Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

From sensory perception to spatial cognition

To interact with the environmet, it is crucial to have a clear space representation. Several findings have shown that the space around our body is split in several portions, which are differentially coded by the brain. Evidences of such subdivision have been reported by studies on people affected by neglect, on space near (peripersonal) and far (extrapersonal) to the body position and considering space around specific different portion of the body. Moreover, recent studies showed that sensory modalities are at the base of important cognitive skills. However, it is still unclear if each sensory modality has a different role in the development of cognitive skills in the several portions of space around the body. Recent works showed that the visual modality is crucial for the development of spatial representation. This idea is supported by studies on blind individuals showing that visual information is fundamental for the development of auditory spatial representation. For example, blind individuals are not able to perform the spatial bisection task, a task that requires to build an auditory spatial metric, a skill that sighted children acquire around 6 years of age. Based these prior researches, we hypothesize that if different sensory modalities have a role on the devlopment of different cognitive skills, then we should be able to find a clear correlation between availability of the sensory modality and the cognitive skill associated. In particular we hypothesize that the visual information is crucial for the development of auditory space represnetation; if this is true, we should find different spatial skill between front and back spaces. In this thesis, I provide evidences that spaces around our body are differently influenced by sensory modalities. Our results suggest that visual input have a pivotal role in the development of auditory spatial representation and that this applies only to the frontal space. Indeed sighted people are less accurated in spatial task only in space where vision is not present (i.e. the back), while blind people show no differences between front and back spaces. On the other hand, people tend to report sounds in the back space, suggesting that the role of hearing in allertness could be more important in the back than frontal spaces. Finally, we show that natural training, stressing the integration of audio motor stimuli, can restore spatial cognition, opening new possibility for rehabilitation programs. Spatial cognition is a well studied topic. However, we think our findings fill the gap regarding how the different availibility of sensory information, across spaces, causes the development of different cognitive skills in these spaces. This work is the starting point to understand the strategies that the brain adopts to maximize its resources by processing, in the more efficient way, as much information as possible