There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Information Theory and Reliable Communication

Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).

MUCKE aims to mine a large volume of images, to structure them conceptually and to use this conceptual structuring in order to improve large-scale image retrieval. The last decade witnessed important progress concerning low-level image representations. However, there are a number problems which need to be solved in order to unleash the full potential of image mining in applications. The central problem with low-level representations is the mismatch between them and the human interpretation of image content. This problem can be instantiated, for instance, by the incapability of existing descriptors to capture spatial relationships between the concepts represented or by their incapability to convey an explanation of why two images are similar in a content-based image retrieval framework. We start by assessing existing local descriptors for image classification and by proposing to use co-occurrence matrices to better capture spatial relationships in images. The main focus in MUCKE is on cleaning large scale Web image corpora and on proposing image representations which are closer to the human interpretation of images. Consequently, we introduce methods which tackle these two problems and compare results to state of the art methods. Note: some aspects of this deliverable are withheld at this time as they are pending review. Please contact the authors for a preview.

http://ieeexplore.ieee.org/iel2/4524/12820/00592460.pdf

Image Processing

High peak-to-average power ratio of the transmit signal is a major drawback of multicarrier transmission such as OFDM or DMT. This article describes some of the important PAPR reduction techniques for multicarrier transmission including amplitude clipping and filtering, coding, partial transmit sequence, selected mapping, interleaving, tone reservation, tone injection, and active constellation extension. Also, we make some remarks on the criteria for PAPR reduction technique selection and briefly address the problem of PAPR reduction in OFDMA and MIMO-OFDM.

An overview of peak-to-average power ratio reduction techniques for multicarrier transmission

1. Introduction F. Marvasti. 2. An Introduction to Sampling Analysis P.L. Butzer, et al. 3. Lagrange Interpolation and Sampling Theorems A.I. Zayed, P.L. Butzer. 4. Random Topics in Nonuniform Sampling F. Marvasti. 5. Iterative and Noniterative Recovery of Missing Samples for 1-{D} Band-Limited Signals P.J.S.G. Ferreira. 6. Numerical and Theoretical Aspects of Nonuniform Sampling of Band-Limited Images K. Grochenig, T. Strohmer. 7. The Nonuniform Discrete Fourier Transform S. Bagchi, S.K. Mitra. 8. Reconstruction of Stationary Processes Sampled at Random Times B. Lacaze. 9. Zero Crossings of Random Processes with Application to Estimation and Detection J. Barnett. 10. Magnetic Resonance Image Reconstruction from Nonuniformly Sampled k-Space Data F.T.A.W. Wajer, et al. 11. Irregular and Sparse Sampling in Exploration Seismology A.J.W. Duijndam, et al. 12. Randomized Digital Optimal Control W.L. de Koning, L.G. van Willigenburg. 13. Prediction of Band-Limited Signals from Past Samples and Applications to Speech Coding D.H. Muler, Y. Wu. 14. Frames, Irregular Sampling, and a Wavelet Auditory Model J.J. Benedetto, S. Scott. 15. Application of the Nonuniform Sampling to Motion Compensated Prediction A. Sharif, et al. 16. Applications of Nonuniform Sampling to Nonlinear Modulation, A/D and D/A Techniques F. Marvasti, M. Sandler. 17. Applications to Error Correction Codes F. Marvasti. 18. Application of Nonuniform Sampling to Error Concealment M. Hasan, F. Marvasti. 19. Sparse Sampling in Array Processing S. Holm, et al. 20. Fractional Delay Filters: Design and Applications V. Valimaki, T.I. Laakso.

Nonuniform sampling : theory and practice

An iterative method to recover a bandlimited signal from its ideal nonuniform samples is proposed. The convergence of iterations is proved, and general regions for convergence are found. It is shown that the iterative method is also applicable to other forms of nonuniform sampling, i.e. natural sampling and interpolated sampling (such as sample-and-hold signal). Simulation results show that this method works effectively and fairly fast, and the errors after a few iterations are negligible if a particular sufficient condition is satisfied or the sampling rate is higher than the Nyquist rate. >

Recovery of signals from nonuniform samples using iterative methods

In this paper, we establish the connection between the Orthogonal Optical Codes (OOC) and binary compressed sensing matrices. We also introduce deterministic bipolar m × n RIP fulfilling ±1 matrices of order k such that m ≤ O (k(log2n)( log2k)/( ln log2k)). The columns of these matrices are binary BCH code vectors where the zeros are replaced by -1. Since the RIP is established by means of coherence, the simple greedy algorithms such as Matching Pursuit are able to recover the sparse solution from the noiseless samples. Due to the cyclic property of the BCH codes, we show that the FFT algorithm can be employed in the reconstruction methods to considerably reduce the computational complexity. In addition, we combine the binary and bipolar matrices to form ternary sensing matrices ({0,1,-1} elements) that satisfy the RIP condition.

/pdf/deterministic-construction-of-binary-bipolar-and-ternary-10wgnrm0mk.pdf

Deterministic Construction of Binary, Bipolar, and Ternary Compressed Sensing Matrices

In this paper we establish the connection between the Orthogonal Optical Codes (OOC) and binary compressed sensing matrices. We also introduce deterministic bipolar $m\times n$ RIP fulfilling $\pm 1$ matrices of order $k$ such that $m\leq\mathcal{O}\big(k (\log_2 n)^{\frac{\log_2 k}{\ln \log_2 k}}\big)$. The columns of these matrices are binary BCH code vectors where the zeros are replaced by -1. Since the RIP is established by means of coherence, the simple greedy algorithms such as Matching Pursuit are able to recover the sparse solution from the noiseless samples. Due to the cyclic property of the BCH codes, we show that the FFT algorithm can be employed in the reconstruction methods to considerably reduce the computational complexity. In addition, we combine the binary and bipolar matrices to form ternary sensing matrices ($\{0,1,-1\}$ elements) that satisfy the RIP condition.

Deterministic Construction of Binary, Bipolar and Ternary Compressed Sensing Matrices

In this paper, an improved multiplicative image watermarking system is presented. Since human visual system is less sensitive to the image edges, watermarking is applied in the contourlet domain, which represents image edges sparsely. In the presented scheme, watermark data is embedded in directional subband with the highest energy. By modeling the contourlet coefficients with General Gaussian Distribution (GGD), the distribution of watermarked noisy coefficients is analytically calculated. The tradeoff between the transparency and robustness of the watermark data is solved in a novel fashion. At the receiver, based on the Maximum Likelihood (ML) decision rule, an optimal detector by the aid of channel side information is proposed. In the next step, a blind extension of the suggested algorithm is presented using the patchwork idea. Experimental results confirm the superiority of the proposed method against common attacks, such as Additive White Gaussian Noise (AWGN), JPEG compression, and rotation attacks, in comparison with the recently proposed techniques.

Farokh Marvasti

Papers

Nonuniform sampling : theory and practice

Recovery of signals from nonuniform samples using iterative methods

Deterministic Construction of Binary, Bipolar, and Ternary Compressed Sensing Matrices

Deterministic Construction of Binary, Bipolar and Ternary Compressed Sensing Matrices

Contourlet-Based Image Watermarking Using Optimum Detector in a Noisy Environment