest generic standard for video coding. As part of the JPEG2000 suite, Motion-JPEG2000 extends JPEG2000 to a range of applications originally associated with a pure video coding standard like H.264/AVC. However, currently little is known about the relative performance of Motion-JPEG2000 and H.264/AVC in terms of coding efficiency on their overlapping domain of target applications requiring the random access of individual pictures. In this paper, we report on a comparative study of the rate-distortion performance of Motion-JPEG2000 and H.264/AVC using a representative set of video material. Our experimental coding results indicate that H.264/AVC performs surprisingly well on individually coded pictures in comparison to the highly sophisticated still image compression technology of JPEG2000. In addition to the rate-distortion analysis, we also provide a brief comparison of the evaluated coding algorithms in terms of complexity and functionality.

Lifting Scheme is actually a widely used second generation multi-resolution technique in image and video processing field. It permits to easily create fast, reversible, separable or no, not necessarily linear, multi-resolution analysis for sound, image, video or even 3D graphics. An interesting feature of lifting scheme is the ability to build adaptive transforms, more easily than with other decompositions. Many works have already be done in this subject, especially in lossless or near-lossless compression framework where there is no orthogonal constraint. However, some applications as lossy compression or de-noising requires well conditioned transforms. Indeed, this is due to the use of shrinking or quantization which has not controlled propagation through inverse transform. Authors have recently presented a technique permitting to determine some lifting scheme filters in order to obtain a high level of adaptivity combined with near-orthogonal properties, useful for most of these applications. Naturly coming into the adaptive near orthogonal framework, the point of interest of this article is affine algebraic filters. Color images and video have especially been studied through point of view of compression. In this way, the treatment of the vector aspect of signal, not only by processing channels independently, becomes the focus point of the article.

Video transmission over variable-bandwidth networks requires instantaneous bit-rate adaptation at the server site to provide an acceptable decoding quality. For this purpose, recent developments in video coding aim at providing a fully embedded bit-stream with seamless adaptation capabilities in bit-rate, frame-rate and resolution. A new promising technology in this context is wavelet-based video coding. Wavelets have already demonstrated their potential for quality and resolution scalability in still-image coding. This led to the investigation of various schemes for the compression of video, exploiting similar principles to generate embedded bit-streams. In this paper we present scalable wavelet-based video-coding technology with competitive rate-distortion behavior compared to standardized non-scalable technology.

The common way to process radar wind profiler (RWP) data by moments estimation of the Fourier power spectrum fails in presence of transient intermittent clutter contributions. Wavelets are especially suitable for detecting and removing transient components because of their high localization in time and frequency domain. We give an overview on the wavelet filtering of contaminated discrete RWP signals and introduce a new technique involving the wavelet packet decomposition and a splitting in progressive and regressive signal components. This technique has been successfully tested on severely real-data sets where classical wavelet routines fail.

This paper presents an algorithm specifically developed for filtering low frequency signals. The application is related to weed detection into aerial images where crop lines are detected as repetitive structures. Theoretical bases of this work are presented first. Then, two methods are compared to select low frequency signals and their limitations are described. A decomposition based on wavelet packet is used to combine advantages of both methods. This algorithm allows a high selectivity of low frequency signals with an interesting computation time. At last, a complete algorithm for weed/crop classification is explained and a few results are shown.

In the last decade, the accessibility of inexpensive and powerful computers has allowed true digital holography to be used for industrial inspection using a microscopy. This technique allows capturing a complex image of a scene, and reconstructing the phase and magnitude information. This type of image gives a new dimension to texture analysis since the topology information can be used as an additional way to extract features. This new technique can be used to extend our previous work on image segmentation of patterned wafers for defect detection. This paper presents a comparison between the features obtained using Gabor filtering on complex (i.e. containing magnitude and phase) images under illumination and focus variations.

First, we present a wavelet-based algorithm for edge detection and characterization, which is an adaptation of Mallat and Hwang’s method. This algorithm relies on a modelization of contours as smoothed singularities of three particular types (transitions, peaks and lines). On the one hand, it allows to detect and locate edges at an adapted scale. On the other hand, it is able to identify the type of each detected edge point and to measure its amplitude and smoothing size. The latter parameters represent respectively the contrast and the smoothness level of the edge point. Second, we explain that this method has been integrated in a 3D bone surface reconstruction algorithm designed for computer-assisted and minimal invasive orthopaedic surgery. In order to decrease the dose to the patient and to obtain rapidly a 3D image, we propose to identify a bone shape from few X-ray projections by using statistical shape models registered to segmented X-ray projections. We apply this approach to pedicle screw insertion (scoliosis, fractures...) where ten to forty percent of the screws are known to be misplaced. In this context, the proposed edge detection algorithm allows to overcome the major problem of vertebrae segmentation in the X-ray images.

In this work, a wavelet representation of multivalued images is presented. The representation is based on a multiresolution extension of the First Fundamental Form that accesses gradient information of vector-valued images. With the extension, multiscale edge information of multivalued images is extracted. Moreover, a wavelet representation is obtained that, after inverse transformation, accumulates all edge information in a single greylevel image. In this work, a redundant wavelet representation is presented using dyadic wavelet frames. It is then extended towards orthogonal wavelet bases using the Discrete Wavelet Transformation (DWT). The representation is shown to be a natural framework for image fusion. An algorithm is presented for fusion of multispectral images.

In order to enhance the speed of image processing we apply the optical wavelet transform to vision system by the method of photoelectric hybrid implementation. The state-of-the-art liquid crystal on silicon (LCoS) technology is applied to improve the signal-to-noise ratio of the wavelet transform. A fan out grating implemented by a phase-only LCoS is used to implement multiple channel optical processing. Therefore the parallelism of the vision system is improved further. The research results shows that the optical wavelet transform based vision system is reasonable and feasible. The image feature extraction by optical information processing can enhance the speed of vision processing.

The presented study, based on the continuous wavelet transform and time-frequency representations, introduce new algorithms which perform different kinds of separation processing depending on the nature of the seismic data. When dealing with a one dimensional recorded signal (one sensor), we propose a segmentation of its time-scale representation. This leads to the automatic detection and separation of the different waves. This algorithm can be applied to a whole seismic profile containing several sensors, by tracking the segmentation features in the time-scale image sequence. The resulting separation algorithm is efficient as long as the patterns of the different waves do not overlap in the time-scale plane. Afterwards, the purpose is to take into account the redundancy of information in more dimensional data to increase the separation possibilities in presence of interference. In the case of vectorial sensors, we use the polarization information to separate the different waves using phase shifts, rotations, and amplifications. At last, in the case of linear array data, we use the propagation velocity information to separate dispersive waves with overlapping patterns. For this purpose, we propose a new time-scale representation which enable the estimation of the wave dispersion function from a small array of sensors.

We study analysis and forecasting strategies for time series based on multiscale analysis. The method is illustrated for a set of data collecting several years of booking information from the air traffic company Lufthansa Systems GmbH, Berlin. In particular, we deal with data where the variability of the forecast units leads to different problems in computing. We consider several years of subsequent data and apply a wavelet decomposition over a certain number of scales. In wavelet domain the data are subdivided in low and high frequency parts. Forecast values on each scale are calculated, the inverse wavelet transform yields a forecast for the whole signal. In the present paper we describe the analysis of several historical booking data sets from Lufthansa Systems GmbH dealing with data over a period of 4 years. Based on the wavelet transform we apply a forecast to the data. The forecast itself depends on the behaviour of the data on each scale. The wavelet decomposition can be used to reveal trends and seasonal influences.

The concept of multiresolution analysis applied to irregular meshes has become more and more important. Previous contributions proposed a variety of methods using simplification and/or subdivision algorithms to build a mesh pyramid. In this paper, we propose a multiresolution analysis framework for irregular meshes with attributes. Our framework is based on simplification and subdivision algorithms to build a mesh pyramid. We introduce a surface relaxation operator that allows to build a non-uniform subdivision for a low computational cost. Furthermore, we generalize the relaxation operator to attributes such as color, texture, temperature, etc. The attribute analysis gives more information on the analysed models allowing more complete processing. We show the efficiency of our framework through a number of applications including filtering, denoising and adaptive simplification.

The object of this work is 3D directional structures detection. The detection is based on steerable filters, which can be steered to any orientation fixed by the user, and are synthesized using a limited number of basis filters. These filters are used in a recursive multi-scale transform: the steerable pyramid. 2D multiscale approaches using oriented filters have proved to be efficient to detect such curvilinear patterns. We develop a 3D extension of the steerable pyramid to analyze volumes with a desired number of filters.