Statistics for Spatial Data.

This paper describes a new approach to low level image processing; in particular, edge and corner detection and structure preserving noise reduction.

Non-linear filtering is used to define which parts of the image are closely related to each individual pixel; each pixel has associated with it a local image region which is of similar brightness to that pixel. The new feature detectors are based on the minimization of this local image region, and the noise reduction method uses this region as the smoothing neighbourhood. The resulting methods are accurate, noise resistant and fast.

Details of the new feature detectors and of the new noise reduction method are described, along with test results.

SUSAN—A New Approach to Low Level Image Processing

Digital watermarking is a key ingredient to copyright protection. It provides a solution to illegal copying of digital material and has many other useful applications such as broadcast monitoring and the recording of electronic transactions. Now, for the first time, there is a book that focuses exclusively on this exciting technology. Digital Watermarking covers the crucial research findings in the field: it explains the principles underlying digital watermarking technologies, describes the requirements that have given rise to them, and discusses the diverse ends to which these technologies are being applied. As a result, additional groundwork is laid for future developments in this field, helping the reader understand and anticipate new approaches and applications.

Digital Watermarking

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

Imaging spectroscopy involves the sensing of a large amount of spatial information across a multitude of wavelengths. Conventional approaches to hyperspectral sensing scan adjacent zones of the underlying spectral scene and merge the results to construct a spectral data cube. Push broom spectral imaging sensors, for instance, capture a spectral cube with one focal plane array (FPA) measurement per spatial line of the scene [1], [2]. Spectrometers based on optical bandpass filters sequentially scan the scene by tuning the bandpass filters in steps. The disadvantage of these techniques is that they require scanning a number of zones linearly in proportion to the desired spatial and spectral resolution. This article surveys compressive coded aperture spectral imagers, also known as coded aperture snapshot spectral imagers (CASSI) [1], [3], [4], which naturally embody the principles of compressive sensing (CS) [5], [6]. The remarkable advantage of CASSI is that the entire data cube is sensed with just a few FPA measurements and, in some cases, with as little as a single FPA shot.

Compressive Coded Aperture Spectral Imaging: An Introduction

Preface. Acknowledgments. Acronyms. 1. Introduction. 1.1 Non--Gaussian Random Processes. 1.1.1 Generalized Gaussian Distributions and Weighted Medians. 1.1.2 Stable Distributions and Weighted Myriads. 1.2 Statistical Foundations. 1.3 The Filtering Problem. 1.3.1 Moment Theory. PART I: STATISTICAL FOUNDATIONS. 2. Non--Gaussian Models. 2.1 Generalized Gaussian Distributions. 2.2 Stable Distributions. 2.2.1 Definitions. 2.2.2 Symmetric Stable Distributions. 2.2.3 Generalized Central Limit Theorem. 2.2.4 Simulation of Stable Sequences. 2.3 Lower Order Moments. 2.3.1 Fractional Lower Order Moments. 2.3.2 Zero Order Statistics. 2.3.3 Parameter Estimation of Stable Distributions. Problems. 3. Order Statistics. 3.1 Distributions of Order Statistics. 3.2 Moments of Order Statistics. 3.2.1 Order Statistics From Uniform Distributions. 3.2.2 Recurrence Relations. 3.3 Order Statistics Containing Outliers. 3.4 Joint Statistics of Ordered and Non--Ordered Samples. Problems. 4. Statistical Foundations of Filtering. 4.1 Properties of Estimators. 4.2 Maximum Likelihood Estimation. 4.3 Robust Estimation. Problems. PART II: SIGNAL PROCESSING WITH ORDER STATISTICS. 5. Median and Weighted Median Smoothers. 5.1 Running Median Smoothers. 5.1.1 Statistical Properties. 5.1.2 Root Signals (Fixed Points). 5.2 Weighted Median Smoothers. 5.2.1 The Center Weighted Median Smoother. 5.2.2 Permutation Weighted Median Smoothers. 5.3 Threshold Decomposition Representation. 5.3.1 Stack Smoothers. 5.4 Weighted Medians in Least Absolute Deviation (LAD) Regression. 5.4.1 Foundation and Cost Functions. 5.4.2 LAD Regression with Weighted Medians. 5.4.3 Simulation. Problems. 6. Weighted Median Filters. 6.1 Weighted Median Filters With Real--Valued Weights. 6.1.1 Permutation Weighted Median Filters. 6.2 Spectral Design of Weighted Median Filters. 6.2.1 Median Smoothers and Sample Selection Probabilities. 6.2.2 SSPs for Weighted Median Smoothers. 6.2.3 Synthesis of WM Smoothers. 6.2.4 General Iterative Solution. 6.2.5 Spectral Design of Weighted Median Filters Admitting Real--Valued Weights. 6.3 The Optimal Weighted Median Filtering Problem. 6.3.1 Threshold Decomposition for Real--Valued Signals. 6.3.2 The Least Mean Absolute (LMA) Algorithm. 6.4 Recursive Weighted Median Filters. 6.4.1 Threshold Decomposition Representation of Recursive WM Filters. 6.4.2 Optimal Recursive Weighted Median Filtering. 6.5 Mirrored Threshold Decomposition and Stack Filters. 6.5.1 Stack Filters. 6.5.2 Stack Filter Representation of Recursive WM Filters. 6.6 Complex Valued Weighted Median Filter. 6.6.1 Phase Coupled Complex WM Filters. 6.6.2 Marginal Phase Coupled Complex WM Filter. 6.6.3 Complex Threshold Decomposition. 6.6.4 Optimal Marginal Phase Coupled Complex WM. 6.6.5 Spectral Design of Complex Valued Weighted Medians. 6.7 Weighted Median Filters for Multichannel Signals. 6.7.1 Marginal WM Filter. 6.7.2 Vector WM Filter. 6.7.3 Weighted Multichannel Median Filtering Structures. 6.7.4 Filter Optimization. Problems. 7. Linear Combination or Order Statistics. 7.1 L--Estimates of Location. 7.2 L--Smoothers. 7.3 L --Filters. 7.3.1 Design and Optimization of L Filters. 7.4 Lj Permutation Filters. 7.5 Hybrid Median/Linear FIR Filters. 7.5.1 Median and FIR Affinity Trimming. 7.6 Linear Combination of Weighted Medians. 7.6.1 LCWM Filters. 7.6.2 Design of LCWM Filters. 7.6.3 Symmetric LCWM Filters. Problems. PART III: SIGNAL PROCESSING WITH THE STABLE MODEL. 8. Myriad Smoothers. 8.1 FLOM Smoothers. 8.2 Running Myriad Smoothers. 8.3 Optimality of the Sample Myriad. 8.4 Weighted Myriad Smoothers. 8.5 Fast Weighted Myriad Computation. 8.6 Weighted Myriad Smoother Design. 8.6.1 Center Weighted Myriads for Image Denoising. 8.6.2 Myriadization. Problems. 9. Weighted Myriad Filters. 9.1 Weighted Myriad Filters with Real--Valued Weights. 9.2 Fast Real--Valued Weighted Myriad Computation. 9.3 Weighted Myriad Filter Design. 9.3.1 Myriadization. 9.3.2 Optimization. Problems. References. Appendix A: Software Guide. Index.

Nonlinear Signal Processing: A Statistical Approach

We introduce a new multiresolution watermarking method for digital images. The method is based on the discrete wavelet transform (DWT). Pseudo-random codes are added to the large coefficients at the high and middle frequency bands of the DWT of an image. It is shown that this method is more robust to often proposed methods to some common image distortions, such as the wavelet transform based image compression, and image halftoning. Moreover, the method is hierarchical. The computation load needed to detect the watermark depends on the noise level in an image.

A multiresolution watermark for digital images

Visual cryptography encodes a secret binary image (SI) into n shares of random binary patterns. If the shares are xeroxed onto transparencies, the secret image can be visually decoded by superimposing a qualified subset of transparencies, but no secret information can be obtained from the superposition of a forbidden subset. The binary patterns of the n shares, however, have no visual meaning and hinder the objectives of visual cryptography. Extended visual cryptography was proposed recently to construct meaningful binary images as shares using hypergraph colourings, but the visual quality is poor. In this paper, a novel technique named halftone visual cryptography is proposed to achieve visual cryptography via halftoning. Based on the blue-noise dithering principles, the proposed method utilizes the void and cluster algorithm to encode a secret binary image into n halftone shares (images) carrying significant visual information. The simulation shows that the visual quality of the obtained halftone shares are observably better than that attained by any available visual cryptography method known to date.

Halftone visual cryptography

In this paper, ultra-wideband (UWB) channel estimation based on the theory of compressive sensing (CS) is developed. The proposed approach relies on the fact that transmitting an ultra-short pulse through a multipath UWB channel leads to a received UWB signal that can be approximated by a linear combination of a few atoms from a pre-defined dictionary, yielding thus a sparse representation of the received UWB signal. The key in the proposed approach is in the design of a dictionary of parameterized waveforms (atoms) that closely matches the information-carrying pulseshape leading thus to higher energy compaction and sparse representation, and, therefore higher probability for CS reconstruction. Two approaches for UWB channel estimation are developed under a data-aided framework. In the first approach, the CS reconstruction capabilities are exploited to recover the composite pulse-multipath channel from a reduced set of random projections. This reconstructed signal is subsequently used as a referent template in a correlator-based detector. In the second approach, from a set of random projections of the received pilot signal, the Matching Pursuit algorithm is used to identify the strongest atoms in the projected signal that, in turn, are related to the strongest propagation paths that composite the multipath UWB channel. A Rake like receiver uses those atoms as templates for the bank of correlators in the detection stage. The bit error rate performances of the proposed approaches are analyzed and compared to that of traditional correlator-based detector. Extensive simulations show that for different propagation scenarios and UWB communication channels, detectors based on CS channel estimation outperform traditional correlator using just 1/3 of the sampling rate leading thus to a reduced use of analog-to-digital resources in the channel estimation stage.

/pdf/ultra-wideband-compressed-sensing-channel-estimation-2nzgxehehm.pdf

Gonzalo R. Arce

Papers

Compressive Coded Aperture Spectral Imaging: An Introduction

Nonlinear Signal Processing: A Statistical Approach

A multiresolution watermark for digital images

Halftone visual cryptography

Ultra-Wideband Compressed Sensing: Channel Estimation