The use of multicomponent images has become widespread with the improvement of multisensor systems having increased spatial and spectral resolutions. However, the observed images are often corrupted by an additive Gaussian noise. In this paper, we are interested in multichannel image denoising based on a multiscale representation of the images. A multivariate statistical approach is adopted to take into account both the spatial and the inter-component correlations existing between the different wavelet subbands. More precisely, we propose a new parametric nonlinear estimator which generalizes many reported denoising methods. The derivation of the optimal parameters is achieved by applying Stein’s principle in the multivariate case. Experiments performed on multispectral remote sensing images clearly indicate that our method outperforms conventional wavelet denoising techniques.

Over-complete representations of images such as undecimated wavelets have enjoyed immense popularity in recent years. Though they are efficient for modeling singularities and edges, natural images also consist of textures that are difficult to capture with any canonical transformation. In this work, we develop a new modeling strategy with a rigorous treatment of textured regions. Using principal components analysis as an approximate classifier for edges and textures, we partition an image into compressible and incompressible regions—with corresponding models matching their behaviors. A posterior median-based denoising method using these models is described with preliminary results that demonstrate the effectiveness of this approach. Index Terms — principal components analysis, sparsity, image denoising, image modeling, textures. 1.

Signal acquisition is a noisy business. In photographic images, there is noise within the light intensity signal (e.g., photon noise), and additional noise can arise within the sensor (e.g., thermal noise in a CMOS chip), as well as in subsequent processing (e.g., quantization). Image noise can be quite noticeable, as in images captured by inexpensive cameras built into cellular telephones, or imperceptible, as in images captured by

Redundancy in wavelets and filter banks has the potential to greatly improve signal and image denoising. Having developed a framework for optimized oversampled complex lapped transforms, we propose their association with the statistically efficient Stein’s principle in the context of mean square error estimation. Under Gaussian noise assumptions, expectations involving the (unknown) original data are expressed using the observation only. Two forms of Stein’s Unbiased Risk Estimators, derived in the coefficient and the spatial domain respectively, are proposed, the latter being more computationally expensive. These estimators are then employed for denoising with linear combinations of elementary threshold functions. Their performances are compared to the oracle, and addressed with respect to the redundancy. They are finally tested against other denoising algorithms. They prove competitive, yielding especially good results for texture preservation. 1.