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  • 1.
    Andersson, Joel
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Strömberg, Jan-Olov
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    On the Theorem of Uniform Recovery of Random Sampling Matrices2014Inngår i: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 60, nr 3, s. 1700-1710Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.

  • 2. Averbuch, A. Z.
    et al.
    Meyer, F.
    Strömberg, Jan-Olov
    KTH, Tidigare Institutioner                               , Matematik.
    Coifman, R.
    Vassiliou, A.
    Low bit-rate efficient compression for seismic data2001Inngår i: IEEE Transactions on Image Processing, ISSN 1057-7149, E-ISSN 1941-0042, Vol. 10, nr 12, s. 1801-1814Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.

  • 3. Boman, J.
    et al.
    Strömberg, Jan-Olov
    KTH, Tidigare Institutioner, Matematik.
    Novikov's inversion formula for the attenuated radon transform - A new approach2004Inngår i: Journal of Geometric Analysis, ISSN 1050-6926, E-ISSN 1559-002X, Vol. 14, nr 2, s. 185-198Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.

  • 4.
    Carlqvist, Håkan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Nikulin, Vadim V.
    Department of Clinical Neuroscience, Karolinska Institutet, Karolinska University Hospital, Stockholm.
    Strömberg, Jan-Olov
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Brismar, T.
    Department of Clinical Neuroscience, Karolinska Institutet, Karolinska University Hospital, Stockholm.
    Amplitude and phase relationship between alpha and beta oscillations in the human electroencephalogram2005Inngår i: Medical and Biological Engineering and Computing, ISSN 0140-0118, E-ISSN 1741-0444, Vol. 43, nr 5, s. 599-607Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.

  • 5.
    Carlqvist, Håkan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Strömberg, Jan-Olov
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Improved classification of multidimensional signals using orthogonality properties of a time-frequency libraryArtikkel i tidsskrift (Annet vitenskapelig)
  • 6.
    Carlqvist, Håkan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Sundberg, Rolf
    Strömberg, Jan-Olov
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    A local discriminant basis algorithm using wavelet packets for discrimination between classes of mulridimensionals signalsArtikkel i tidsskrift (Annet vitenskapelig)
  • 7. Ericsson, S.
    et al.
    Grip, N.
    Johansson, E.
    Persson, L. E.
    Sjoberg, R.
    Strömberg, Jan-Olov
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Towards automatic detection of local bearing defects in rotating machines2005Inngår i: Mechanical systems and signal processing, ISSN 0888-3270, E-ISSN 1096-1216, Vol. 19, nr 3, s. 509-535Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    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.

  • 8.
    Iakovlev, Alexander S.
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Strömberg, Jan-Olov
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Lower bounds for the weak type (1, 1) estimate for the maximal function associated to cubes in high dimensions2013Inngår i: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 20, nr 5, s. 907-918Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we will provide the quantitative estimation for the dependence of a lower bound of the Hardy-Littlewood maximal function. This work was inspired by the paper [1] of Stein and Strömberg where general properties of the maximal function were studied. In that work, the increase with the dimension d of the constant Ad that appears in the weak type (1, 1) inequality for the maximal function was proved however no estimation were given. In a recent paper [2], J.M. Aldaz showed that the lowest constant Ad tends to infinity as the dimension d → ∞. In this paper, we improve the result of J.M. Aldaz providing quantitative estimation of Ad ≥ Cd1/4, where C is a constant independent of d.

  • 9. Meyer, F. G.
    et al.
    Averbuch, A. Z.
    Strömberg, Jan-Olov
    KTH, Tidigare Institutioner                               , Matematik.
    Fast adaptive wavelet packet image compression2000Inngår i: IEEE Transactions on Image Processing, ISSN 1057-7149, E-ISSN 1941-0042, Vol. 9, nr 5, s. 792-800Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Wavelets are ill-suited to represent oscillatory patterns: rapid variations of intensity can only be described by the small scale wavelet coefficients, which are often quantized to zero, even at high bit rates. Our goal in this paper is to provide a fast numerical implementation of the best wavelet packet algorithm [1] in order to demonstrate that an advantage can be gained by constructing a basis adapted to a target image. Emphasis in this paper has been placed on developing algorithms that are computationally efficient. We developed a new fast two-dimensional (2-D) convolution-decimation algorithm with factorized nonseparable 2-D filters. The algorithm is four times faster than a standard convolution-decimation, An extensive evaluation of the algorithm was performed on a large class of textured images. Because of its ability to reproduce textures so well, the wavelet packet coder significantly out performs one of the best wavelet coder [2] on images such as Barbara and fingerprints, both visually and in term of PSNR.

  • 10. Ryner, Martin
    et al.
    Strömberg, Jan-Olov
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Soderberg-Naucler, Cecilia
    Homman-Loudiyi, Mohammed
    Identification and classification of human cytomegalovirus capsids in textured electron micrographs using deformed template matching2006Inngår i: Virology Journal, ISSN 1743-422X, Vol. 3Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Background: Characterization of the structural morphology of virus particles in electron micrographs is a complex task, but desirable in connection with investigation of the maturation process and detection of changes in viral particle morphology in response to the effect of a mutation or antiviral drugs being applied. Therefore, we have here developed a procedure for describing and classifying virus particle forms in electron micrographs, based on determination of the invariant characteristics of the projection of a given virus structure. The template for the virus particle is created on the basis of information obtained from a small training set of electron micrographs and is then employed to classify and quantify similar structures of interest in an unlimited number of electron micrographs by a process of correlation. Results: Practical application of the method is demonstrated by the ability to locate three diverse classes of virus particles in transmission electron micrographs of fibroblasts infected with human cytomegalovirus. These results show that fast screening of the total number of viral structures at different stages of maturation in a large set of electron micrographs, a task that is otherwise both time-consuming and tedious for the expert, can be accomplished rapidly and reliably with our automated procedure. Using linear deformation analysis, this novel algorithm described here can handle capsid variations such as ellipticity and furthermore allows evaluation of properties such as the size and orientation of a virus particle. Conclusion: Our methodological procedure represents a promising objective tool for comparative studies of the intracellular assembly processes of virus particles using electron microscopy in combination with our digitized image analysis tool. An automated method for sorting and classifying virus particles at different stages of maturation will enable us to quantify virus production in all stages of the virus maturation process, not only count the number of infectious particles released from un infected cell.

  • 11. Sennerstam, R. B.
    et al.
    Strömberg, Jan-Olov
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
    Young breast cancer patients aged <40 years and tumor DNA ploidy progression2017Inngår i: Bulletin of the John Rylands University Library of Manchester, ISSN 0301-102X, Vol. 39, nr 2, s. 57-68Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    OBJECTIVE: To study tumor progression in a simulation model following tetraploidization (TPZ) and the establishment of aneuploid tumors in a population of young women (aged < 40 years) with breast cancer. STUDY DESIGN: A sample of 284 women aged < 40 years, retrieved from 5,875 randomized breast cancer patients treated from 1991-2000, were studied. The tumors were analyzed for chromosomal instability and proliferative activity called the stem-line scatter index (SSI). The dynamic interactive relationship between diploid, tetraploid, and aneuploid tumors was followed during increasing age and related to SSI values and tumor size. RESULTS: TPZ occurred early in tumor progression in the lower ages and was followed by hypotetraploid and further down to hypertriploid tumors, in the end reaching hypotriploid tumors for women aged >34 years. During tumor progression we observed a reduced frequency of diploid tumors from 71.7% to 14.3% (p < 0.00001), and triploid tumors increased from 13.2% (6 < SSI < 15 relative units) to 40.2% (20<SSI<60 relative units) (p<0.0001). CONCLUSION: During carcinogenesis aneuploid tumors appeared mainly from genomically destabilized tetraploid tumors, subsequently reaching the aggressive aneuploid tumors mainly in the hypertriploid region. These results increase our understanding of the importance of TPZ during carcinogenesis of breast cancer.

  • 12.
    Strömberg, Jan-Olov
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Detection and classification of virus from electron micrograms2010Inngår i: INDEPENDENT COMPONENT ANALYSES, WAVELETS, NEURAL NETWORKS, BIOSYSTEMS, AND NANOENGINEERING VIII / [ed] Szu HH; Agee FJ, 2010, Vol. 7703Konferansepaper (Fagfellevurdert)
    Abstract [en]

    I will present a PhD project were Diffusion Geometry is used in classification of virus particles in cell kernels from electron micrograms. I will give a very short introduction to Diffusion Geometry and discuss the main classification steps. Some preliminary result from a Master Thesis will be presented.

  • 13.
    Strömberg, Jan-Olov
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Andersson, Joel
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    An identity for triplets of double Hilbert transforms, with applications to the attenuated Radon transform2012Inngår i: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 28, nr 12, s. 125007-Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider an elementary identity for double singular integrals in the plane and show that one can apply this to deduce inversion and product formulae for the Hilbert transform and inversion formulae for the affine and weighted Radon transforms. We will be able to allow many of the previously known weights for which there is an inversion formula for the weighted Radon transform and also pose some new conditions on which weights that can be used.

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