Filter Bank Fusion Frames

In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly designed, fusion frames can provide redundant encodings of signals which are optimally robust against certain types of noise and erasures. However, up to this point, few implementable constructions of such frames were known; we show how to construct them using oversampled filter banks. In this work, we first provide polyphase domain characterizations of filter bank fusion frames. We then use these characterizations to construct filter bank fusion frame versions of discrete wavelet and Gabor transforms, emphasizing those specific finite impulse response filters whose frequency responses are well-behaved.Comment: keywords: filter banks, frames, tight, fusion, erasures, polyphas

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Adaptive Speech Compression Based on Discrete Wave Atoms Transform

This paper proposes a new adaptive speech compression system based on discrete wave atoms transform. First, the signal is decomposed on wave atoms, then wave atom coefficients are truncated using a new adaptive thresholding which depends on the SNR estimation. The thresholded coefficients are quantized using Max Lloyd scalar quantizer. Besides, they are encoded using zero run length encoding followed by Huffman coding. Numerous simulations are performed to prove the robustness of our approach. The results of current work are compared with wavelet based compression by using objective criteria, namely CR, SNR, PSNR and NRMSE. This study shows that the wave atoms transform is more appropriate than wavelets transform since it offers a higher compression ratio and a better speech quality

Cognitive Radio Communications for Vehicular Technology – Wavelet Applications

Wireless communications are nowadays a dominant part of our lives: from domotics, through industrial applications and up to infomobility services. The key to the co-existence of wireless systems operating in closely located or even overlapping areas, is sharing of the spectral resource. The optimization of this resource is the main driving force behind the emerging changes in the policies for radio resources allocation. The current approach in spectrum usage specifies fixed frequency bands and transmission power limits for each radio transmitting system. This approach leads to a very low medium utilization factor for some frequency bands, caused by inefficient service allocation over vast geographical areas (radiomobile, radio and TV broadcasting, WiMAX) and also by the usage of large guard bands, obsolete now due to technological progress. A more flexible use of the spectral resource implies that the radio transceivers have the ability to monitor their radio environment and to adapt at specific transmission conditions. If this concept is supplemented with learning and decision capabilities, we refer to the Cognitive Radio (CR) paradigm. Some of the characteristics of a CR include localization, monitoring of the spectrum usage, frequency changing, transmission power control and, finally, the capacity of dynamically altering all these parameters (Haykin, 2005). This new cognitive approach is expected to have an important impact on the future regulations and spectrum policies. The dynamic access at the spectral resource is of extreme interest both for the scientific community as, considering the continuous request for wideband services, for the development of wireless technologies. From this point of view, a fundamental role is played by the Institute of Electrical and Electronic Engineers (IEEE) which in 2007 formed the Standards Coordinating Committee (SCC) 41 on Dynamic Spectrum Access Networks (DySPAN) having as main objective a standard for dynamic access wireless networks. Still within the IEEE frame, the 802.22 initiative defines a new WRAN (Wireless Regional Area Network) interface for wideband access based on cognitive radio techniques in the TV guard bands (the so-called “white spaces”). Coupled with the advantages and flexibility of CR systems and technologies, there is an ever-growing interest around the world in exploiting CR-enabled communications in vehicular and transportation environments. The integration of CR devices and cognitive radio networks into vehicles and associated infrastructures can lead to intelligent interactions with the transportation system, among vehicles, and even among radios within vehicles. Thus, improvements can be achieved in radio resource management and energy efficiency, road traffic management, network management, vehicular diagnostics, road traffic awareness for applications such as route planning, mobile commerce, and much more. Still open within the framework of dynamic and distributed access to the radio resource are the methods for monitoring the radio environment (the so-called “spectrum sensing”) and the transceiver technology to be used on the radio channels. A CR system works on a opportunistic basis searching for unused frequency bands called “white spaces” within the radio frequency spectrum with the intent to operate invisibly and without disturbing the primary users (PU) holding a license for one or more frequency bands. Spectrum sensing, that is, the fast and reliable detection of the PU’s even in the presence of in-band noise, is still a very complex problem with a decisive impact on the functionalities and capabilities of the CRs. The spectrum sensing techniques can be classified in two types: local and cooperative (distributed). The local techniques are performed by single devices exploiting the spectrum occupancy information in their spatial neighbourhood and can be divided into three categories (Budiarjo et al., 2008): "matched filter" (detection of pilot signals, preambles, etc.), "energy detection” (signal strength analysis) and “feature detection" (classification of signals according to their characteristics). Also, a combination of local techniques in a multi-stage design can be used to improve the sensing accuracy (Maleki et al., 2010). Nevertheless, the above-mentioned techniques are mostly inefficient for signals with reduced power or affected by phenomena typical for vehicular technology applications, such as shadowing and multi-path fading. To overcome such problems, cooperatives techniques can be used. Cooperative sensing is based on the aggregation of the spectrum data detected by multiple nodes using cognitive convergence algorithms in order to avoid the channel impairment problems that can lead to false detections. (Sanna et al., 2009). Within the energy detection method, a particular attention needs to be paid to the properties of the packets wavelet transformation for subband analysis, which, according to the literature, seems to be a feasible alternative to the classical FFT-based energy detection. Vehicular applications are in most cases characterized by the need of coping with fast changes in the radio environment, which lead, in this specific case of cognitive communication, to constrains in terms of short execution time of the spectrum sensing operations. From this point of view, the computational complexity of the wavelet packets method is of the same order of the state-of-the-art FFT algorithms, but the number of mathematical operations is lower using IIR polyphase filters (Murroni et al., 2010). In our work we are investigating the use of the wavelet packets for energy detection spectrum sensing operations based on the consideration that they have a finite duration and are self- and mutually-orthogonal at integer multiples of dyadic intervals. Hence, they are suitable for subband division and analysis: a generic signal can be then decomposed on the wavelet packet basis and represented as a collection of coefficients belonging to orthogonal subbands. Therefore, the total power of the signal can be evaluated as sum of the contributions of each subband, which can be separately computed in the wavelet domain. Furthermore, the wavelet packets can be used also for the feature detection spectrum sensing, using statistical parameters such as moments and medians. We concentrate in our research on both applications of the wavelet packets to the spectrum sensing operations, investigating their efficiency in terms of reliability and execution time, applied specifically to the needs of vehicular technology and transportation environments. The other key issue for the development of the previously mentioned standard is the choice of an adaptive/multicarrier modulation as basic candidate for data transmission, having as the most known representative the Orthogonal Frequency Division Multiplexing (OFDM) modulation. OFDM-like schemes are mature enough to be chosen as a core technology for dynamic access wireless networks. At the same time, the potentialities in terms of optimization for this specific purpose are not yet thoroughly investigated. Particularly, the Wavelet Packet Division Multiplexing (WPDM) modulation method, already known for about ten years to the scientific community, is a suitable candidate to satisfy the requirements on physical level for a dynamic access network (Wong et al., 1997): WPDM has already proven to be able to overcome some of the OFDM limits (limited spectral efficiency, problems with temporal synchronization especially in channels affected by fading) and is at the same time based on use of the same wavelet packets employed for subband analysis used for spectrum sensing operations . Our research investigates the use of the WPDM for cognitive radio purposes, combined with the wavelet approach for spectrum sensing, for offering a complete, wavelet-based solution for cognitive application focused on the problematic of vehicular communication (channel impairments, high relative velocity of the communication peers etc.)

MULTIRIDGELETS FOR TEXTURE ANALYSIS

Directional wavelets have orientation selectivity and thus are able to efficiently represent highly anisotropic elements such as line segments and edges. Ridgelet transform is a kind of directional multi-resolution transform and has been successful in many image processing and texture analysis applications. The objective of this research is to develop multi-ridgelet transform by applying multiwavelet transform to the Radon transform so as to attain attractive improvements. By adapting the cardinal orthogonal multiwavelets to the ridgelet transform, it is shown that the proposed cardinal multiridgelet transform (CMRT) possesses cardinality, approximate translation invariance, and approximate rotation invariance simultaneously, whereas no single ridgelet transform can hold all these properties at the same time. These properties are beneficial to image texture analysis. This is demonstrated in three studies of texture analysis applications. Firstly a texture database retrieval study taking a portion of the Brodatz texture album as an example has demonstrated that the CMRT-based texture representation for database retrieval performed better than other directional wavelet methods. Secondly the study of the LCD mura defect detection was based upon the classification of simulated abnormalities with a linear support vector machine classifier, the CMRT-based analysis of defects were shown to provide efficient features for superior detection performance than other competitive methods. Lastly and the most importantly, a study on the prostate cancer tissue image classification was conducted. With the CMRT-based texture extraction, Gaussian kernel support vector machines have been developed to discriminate prostate cancer Gleason grade 3 versus grade 4. Based on a limited database of prostate specimens, one classifier was trained to have remarkable test performance. This approach is unquestionably promising and is worthy to be fully developed

Noise Covariance Properties in Dual-Tree Wavelet Decompositions

Dual-tree wavelet decompositions have recently gained much popularity, mainly due to their ability to provide an accurate directional analysis of images combined with a reduced redundancy. When the decomposition of a random process is performed -- which occurs in particular when an additive noise is corrupting the signal to be analyzed -- it is useful to characterize the statistical properties of the dual-tree wavelet coefficients of this process. As dual-tree decompositions constitute overcomplete frame expansions, correlation structures are introduced among the coefficients, even when a white noise is analyzed. In this paper, we show that it is possible to provide an accurate description of the covariance properties of the dual-tree coefficients of a wide-sense stationary process. The expressions of the (cross-)covariance sequences of the coefficients are derived in the one and two-dimensional cases. Asymptotic results are also provided, allowing to predict the behaviour of the second-order moments for large lag values or at coarse resolution. In addition, the cross-correlations between the primal and dual wavelets, which play a primary role in our theoretical analysis, are calculated for a number of classical wavelet families. Simulation results are finally provided to validate these results

IEEE 802.11 wireless LAN traffic analysis: a cross-layer approach

textThe deployment of broadband wireless data networks, e.g., wireless local area networks (WLANs) [29], experienced tremendous growth in the last several years, and this trend is continuously gaining momentum. In fact, WLAN is becoming an indispensable component of the modern telecommunication infrastructure. Despite this optimistic outlook, however, little is known about the impact of the wireless channel on the characteristics of WLAN traffic. This dissertation characterizes the correlation structures of WLAN channel with traffic statistics from a cross-layer point of view, and provides new measurement methodologies and statistical models for WLAN networks. Currently WLAN standards are designed within the paradigm of the layered network architecture. For example, the architecture of IEEE 802.11 vii is almost identical to the Ethernet. However, wireless networks are fundamentally different from their wired peers due to the shift of transmission media from cables to over-the-air radio waves. This transition exposes wireless systems to the influence of radio propagation, and more importantly, to the temporal and spacial fluctuations of the radio channel that can actually be propagated up to upper layers. However, the current WLAN architecture isolates network layers, and largely ignores this impact. Therefore, we believe that a cross-layer based approach is necessary to understand and reflect this underlying impact of the channel to the upper layers of the network, especially in relation to WLAN traffic behavior. Measurement is one of the fundamental tools used to quantify radio propagation. As part of this dissertation, a complete framework for a measurement methodology, including hardware, software, and measurement procedures, is established. Characteristics of the propagation channel are estimated from measurement data, and the channel knowledge is applied to the upper layers for more realistic and accurate modeling. In WLAN environments, knowledge of the traffic characteristics is essential for proper network provisioning, and for improving the performance of the IEEE 802.11 standard and network devices, e.g., to design improved MAC schemes, or to build better buffer scheduling algorithms with channel knowledge, etc. Built upon extensive WLAN traffic traces, this dissertation work presents cross-layer models for WLAN throughput predictions, traffic statistics, and link layer characteristics. viii The main goal of this dissertation work is to experiment with and develop new methods for identifying channel characteristics. Thereby utilizing this knowledge, we show how to predict and improve WLAN performance. Within the framework of the developed cross-layer measurement methodology, we conducted extensive measurements in different physical environments and different settings such as office buildings and stores, and (1) show that the impact of the propagation channel can be quantified by using simple large scale channel metric (throughput over longer period of time), and (2) also present the existence of a Doppler effect within today’s WLAN packet traffic at sub-second time scales. We also show the real-world WLAN usage pattern from our measurement results. From this data, we conclude that the key issues to study WLAN networks include accurate site-specific propagation channel modeling and real-time autonomous traffic control.Electrical and Computer Engineerin