Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes.

http://ahvazdownload.persiangig.com/document/article/39.pdf

A wavelet tour of signal processing

First published in 1995, Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding. The book developed the theory in both continuous and discrete time, and presented important applications. During the past decade, it filled a useful need in explaining a new view of signal processing based on flexible time-frequency analysis and its applications. Since 2007, the authors now retain the copyright and allow open access to the book.

Wavelets and Subband Coding

We present a universal statistical model for texture images in the context of an overcomplete complex wavelet transform. The model is parameterized by a set of statistics computed on pairs of coefficients corresponding to basis functions at adjacent spatial locations, orientations, and scales. We develop an efficient algorithm for synthesizing random images subject to these constraints, by iteratively projecting onto the set of images satisfying each constraint, and we use this to test the perceptual validity of the model. In particular, we demonstrate the necessity of subgroups of the parameter set by showing examples of texture synthesis that fail when those parameters are removed from the set. We also demonstrate the power of our model by successfully synthesizing examples drawn from a diverse collection of artificial and natural textures.

/pdf/a-parametric-texture-model-based-on-joint-statistics-of-2p5nbgtfy6.pdf

A Parametric Texture Model Based on Joint Statistics of Complex Wavelet Coefficients

We present the results of a recent large-scale subjective study of video quality on a collection of videos distorted by a variety of application-relevant processes. Methods to assess the visual quality of digital videos as perceived by human observers are becoming increasingly important, due to the large number of applications that target humans as the end users of video. Owing to the many approaches to video quality assessment (VQA) that are being developed, there is a need for a diverse independent public database of distorted videos and subjective scores that is freely available. The resulting Laboratory for Image and Video Engineering (LIVE) Video Quality Database contains 150 distorted videos (obtained from ten uncompressed reference videos of natural scenes) that were created using four different commonly encountered distortion types. Each video was assessed by 38 human subjects, and the difference mean opinion scores (DMOS) were recorded. We also evaluated the performance of several state-of-the-art, publicly available full-reference VQA algorithms on the new database. A statistical evaluation of the relative performance of these algorithms is also presented. The database has a dedicated web presence that will be maintained as long as it remains relevant and the data is available online.

/pdf/study-of-subjective-and-objective-quality-assessment-of-3sgusnzbfc.pdf

Study of Subjective and Objective Quality Assessment of Video

This correspondence introduces a new approach to characterize textures at multiple scales The performance of wavelet packet spaces are measured in terms of sensitivity and selectivity for the classification of twenty-five natural textures Both energy and entropy metrics were computed for each wavelet packet and incorporated into distinct scale space representations, where each wavelet packet (channel) reflected a specific scale and orientation sensitivity Wavelet packet representations for twenty-five natural textures were classified without error by a simple two-layer network classifier An analyzing function of large regularity (D/sub 20/) was shown to be slightly more efficient in representation and discrimination than a similar function with fewer vanishing moments (D/sub 6/) In addition, energy representations computed from the standard wavelet decomposition alone (17 features) provided classification without error for the twenty-five textures included in our study The reliability exhibited by texture signatures based on wavelet packets analysis suggest that the multiresolution properties of such transforms are beneficial for accomplishing segmentation, classification and subtle discrimination of texture >

/pdf/texture-classification-by-wavelet-packet-signatures-20sx9talir.pdf

Texture Classification by Wavelet Packet Signatures.

The authors derive, implement, and demonstrate a computational approach for the measurement of emergent image frequencies. Measuring emergent signal frequencies requires spectral measurements accurate in both frequency and time or space, conflicting requirements that are shown to be balanced by a generalized uncertainty relationship. Such spectral measurements can be obtained from the responses of multiple wavelet-like channel filters that sample the signal spectrum, and that yield a locus of possible solutions for each locally emergent frequency. It is shown analytically that this locus of solutions is maximally localized in both space and frequency if the channel filters used are Gabor wavelets. A constrained solution is obtained by imposing a stabilizing term that develops naturally from the assumptions on the signal. The measurement of frequencies is then cast as an ill-posed extremum problem regularized by the stabilizing term, leading to an iterative constraint propagation algorithm. The technique is demonstrated by application to a variety of 2-D textured images. >

Localized measurement of emergent image frequencies by Gabor wavelets

An adaptive smoothing filter is proposed for reducing noise in digital signals of any dimensionality. The adaptive procedure is based on the selection of an appropriate inner or outer trimmed mean filter according to local measurements of the tail behavior (impulsivity) of the noise process. The set of trimmed means used provides robustness against a wide range of noise possibilities ranging from very shallow tailed to very heavy tailed. A Monte Carlo analysis using a family of generalized exponential distributions supports the choice of the trimmed mean selected for measured values of an impulsivity statistic. The assumption underlying the definition of the filter is that the signal to be filtered is locally smoothly varying, and that the noise process is uncorrelated and derives from an unknown, unimodal symmetric distribution. For image-processing applications, a second statistic is used to mark the location of abrupt intensity changes, or edges; in the vicinity of an edge, the trend-preserving median filter is used. Since the impulsivity and edge statistics used in defining the adaptive filter are both functions of order statistics, the extra computation required for their calculation is minimal. Examples are provided of the filter as applied to images corrupted by a variety of noises. >

Adaptive trimmed mean filters for image restoration

A derivation of the joint probability distribution and mass functions of order statistics coming from overlapping samples is presented. The general formulation allows for samples of any size overlapping (coinciding) in any number of observed values ranging from zero to the number of observations in the smaller sample. These expressions are used to compute the autocovariance function of a moving L -estimate (linear combination of order statistics) of a sequence of independent, identically distributed second-order random variables, under a variety of assumptions on the parent distribution. The associated variance spectral density is also computed for several filters of interest, including median filters, and inner and outer trimmed mean filters.

Spectral properties of moving L-estimates of independent data

We derive the maximum likelihood (ML) estimators for estimating locally monotonic signals embedded in white additive noise, when the noise is assumed to have a density function that is a member of a family of generalized exponential densities with parameter p that includes the Laplacian (p = 1), Gaussian (p = 2) and, as a limiting case, the uniform (p = ∞) densities. The estimators are given by the so-called locally monotonic regression of the noisy signal, a tool of recent introduction in signal processing. The approach that is used in the paper results from a geometric interpretation of the likelihood function of the sample; it takes advantage of the fact that a term in the likelihood function is the p-distance between the vector formed by the data in the given signal (sample) and the vector formed by the elements in the desired signal (estimator). Isotonic regression is a technique used in statistical estimation theory when the data are assumed to obey certain order restrictions. Local monotonicity is a generalization of the concept of isotonicity which is useful for some problems in signal processing.

Statistical optimality of locally monotonic regression

We analyze the effect of filter coefficient selection on the power spectral density of an order statistic filtered signal. Assuming that the input signal is a sequence of independent and identically distributed random variates, the autocovariance and the power spectrum of the output are computed. These PSDs are compared with those of the corresponding linear finite impulse response filters with identical coefficients. It is found that, in general, low frequency components predominate regardless of coefficient selection, suggesting an inherent smoothing in the ordering process.

A. Restrepo

Papers

Localized measurement of emergent image frequencies by Gabor wavelets

Adaptive trimmed mean filters for image restoration

Spectral properties of moving L-estimates of independent data

Statistical optimality of locally monotonic regression

Spectral analysis of order statistic filters