Astronomical Image and Data Analysis (Astronomy and Astrophysics Library)
J.-L. Starck
Language: English
Pages: 338
ISBN: 3540330240
Format: PDF / Kindle (mobi) / ePub
Thisbookpresentsmaterialwhichismorealgorithmicallyorientedthanmost alternatives.Italsodealswithtopicsthatareatorbeyondthestateoftheart. Examples include practical and applicable wavelet and other multiresolution transform analysis. New areas are broached like the ridgelet and curvelet transforms. The reader will ?nd in this book an engineering approach to the interpretation of scienti?c data. Compared to the 1st Edition, various additions have been made throu- out, and the topics covered have been updated. The background or en- ronment of this book's topics include continuing interest in e-science and the virtual observatory, which are based on web based and increasingly web service based science and engineering. Additional colleagues whom we would like to acknowledge in this 2nd edition include: Bedros Afeyan, Nabila Aghanim, Emmanuel Cand es, David Donoho, Jalal Fadili, and Sandrine Pires, We would like to particularly - knowledge Olivier Forni who contributed to the discussion on compression of hyperspectral data, Yassir Moudden on multiwavelength data analysis and Vicent Mart ?nez on the genus function. The cover image to this 2nd edition is from the Deep Impact project. It was taken approximately 8 minutes after impact on 4 July 2005 with the CLEAR6 ?lter and deconvolved using the Richardson-Lucy method. We thank Don Lindler, Ivo Busko, Mike A'Hearn and the Deep Impact team for the processing of this image and for providing it to us.
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use an overlap to avoid blocking artifacts. For an 14 1. Introduction to Applications and Methods Fig. 1.6. Example of 2D ridgelet function. n × n image, we count 2n/B such blocks in each direction. The partitioning introduces redundancy, since a pixel belongs to 4 neighboring blocks. More details on the implementation of the digital ridgelet transform can be found in Starck et al. (2002; 2003a). The ridgelet transform is therefore optimal for detecting lines of a given size, equal to the
matching, identifying and locating object position. In this schema we start off with raw data (an array of grey-levels) and we end up with information – the identification and position of an object. As we progress, the data and processing move from low-level to high-level. Haralick and Shapiro (1985) give the following wish-list for segmentation: “What should a good image segmentation be? Regions of an image segmentation should be uniform and homogeneous with respect to some characteristic
oversampled images, the (I) values of the wavelet image corresponding to the first scale (w0 ) are nearly always due to the noise. The histogram shows a Gaussian peak around 0. We compute the standard deviation of this Gaussian function, with a 3σ clipping, rejecting pixels where the signal could be significant. 5. Computation of the wavelet transform of the clean beam. We get w(B) . j (B) u,2j v) . If the clean beam is a Dirac, then w ˆj (u, v) = ψ(2φ(u,v) 6. Set j to 0. 7. Estimation of the
The wavelet function is overplotted on the Sunyaev-Zel’dovich map and the curvelet function is overplotted on the cosmic string map. In order to illustrate this, we show in Fig. 4.11 a set of simulated maps. Primary CMB, kinetic SZ and cosmic string maps are shown respectively in Fig. 4.11 top left, top right and bottom left. The “simulated observed map”, containing the three previous components, is displayed in Fig. 4.11 bottom right. The primary CMB anisotropies dominate all the signals except
quantizer for example (Proakis, 1995). All other steps, shown in Table 5.1, such as reorganizing the quantized coefficients, hierarchical and statistical redundancy coding, and so on, will not compromise data integrity. This statement can be made for all packages. The main improvement clearly comes from an appropriate noise/signal discrimination and the choice of a transform appropriate to the objects’ properties. 5.2.6 Other Lossy Compression Methods The number of bits that we need for an accurate
