Multiresolution analysis

About: Multiresolution analysis is a research topic. Over the lifetime, 4032 publications have been published within this topic receiving 140743 citations. The topic is also known as: Multiresolution analysis, MRA.

Space-Frequency Quantization for Image Compression With Directionlets

Abstract: The standard separable 2-D wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to efficiently capture 1-D discontinuities, like edges or contours. These features, being elongated and characterized by geometrical regularity along different directions, intersect and generate many large magnitude wavelet coefficients. Since contours are very important elements in the visual perception of images, to provide a good visual quality of compressed images, it is fundamental to preserve good reconstruction of these directional features. In our previous work, we proposed a construction of critically sampled perfect reconstruction transforms with directional vanishing moments imposed in the corresponding basis functions along different directions, called directionlets. In this paper, we show how to design and implement a novel efficient space-frequency quantization (SFQ) compression algorithm using directionlets. Our new compression method outperforms the standard SFQ in a rate-distortion sense, both in terms of mean-square error and visual quality, especially in the low-rate compression regime. We also show that our compression method, does not increase the order of computational complexity as compared to the standard SFQ algorithm.

Wavelets and Fast Numerical Algorithms

Abstract: Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive definition of wavelets, their controllable localization in both space and wave number (time and frequency) domains, and the vanishing moments property, wavelet based algorithms exhibit new and important properties. For example, the multiresolution structure of the wavelet expansions brings about an efficient organization of transformations on a given scale and of interactions between different neighbouring scales. Moreover, wide classes of operators which naively would require a full (dense) matrix for their numerical description, have sparse representations in wavelet bases. For these operators sparse representations lead to fast numerical algorithms, and thus address a critical numerical issue. We note that wavelet based algorithms provide a systematic generalization of the Fast Multipole Method (FMM) and its descendents. These topics will be the subject of the lecture. Starting from the notion of multiresolution analysis, we will consider the so-called non-standard form (which achieves decoupling among the scales) and the associated fast numerical algorithms. Examples of non-standard forms of several basic operators (e.g. derivatives) will be computed explicitly.

Content adaptive watermarking based on a stochastic multiresolution image modeling

Abstract: In this paper, a wavelet domain robust watermarking technique for still images is presented. The proposed watermarking algorithm is based on 3 key aspects. First, message encoding is accomplished based on iterative error correction codes to reach channel capacity with reasonable decoder complexity. Secondly, watermark embedding is performed in the wavelet domain using a stochastically driven perceptual criterion to provide watermark invisibility. Thirdly, a new principle of watermark spatial allocation, based on the watermark magnitude spectrum, is proposed to recover from general affine geometrical distortions.

Orthonormal Bases of Wavelets with Finite Support — Connection with Discrete Filters

Abstract: We define wavelets and the wavelet transform. After discussing their basic properties, we focus on orthonormal bases of wavelets, in particular bases of wavelets with finite support.

Automatic registration of satellite images

Abstract: Image registration is one of the basic image processing operations in remote sensing. With the increase in the number of images collected every day from different sensors, automated registration of multi-sensor/multi-spectral images has become an important issue. A wide range of registration techniques has been developed for many different types of applications and data. Given the diversity of the data, it is unlikely that a single registration scheme will work satisfactorily for all different applications. A possible solution is to integrate multiple registration algorithms into a rule-based artificial intelligence system, so that appropriate methods for any given set of multisensor data can be automatically selected. The objective of this paper is to present an automatic registration algorithm which has been developed at INPE. It uses a multiresolution analysis procedure based upon the wavelet transform. The procedure is completely automatic and relies on the grey level information content of the images and their local wavelet transform modulus maxima. The algorithm was tested on SPOT and TM images from forest, urban and agricultural areas. In all cases we obtained very encouraging results.