Time-scale analysis of abrupt changes corrupted by multiplicative noise

Multiplicative Abrupt Changes (ACs) have been considered in many applications. These applications include image processing (speckle) and random communication models (fading). Previous authors have shown that the Continuous Wavelet Transform (CWT) has good detection properties for ACs in additive noise. This work applies the CWT to AC detection in multiplicative noise. CWT translation invariance allows to define an AC signature. The problem then becomes signature detection in the time-scale domain. A second-order contrast criterion is defined as a measure of detection performance. This criterion depends upon the first- and second-order moments of the multiplicative process's CWT. An optimal wavelet (maximizing the contrast) is derived for an ideal step in white multiplicative noise. This wavelet is asymptotically optimal for smooth changes and can be approximated for small AC amplitudes by the Haar wavelet. Linear and quadratic suboptimal signature-based detectors are also studied. Closed-form threshold expressions are given as functions of the false alarm probability for three of the detectors. Detection performance is characterized using Receiver Operating Characteristic (ROC) curves computed from Monte-Carlo simulations

The near shift-invariance of the dual-tree complex wavelet transform revisited

The dual-tree complex wavelet transform (DTCWT) is an enhancement of the conventional discrete wavelet transform (DWT) due to a higher degree of shift-invariance and a greater directional selectivity, finding its applications in signal and image processing. This paper presents a quantitative proof of the superiority of the DTCWT over the DWT in case of modulated wavelets.Comment: 15 page

Scale Invariant Interest Points with Shearlets

Shearlets are a relatively new directional multi-scale framework for signal analysis, which have been shown effective to enhance signal discontinuities such as edges and corners at multiple scales. In this work we address the problem of detecting and describing blob-like features in the shearlets framework. We derive a measure which is very effective for blob detection and closely related to the Laplacian of Gaussian. We demonstrate the measure satisfies the perfect scale invariance property in the continuous case. In the discrete setting, we derive algorithms for blob detection and keypoint description. Finally, we provide qualitative justifications of our findings as well as a quantitative evaluation on benchmark data. We also report an experimental evidence that our method is very suitable to deal with compressed and noisy images, thanks to the sparsity property of shearlets

IVUS-based histology of atherosclerotic plaques: improving longitudinal resolution

Although Virtual Histology (VH) is the in-vivo gold standard for atherosclerosis plaque characterization in IVUS images, it suffers from a poor longitudinal resolution due to ECG-gating. In this paper, we propose an image- based approach to overcome this limitation. Since each tissue have different echogenic characteristics, they show in IVUS images different local frequency components. By using Redundant Wavelet Packet Transform (RWPT), IVUS images are decomposed in multiple sub-band images. To encode the textural statistics of each resulting image, run-length features are extracted from the neighborhood centered on each pixel. To provide the best discrimination power according to these features, relevant sub-bands are selected by using Local Discriminant Bases (LDB) algorithm in combination with Fisher’s criterion. A structure of weighted multi-class SVM permits the classification of the extracted feature vectors into three tissue classes, namely fibro-fatty, necrotic core and dense calcified tissues. Results shows the superiority of our approach with an overall accuracy of 72% in comparison to methods based on Local Binary Pattern and Co-occurrence, which respectively give accuracy rates of 70% and 71%