Search results for "wavelet"

The Myriad Virtues of Wavelet Trees

2009

Wavelet Trees have been introduced in [Grossi, Gupta and Vitter, SODA '03] and have been rapidly recognized as a very flexible tool for the design of compressed full-text indexes and data compressors. Although several papers have investigated the beauty and usefulness of this data structure in the full-text indexing scenario, its impact on data compression has not been fully explored. In this paper we provide a complete theoretical analysis of a wide class of compression algorithms based on Wavelet Trees. We also show how to improve their asymptotic performance by introducing a novel framework, called Generalized Wavelet Trees, that aims for the best combination of binary compressors (like,…

Deconvolution by Regularized Matching Pursuit

2014

In this chapter, an efficient method that restores signals from strongly noised blurred discrete data is presented. The method can be characterized as a Regularized Matching Pursuit (RMP), where dictionaries consist of spline wavelet packets. It combines ideas from spline theory, wavelet analysis and greedy algorithms. The main distinction from the conventional matching pursuit is that different dictionaries are used to test the data and to approximate the solution. In addition, oblique projections of data onto dictionary elements are used instead of orthogonal projections, which are used in the conventional Matching Pursuit (MP). The slopes of the projections and the stopping rule for the …

Non-periodic Polynomial Splines

2015

In this chapter, we outline the essentials of the splines theory. By themselves, they are of interest for signal processing research. We use the Zak transform to derive an integral representation of polynomial splines on uniform grids. The integral representation facilitated design of different generators of spline spaces and their duals. It provides explicit expressions for interpolating and smoothing splines of any order. In forthcoming chapters, the integral representation of splines will be used for the constructions of efficient subdivision schemes and so also for the design spline-based wavelets and wavelet frames.

Noise reduction in magnetic resonance images by Wavelet transforms: an application to the study of capillary water absorption in sedimentary rocks

2007

Magnetic resonance imaging (MRI) is a powerful technique to study capillary water absorption kinetics in sedimentary rocks. However, the noise in the images can limit the correct identification and the quantitative measurement of the average height reached by the wetting front inside the porous material where imbibition occurs. Therefore, denoising methods can be applied to improve the image quality for a more accurate analysis, without the disadvantages of longer acquisition times. This study attempts to improve the signal-to-noise ratio of the images acquired by MRI on a sedimentary rock (Pietra di Lecce) using a waveletbased thresholding technique. The idea is to average some slightly di…

Cartoon filter via adaptive abstraction

2016

We propose a non-parametric methodology to realize abstraction images.The redundant wavelet "a trous" algorithm is applied for details detection.An multi-scale circular median filter is used as a smoothing filter.The proposed algorithm is simple and fast on low-cost entry-level hardware. Abstraction in computer graphics defines a procedure that discriminates the essential information that is worth keeping. Usually details, that correspond to higher frequency components, allow to distinguish otherwise similar images. Vice versa, low frequencies are related to the main information, which are larger structures. Contours themselves may also be identified by high frequencies and separate each pi…

Differential diagnostic features of bone marrow biopsies in essential thrombocythemia

2004

Essential Thrombocythemia (ET) is a chronic myeloproliferative disorder (CMPD) characterized by a high platelet count and originating from a multipotent stem cell. For a long time, according to Polycythaemia Vera Study Group (PVSG) criteria, ET diagnosis has not included histopathological data. Bone Marrow (BM) histology was used only to exclude previous or other subtypes of Ph-CMD or Myelodysplastic syndromes (MDS). In addition, the lack of any cytogenetic or molecular-biological marker has made the discrimination between ET and cases of Reactive Thrombocytosys (RT) without a well known cause quite problematic. Analogously, the distinction of ET from the other Ph- CMPDs with similar clinic…

A new approach for the visualization of DNA methylation results

2019

Multilevel preconditioning and adaptive sparse solution of inverse problems

2012

The windowed scalogram difference: A novel wavelet tool for comparing time series

2017

Abstract We introduce a new wavelet-based tool called windowed scalogram difference (WSD), which has been designed to compare time series. This tool allows quantifying if two time series follow a similar pattern over time, comparing their scalograms and determining if they give the same weight to the different scales. The WSD can be seen as an alternative to another tool widely used in wavelet analysis called wavelet squared coherence (WSC) and, in some cases, it detects features that the WSC is not able to identify. As an application, the WSD is used to examine the dynamics of the integration of government bond markets in the euro area since the inception of the euro as a European single c…

Use of wavelet for image processing in smart cameras with low hardware resources

2013

International audience; Images from embedded sensors need digital processing to recover high-quality images and to extract features of a scene. Depending on the properties of the sensor and on the application, the designer fits together different algorithms to process images. In the context of embedded devices, the hardware supporting those applications is very constrained in terms of power consumption and silicon area. Thus, the algorithms have to be compliant with the embedded specifications i.e. reduced computational complexity and low memory requirements. We investigate the opportunity to use the wavelet representation to perform good quality image processing algorithms at a lower compu…