By Jean-Luc Starck Fionn D. Murtagh Albert Bijaoui
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Extra info for Image Processing and Data Analysis : The Multiscale Approach, 1st Edition
In this case, we take the logarithm of the image, and the resulting image is treated as for additive nonuniform noise above. Unknown noise. 1 Definition The multiresolution support (Starck, Murtagh and Bijaoui, 1995) of an image describes in a logical or boolean way whether an image / contains information at a given scale j and at a given position (x, y). If M (/) (j,x,y) = 1 (or true), then / contains information at scale j and at the position (x,j/). M depends on several parameters: - The input image.
We get the array Tj+1. Its inverse FFT gives the image at scale 2-/'+1. The frequency band is reduced by a factor 2. 6 Increment j . 7 If j < np, go back to step 4. ,wnp,cnp} describes the wavelet transform. e. 71) then the wavelet coefficients w/(v) can be computed by c;-_i(v) — c/(v). Reconstruction. 72) But this is a particular case, and other alternative wavelet functions can be chosen. The reconstruction can be made step-by-step, starting from the lowest resolution. 74) We look for Cj knowing c 7+ i, w/ + i, h and g.
We would simply correct, in a multiplicative manner, for the consistent underestimate of results in this range of intensity values, as evidenced by Fig. 1c. Such situations may be particularly relevant for the outlying parts of extended objects where intensity values are close to low background values. We expect the centers of extended astronomical objects, or point sources (respectively galaxies and stars, for instance), to have sufficient associated counts such that a bias correction is not needed.