Processing the data at large dimension scale is becoming one of the great challenges of the 21st century. The most notable recent advances in statistical data analysis and numerical simulation are based on the idea that in several situations, even for very complex phenomena, only a few governing components turn out to efficiently describe the whole dynamics: a dimensionality reduction can be achieved by considering the solution be "sparse" or "compressible". Since the relevant degrees of freedom are not prescribed and may depend on the particular solution, we need computationally efficient statistical methods for solving the hard combinatorial problem of identifying them. Sparsity is now a cornerstone of many modern statistical methods which exploits in different ways the well known principle that statistical estimation becomes easier when the underlying object lies in a low dimensional subspace even though this subspace is unknown and lives within a high dimensional space. In the early 90's, Donoho and Johnstone exploited the sparsity of Besov body spaces modelled on an arbitrary unconditional basis and proved that it suffices to threshold the empirical coefficients to obtain a (quasi) optimal estimator in the minimax sense. If the unconditional basis is chosen to be a wavelet basis, this methodology produces a fast, simple and efficient algorithm to estimate function lying in standard Besov spaces. Several extensions have since been provided: with different thresholding scheme, different bases or frames, or for different kind of data, including dependent data as well as indirect data. If one relax the ``orthogonal'' structure of the basis, allowing more general dictionaries, thresholding is not efficient anymore and the related model selection with dimension penalization becomes computationally untractable. Replacing the dimension ( l^0 norm), by the l^1 norm yields a tractable convex minimization problem socalled Lasso. These estimators are surprisingly efficient. Their properties have been studied, especially in the aggregation context, to understand the minimal assumptions required on the family of atoms. Several variations on the penalization scheme have then been proposed: data driven penalties, non convex penalties,... More recently, a novel efficient principle of aggregation EAW, based on PAC Bayesian approach, has been developed to further reduce the assumptions. The PARCIMONIE project is dedicated to the study of sparsity based estimators. Our main goal is to derive several novel sparsity based estimators and investigate their properties using various criteria: theoretical ones (minimaxity, maxisets, oracle type inequalities), experimental ones (comparison on simulation, competition on several common targets). Applications of our methods is an important issue as well as a motivation. As a consequence an important part of the project is oriented toward real applications (Biology, Astrophysics and Image processing). We need to understand the type of representations that need be used in each application, choosing the proper building blocks; we need to implement the estimators. The project is organized around 4 tasks: Estimation (How to select atoms'), Representations (Which atoms/representation to use'), Algorithms (How to compute the estimators'), and Applications (Which estimator to use'). In the Estimation task, we will focus on sparse estimators linked to 5 different (but related) techniques: model selection and thresholding, especially in the inverse problem context, multiple testing procedures, lasso and l^p penalization with p<1, individual sequences, and EAC/BAC bayesian aggregation. The Representation task is devoted to the study of the building blocks of the sparse estimators, we will look particularly to adapted wavelets and needlets, single index models and graphical models. In the Algorithm task, since our estimators will require in their implementation minimization algorithms or MCMC computations, we will have to tackle the issue of the computability. The Application task will use the estimation of biological networks, the CMB anisotropy, the AUGER experiment, and the Radon transform as both a benchmark and an inspiration source. Besides the classical scientific communication of our results (talks, conferences and publications in journal), the PARCIMONIE project intends to deliver three contributions: the organization of 2 international workshops, the publication of the algorithms with their source code in a web site -so that they are available to the community and can be used by practitioners-, and a web page on sparse estimation that could be the reference on the subject -as Rice's website is on the related subject of ``compressive sensing''-.