| I. Cohen, S. Raz and D. Malah, "Translation-invariant denoising using the minimum description length criterion", Technical Report, CC PUB No. 246, Technion - Israel Institute of Technology, Haifa, Israel, June 1998 (submitted to Signal Processing). |
....chosen bases from the library than in a fixed basis. Oracle inequalities do not deal with this part of the chain. For performance examples of specific libraries and signals, as well as more application oriented designs of thresholding and basis choice strategies, we refer to [KS] KTMD] [CRM]. In Section 2, we review the elements of hard thresholding for estimation and introduce our preferred brand of oracle inequality. Some basic inequalities and properties of Gaussian vectors are collected in Section 3. This material is an adaption to the present setting of the techniques from ....
I. Cohen, S. Raz and D. Malah, Translation-invariant denoising using the minimum description length criterion, Signal Processing, 75, 3, 201--223, (1999).
....research directions. We would like to note that Chapters 2 and 3 and part of Chapter 4 are the detailed and expanded version of our published materials. Chapter 2 is based on [27, 28] Chapter 3 is based on [29, 30, 31, 32] and part of Chapter 4 is based on [31, 33] Additional manuscripts [34, 35, 36, 37, 38], based on Chapters 4 and 5, are about to be published. 1.4 Background A natural framework for the understanding of wavelet bases, and for the construction of new examples, is provided by the multiresolution analysis (MRA) 92, 102, 53] A multiresolution analysis of L (IR) is a chain of ....
I. Cohen, S. Raz and D. Malah, "Translation-invariant denoising using the minimum description length criterion", Technical Report, CC PUB No. 246, Technion - Israel Institute of Technology, Haifa, Israel, June 1998 (submitted to Signal Processing).
.... 3 ln N; 1 n N Psi : 9) Hence, L1 L2 = 1 2oe 2 ln 2 N X n=1 min Gamma y 2 n ; 3oe 2 ln N Delta : 10) Step 3: A SIWPD tree can be specified by a 3 ary string, which contains 2s for terminal nodes, and either 0s or 1s for internal nodes, depending on their expansion mode [12]. There are jEj terminal nodes and jEj Gamma 1 internal nodes, where jEj is the cardinality of E. Since the tree always ends with a terminal node, the last 2 in the string can be discarded, and thus we need to encode a sequence containing jEj Gamma 1 2s and jEj Gamma 1 symbols from f0; 1g, The ....
....the widths (uncertainties) in time and frequency. Similar notations apply to OE k 0 . The proposed estimate is robust to noise and possesses the useful properties of the modified Wigner distribution, namely high energy concentration, well delineated components, low interference terms, etc. [12]. 5. AN EXAMPLE A synthetic signal, created by a linear superposition of a few wavelet packets (12 Gammatap coiflet filters) and a noisy version with signal to noise ratio SNR= 7dB are depicted in Figs. 1(a) b) The optimal SIWPD of the noisy signal using the MDL criterion is shown in Fig. ....
I. Cohen, S. Raz and D. Malah, "Translation-invariant denoising using the minimum description length criterion ", Tech. Rep., CC PUB No. 246, Dept. of Elect. Eng., Technion - IIT, Israel, June 1998.
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