| 1. |
- Andersson, Joel
(författare)
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On Invertibility of the Radon Transform and Compressive Sensing
- 2014
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis contains three articles. The first two concern inversion andlocal injectivity of the weighted Radon transform in the plane. The thirdpaper concerns two of the key results from compressive sensing.In Paper A we prove an identity involving three singular double integrals.This is then used to prove an inversion formula for the weighted Radon transform,allowing all weight functions that have been considered previously.Paper B is devoted to stability estimates of the standard and weightedlocal Radon transform. The estimates will hold for functions that satisfy an apriori bound. When weights are involved they must solve a certain differentialequation and fulfill some regularity assumptions.In Paper C we present some new constant bounds. Firstly we presenta version of the theorem of uniform recovery of random sampling matrices,where explicit constants have not been presented before. Secondly we improvethe condition when the so-called restricted isometry property implies the nullspace property.
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| 2. |
- Andersson, Joel, et al.
(författare)
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On the Theorem of Uniform Recovery of Random Sampling Matrices
- 2014
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Ingår i: IEEE Transactions on Information Theory. - 0018-9448 .- 1557-9654. ; 60:3, s. 1700-1710
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Tidskriftsartikel (refereegranskat)abstract
- We consider two theorems from the theory of compressive sensing. Mainly a theorem concerning uniform recovery of random sampling matrices, where the number of samples needed in order to recover an s-sparse signal from linear measurements (with high probability) is known to be m greater than or similar to s(ln s)(3) ln N. We present new and improved constants together with what we consider to be a more explicit proof. A proof that also allows for a slightly larger class of m x N-matrices, by considering what is called effective sparsity. We also present a condition on the so-called restricted isometry constants, delta s, ensuring sparse recovery via l(1)-minimization. We show that delta(2s) < 4/root 41 is sufficient and that this can be improved further to almost allow for a sufficient condition of the type delta(2s) < 2/3.
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| 3. |
- Averbuch, A. Z., et al.
(författare)
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Low bit-rate efficient compression for seismic data
- 2001
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Ingår i: IEEE Transactions on Image Processing. - : Institute of Electrical and Electronics Engineers (IEEE). - 1057-7149 .- 1941-0042. ; 10:12, s. 1801-1814
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Tidskriftsartikel (refereegranskat)abstract
- Compression is a relatively new introduced technique for seismic data operations. The main drive behind the use of data compression in seismic data is the very large size of seismic data acquired. Some of the most recent acquired marine seismic data sets exceed 10 Tbytes, and in fact there are currently seismic surveys planned with a volume of around 120 Tbytes. Thus, the need to compress these very large seismic data riles is imperative. Nevertheless, seismic data are quite different from the typical images used in image processing and multimedia applications. Some of their major differences are the data dynamic range exceeding 100 dB in theory, very often it is data with extensive oscillatory nature, the x and y directions represent different physical meaning, and there is significant amount of coherent noise which is often present in seismic data. Up to now some of the algorithms used for seismic data compression were based on some form of wavelet or local cosine transform. while using a uniform or quasiuniform quantization scheme and they finally employ a Huffman coding scheme. Using this family of compression algorithms we achieve compression results which are acceptable to geophysicists, only at low to moderate compression ratios. For higher compression ratios or higher decibel quality, significant compression artifacts are introduced in the reconstructed images, even with high-dimensional transforms. The objective of this paper is to achieve higher compression ratio, than achieved with the wavelet/uniform quantization/Huffman coding family of compression schemes, with a comparable level of residual noise. The goal is to achieve above 40 dB in the decompressed seismic data sets. Several established compression algorithms are reviewed, and some new compression algorithms are introduced. All of these compression techniques are applied to a good representation of seismic data sets, and their results are documented in this paper. One of the conclusions is that adaptive multiscale local cosine transform with different windows sizes performs well on all the seismic data sets and outperforms the other methods from the SNR point of view. All the described methods cover wide range of different data sets. Each data set will have his own best performed method chosen from this collection. The results were performed on four different seismic data sets. Special emphasis was given to achieve faster processing speed which is another critical issue that is examined in the paper. Some of these algorithms are also suitable for multimedia type compression.
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| 4. |
- Boman, J., et al.
(författare)
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Novikov's inversion formula for the attenuated radon transform - A new approach
- 2004
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Ingår i: Journal of Geometric Analysis. - 1050-6926 .- 1559-002X. ; 14:2, s. 185-198
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Tidskriftsartikel (refereegranskat)abstract
- We study the inversion of weighted Radon transforms in two dimensions, R-rho f (L) = f(L) f((.)) rho (L, (.)) ds, where the weight function rho (L, x), L a line and x is an element of L, has a special form. It was an important breakthrough when R. G. Novikov recently gave an explicit formula for the inverse of R-rho When rho has the form (1.2); in this case R-rho is called the attenuated Radon transform. Here. we prove similar results,for a somewhat larger class of rho using completely different and quite elementary methods.
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| 5. |
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| 6. |
- Carlqvist, Håkan, et al.
(författare)
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Amplitude and phase relationship between alpha and beta oscillations in the human electroencephalogram
- 2005
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Ingår i: Medical and Biological Engineering and Computing. - 0140-0118 .- 1741-0444. ; 43:5, s. 599-607
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Tidskriftsartikel (refereegranskat)abstract
- The relationship between the electro-encephalographic (EEG) alpha and beta oscillations in the resting condition was investigated in the study. EEGs were recorded in 33 subjects, and alpha (7.5-12.5Hz) and beta (15-25Hz) oscillations were extracted with the use of a modified wavelet transform. Power, peak frequency and phase synchronisation were evaluated for both types of oscillation. The average beta-alpha peak frequency ratio was about 1.9-2.0 for all electrode derivations. The peak frequency of beta activity was within 70-90 % of the 95 % confidence interval of twice the alpha frequency. A significant (p < 0.05) linear regression was found between beta and alpha power in all derivations in 32 subjects, with the slope of the regression line being approximate to 0.3. There was no significant difference in the slope of the line in different electrode locations, although the power correlation was strongest in the occipital locations where alpha and beta oscillations had the largest power. A significant 1:2 phase synchronisation was present between the alpha and beta oscillations, with a phase lag of about pi/2 in all electrode derivations. The strong frequency relationship between the resting beta and alpha oscillations suggests that they are generated by a common mechanism. Power and phase relationships were weaker suggesting that these properties can be modulated by additional mechanisms as well as be influenced by noise. A careful distinction between alpha-dependent and alpha-independent beta activity should be considered when making statements about the possible significance of genuine beta activity in different neurophysiological mechanisms.
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| 7. |
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| 8. |
- Carlqvist, Håkan, 1967-
(författare)
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Multiscale analysis of multi-channel signals
- 2005
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- I: Amplitude and phase relationship between alpha and beta oscillations in the human EEG We have studied the relation between two oscillatory patterns within EEG signals (oscillations with main frequency 10 Hz and 20 Hz), with wavelet-based methods. For better comparison, a variant of the continuous wavelet transform, was derived. As a conclusion, the two patterns were closely related and 70-90 % of the activity in the 20 Hz pattern could be seen as a resonance phenomenon of the 10 Hz activity. II: A local discriminant basis algorithm using wavelet packets for discrimination between classes of multidimensional signals We have improved and extended the local discriminant basis algorithm for application on multidimensional signals appearing from multichannels. The improvements includes principal-component analysis and crossvalidation- leave-one out. The method is furthermore applied on two classes of EEG signals, one group of control subjects and one group of subjects with type I diabetes. There was a clear discrimination between the two groups. The discrimination follows known differences in the EEG between the two groups of subjects. III: Improved classification of multidimensional signals using orthogonality properties of a time-frequency library We further improve and refine the method in paper2 and apply it on 4 classes of EEG signals from subjects differing in age and/or sex, which are known factors of EEG alterations. As a method for deciding the best basis we derive an orthogonalbasis- pursuit-like algorithm which works statistically better (Tukey's test for simultaneous confidence intervals) than the basis selection method in the original local discriminant basis algorithm. Other methods included were Fisher's class separability, partial-least-squares and cross-validation-leave-one-subject out. The two groups of younger subjects were almost fully discriminated between each other and to the other groups, while the older subjects were harder to discriminate.
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| 9. |
- Ericsson, Stefan, et al.
(författare)
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Towards automatic detection of local bearing defects in rotating machines
- 2005
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Ingår i: Mechanical systems and signal processing. - : Elsevier BV. - 0888-3270 .- 1096-1216. ; 19:3, s. 509-535
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we derive and compare several different vibration analysis techniques for automatic detection of local defects in bearings. Based on a signal model and a discussion on to what extent a good bearing monitoring method should trust it, we present several analysis tools for bearing condition monitoring and conclude that wavelets are especially well suited for this task. Then we describe a large-scale evaluation of several different automatic bearing monitoring methods using 103 laboratory and industrial environment test signals for which the true condition of the bearing is known from visual inspection. We describe the four best performing methods in detail (two wavelet-based, and two based on envelope and periodisation techniques). In our basic implementation, without using historical data or adapting the methods to (roughly) known machine or signal parameters, the four best methods had 9-13% error rate and are all good candidates for further fine-tuning and optimisation. Especially for the wavelet-based methods, there are several potentially performance improving additions, which we finally summarise into a guiding list of suggestion.
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| 10. |
- Hellgren, Mikko, 1972-, et al.
(författare)
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Alcohol dehydrogenase 2 is a major hepatic enzyme for human retinol metabolism
- 2007
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Ingår i: Cellular and Molecular Life Sciences (CMLS). - : Springer. - 1420-682X .- 1420-9071. ; 64:4, s. 498-505
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Tidskriftsartikel (refereegranskat)abstract
- The metabolism of all-trans- and 9-cis-retinol/ retinaldehyde has been investigated with focus on the activities of human, mouse and rat alcohol dehydrogenase 2 (ADH2), an intriguing enzyme with apparently different functions in human and rodents. Kinetic constants were determined with an HPLC method and a structural approach was implemented by in silico substrate dockings. For human ADH2, the determined K(m) values ranged from 0.05 to 0.3 microM and k(cat) values from 2.3 to 17.6 min(-1), while the catalytic efficiency for 9-cis-retinol showed the highest value for any substrate. In contrast, poor activities were detected for the rodent enzymes. A mouse ADH2 mutant (ADH2Pro47His) was studied that resembles the human ADH2 setup. This mutation increased the retinoid activity up to 100-fold. The K(m) values of human ADH2 are the lowest among all known human retinol dehydrogenases, which clearly support a role in hepatic retinol oxidation at physiological concentrations.
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