Building robust wavelet estimators for multicomponent images using Stein's principle.

Multichannel imaging systems provide several observations of the same scene which are often corrupted by noise. In this paper, we are interested in multispectral image denoising in the wavelet domain. We adopt a multivariate statistical approach in order to exploit the correlations existing between the different spectral components. Our main contribution is the application of Stein's principle to build a new estimator for arbitrary multichannel images embedded in additive Gaussian noise. Simulation tests carried out on optical satellite images show that the proposed method outperforms conventional wavelet shrinkage techniques.     

Locally adaptive wavelet domain Bayesian processor for denoising medical ultrasound images using Speckle modelling based on Rayleigh distribution

The authors present a statistical approach to speckle reduction in medical ultrasound B-scan images based on maximum a posteriori (MAP) estimation in the wavelet domain. In this framework, a new class of statistical model for speckle noise is proposed to obtain a simple and tractable solution in a closed analytical form. The proposed method uses the Rayleigh distribution for speckle noise and a Gaussian distribution for modelling the statistics of wavelet coefficients in a logarithmically transformed ultrasound image. The method combines the MAP estimation with the assumption that speckle is spatially correlated within a small window and designs a locally adaptive Bayesian processor whose parameters are computed from the neighboring coefficients. Further, the locally adaptive estimator is extended to the redundant wavelet representation, which yields better results than the decimated wavelet transform. The experimental results show that the proposed method clearly outperforms the state-of-the-art medical image denoising algorithm of Pizurica et al., spatially adaptive single-resolution methods and band-adaptive multi-scale soft-thresholding techniques in terms of quantitative performance as well as in terms of visual quality of the images. The main advantage of the new method over the existing techniques is that it suppresses speckle noise well, while retaining the structure of the image, particularly the thin bright streaks, which tend to occur along boundaries between tissue layers.     

Reversible data embedding into images using wavelet techniques and sorting.

The proliferation of digital information in our society has enticed a lot of research into data-embedding techniques that add information to digital content, like images, audio, and video. In this paper, we investigate high-capacity lossless data-embedding methods that allow one to embed large amounts of data into digital images (or video) in such a way that the original image can be reconstructed from the watermarked image. We present two new techniques: one based on least significant bit prediction and Sweldens' lifting scheme and another that is an improvement of Tian's technique of difference expansion. The new techniques are then compared with various existing embedding methods by looking at capacity-distortion behavior and capacity control.     

Processing and recognition of the thermal images using wavelet transforms

This paper presents methods for improving the quality of IR images that significantly facilitate the detection of physical and structural non-uniformities in layered objects. The methods are based on wavelets transformations. Both, discrete and continuous wavelet transforms were used. The space-scale representation of thermal image are used for the detection thermal non-uniformities in the objects examined. Examples of recorded and improved images are presented in this paper.     

Blind self-authentication of images for robust watermarking using integer wavelet transform

In this letter a new technique for robust watermarking of images is proposed based on second-generation wavelets (lifting-based integer wavelet transform). The scheme along with its robustness has got the capability of blind self-authentication of the watermarked images. The watermarked images show no perpetual degrading and gives peak signal to noise ratio (PSNR) in excess of 40 dB due to the use of integer-to-integer transform. Simulation results show the superior performance of the proposed technique as compared to a similar existing scheme under different attacks such as filtering, compression and rotation. Further, due to two independent process of watermark sequence extraction proposed in this letter, any alteration in the image results into dissimilar sequences, thereby detecting tampering in the image.     

Despeckling of medical ultrasound images using Daubechies complex wavelet transform

The paper presents a novel despeckling method, based on Daubechies complex wavelet transform, for medical ultrasound images. Daubechies complex wavelet transform is used due to its approximate shift invariance property and extra information in imaginary plane of complex wavelet domain when compared to real wavelet domain. A wavelet shrinkage factor has been derived to estimate the noise-free wavelet coefficients. The proposed method firstly detects strong edges using imaginary component of complex scaling coefficients and then applies shrinkage on magnitude of complex wavelet coefficients in the wavelet domain at non-edge points. The proposed shrinkage depends on the statistical parameters of complex wavelet coefficients of noisy image which makes it adaptive in nature. Effectiveness of the proposed method is compared on the basis of signal to mean square error (SMSE) and signal to noise ratio (SNR). The experimental results demonstrate that the proposed method outperforms other conventional despeckling methods as well as wavelet based log transformed and non-log transformed methods on test images. Application of the proposed method on real diagnostic ultrasound images has shown a clear improvement over other methods.     

Automated segmentation of stromal tissue in histology images using a voting Bayesian model

Over the past two decades, digital histology has been clinically approved for the various cancer diagnosis and prognosis tasks including proliferation rate estimation (PRE). Histology images contain two types of regions: epithelial and stromal. PRE is clinically restricted to epithelial tissue because stromal cells do not become cancerous. PRE has very high inter- and intra-pathologist variability and especially among juniors. The major cause of this variability is the stromal area. In this paper, we digitally segment out all stromal areas and present the pathologist with only epithelial areas for PRE. This reduces inter- and intra-pathologist variability. To that end, we propose a Bayesian voting-based model for removal of stromal cells utilizing cells texture and color. Our results on fifty clinical images show that pathologists’ PRE become more accurate and reproducible. Furthermore, PRE of expert pathologists shows very high inter-observer reliability after our fully automated segmentation. We validate our proposed model by testing three aspects and we find: (i) the effect of our segmentation on the clinical decision is the same before and after our segmentation. (ii) the segmentation similarity dice measure is 86.78 % which is a high similarity level. (iii) the time reduction of the pathologist is, on average, over 39 % which also supports the clinical benefit of our proposed work.     

Despeckling of ultrasound images using novel adaptive wavelet thresholding function

Multidimensional Systems and Signal Processing - In the present work, a new thresholding function has been proposed for despeckling of ultrasound images. The main limitation of ultrasound images is...     

Motion compensated lossy-to-lossless compression of 4-D medical images using integer wavelet transforms.

This paper proposes a method for progressive lossy-to-lossless compression of four-dimensional (4-D) medical images (sequences of volumetric images over time) by using a combination of three-dimensional (3-D) integer wavelet transform (IWT) and 3-D motion compensation. A 3-D extension of the set-partitioning in hierarchical trees (SPIHT) algorithm is employed for coding the wavelet coefficients. To effectively exploit the redundancy between consecutive 3-D images, the concepts of key and residual frames from video coding is used. A fast 3-D cube matching algorithm is employed to do motion estimation. The key and the residual volumes are then coded using 3-D IWT and the modified 3-D SPIHT. The experimental results presented in this paper show that our proposed compression scheme achieves better lossy and lossless compression performance on 4-D medical images when compared with JPEG-2000 and volumetric compression based on 3-D SPIHT.     

Bayesian reconstruction of functional images using anatomical information as priors

Proposes a Bayesian method whereby maximum a posteriori (MAP) estimates of functional (PET and SPECT) images may be reconstructed with the aid of prior information derived from registered anatomical MR images of the same slice. The prior information consists of significant anatomical boundaries that are likely to correspond to discontinuities in an otherwise spatially smooth radionuclide distribution. The authors' algorithm, like others proposed recently, seeks smooth solutions with occasional discontinuities; the contribution here is the inclusion of a coupling term that influences the creation of discontinuities in the vicinity of the significant anatomical boundaries. Simulations on anatomically derived mathematical phantoms are presented. Although computationally intense in its current implication, the reconstructions are improved (ROI-RMS error) relative to filtered backprojection and EM-ML reconstructions. The simulations show that the inclusion of position-dependent anatomical prior Information leads to further improvement relative to Bayesian reconstructions without the anatomical prior. The algorithm exhibits a certain degree of robustness with respect to errors in the location of anatomical boundaries.     

Combining wavelet analysis and Bayesian networks for the classification of auditory brainstem response.

The auditory brainstem response (ABR) has become a routine clinical tool for hearing and neurological assessment. In order to pick out the ABR from the background EEG activity that obscures it, stimulus-synchronized averaging of many repeated trials is necessary, typically requiring up to 2000 repetitions. This number of repetitions can be very difficult, time consuming and uncomfortable for some subjects. In this study, a method combining wavelet analysis and Bayesian networks is introduced to reduce the required number of repetitions, which could offer a great advantage in the clinical situation. 314 ABRs with 64 repetitions and 155 ABRs with 128 repetitions recorded from eight subjects are used here. A wavelet transform is applied to each of the ABRs, and the important features of the ABRs are extracted by thresholding and matching the wavelet coefficients. The significant wavelet coefficients that represent the extracted features of the ABRs are then used as the variables to build the Bayesian network for classification of the ABRs. In order to estimate the performance of this approach, stratified ten-fold cross-validation is used.     

On rate-distortion models for natural images and wavelet coding performance.

Operational rate-distortion (RD) functions of most natural images, when compressed with state-of-the-art wavelet coders, exhibit a power-law behavior D alpha R(-gamma) at moderately high rates, with gamma being a constant depending on the input image, deviating from the well-known exponential form of the RD function D alpha 2(-xiR) for bandlimited stationary processes. This paper explains this intriguing observation by investigating theoretical and operational RD behavior of natural images. We take as our source model the fractional Brownian motion (fBm), which is often used to model nonstationary behaviors in natural images. We first establish that the theoretical RD function of the fBm process (both in 1-D and 2-D) indeed follows a power law. Then we derive operational RD function of the fBm process when wavelet encoded based on water-filling principle. Interestingly, both the operational and theoretical RD functions behave as D alpha R(-gamma). For natural images, the values of gamma are found to be distributed around 1. These results lend an information theoretical support to the merit of multiresolution wavelet compression of self-similar processes and, in particular, natural images that can be modelled by such processes. They may also prove useful in predicting performance of RD optimized image coders.     

A wavelet approach for the identification of axonal synaptic varicosities from microscope images.

Direct visualization of synapses is a prerequisite to the analysis of the spatial distribution patterns of synaptic systems. Such an analysis is essential to the understanding of synaptic circuitry. In order to facilitate the visualization of individual synapses at the subcellular level from microscope images, we have introduced a wavelet-based approach for the semiautomated recognition of axonal synaptic varicosities. The proposed approach to image analysis employs a family of redundant wavelet representations. They are specifically designed for the recognition of signal peaks, which correspond to the presence of axonal synaptic varicosities. In this paper, the two-dimensional image of an axon together with its synaptic varicosities is first transformed into a one-dimensional (1-D) profile in which the axonal varicosities are represented by peaks in the signal. Next, by decomposing the 1-D profile in the differential wavelet domain, we employ the multi-scale point-wise product to distinguish between peaks and noises. The ability to separate the true signals (due to synaptic varicosities) from noise makes possible a reliable and accurate recognition of axonal synaptic varicosities. The proposed algorithms are also designed with a variable threshold that effectively allows variable sensitivities in varicosity detection. The algorithm has been systematically validated using images containing varicosities (< or =30) that have been consistently identified by seven human observers. The proposed algorithm can give high sensitivity and specificity with appropriate threshold. The results have indicated that the semiautomatic approach is satisfactory for processing a variety of microscopic images of axons under different conditions.     

Analytical design of 3-D wavelet filter banks using themultivariate Bernstein polynomial

The design of 3-D multirate filter banks where the downsampling/upsampling is on the FCO (face centred orthorhombic) lattice is addressed. With such a sampling lattice, the ideal 3-D sub-band of the low-pass filter is of the TRO (truncated octahedron) shape. The transformation of variables has been shown previously to be an effective technique for designing M-D (multidimensional) filter banks. A design technique is presented for the transformation function using the multivariate Bernstein polynomial which provides a good approximation to the TRO sub-band shape. The method is analytically based and does not require any optimisation procedure. Closed form expressions are obtained for the filters of any order. Another advantage of this technique is that it yields filters with a flat frequency response at the aliasing frequency (ω₁, ω₂ , ω₃)=(π, π, π). This flatness is important for giving regular discrete wavelet transform systems     

Diagonal preconditioners for the EFIE using a wavelet basis

The electric field integral equation (EFIE) has found widespread use and in practice has been accepted as a stable method. However, mathematically, the solution of the EFIE is an “ill-posed” problem. In practical terms, as one uses more and more expansion and testing functions per wavelength, the condition number of the resulting moment-method matrix increases (without bound). This means that for high-sampling densities, iterative methods such as conjugate gradients converge more slowly. However, there is a way to change all this. The EFIE is considered using a wavelet basis for expansion and for testing functions. Then, the resulting matrix is multiplied on both sides by a diagonal matrix. This results in a well-conditioned matrix which behaves much like the matrix for the magnetic field integral equation (MFIE). Consequences for the stability and convergence rate of iterative methods are described     

Bayesian decision feedback for segmentation of binary images

We present real-time algorithms for the segmentation of binary images modeled by Markov mesh random fields (MMRFs) and corrupted by independent noise. The goal is to find a recursive algorithm to compute the maximum a posteriori (MAP) estimate of each pixel of the scene using a fixed lookahead of D rows and D columns of the observations. First, this MAP fixed-lag estimation problem is set up and the corresponding optimal recursive (but computationally complex) estimator is derived. Then, both hard and soft (conditional) decision feedbacks are introduced at appropriate stages of the optimal estimator to reduce the complexity. The algorithm is applied to several synthetic and real images. The results demonstrate the viability of the algorithm both complexity-wise and performance-wise, and show its subjective relevance to the image segmentation problem.     

一种改进的小波阈值图像去噪方法

介绍了小波阈值图像去噪的原理,并对常规的软、硬阈值函数在图像去噪中存在的缺陷进行分析,在软、硬阈值函数的基础上提出了一种改进的阈值函数。通过对含噪声图像分别采用常规的软、硬阈值函数和改进的阈值函数进行去噪处理,实验对比得出:当选取了合适的控制系数时,改进的阈值函数在图像去噪中不仅保留了常规软、硬阈值函数的去噪优越性,而且还克服了常规软、硬阈值函数存在的去噪缺陷,比常规的软、硬阈值函数去噪效果更好。     

Image analysis using a dual-tree M-band wavelet transform.

We propose a two-dimensional generalization to the M-band case of the dual-tree decomposition structure (initially proposed by Kingsbury and further investigated by Selesnick) based on a Hilbert pair of wavelets. We particularly address: 1) the construction of the dual basis and 2) the resulting directional analysis. We also revisit the necessary pre-processing stage in the M-band case. While several reconstructions are possible because of the redundancy of the representation, we propose a new optimal signal reconstruction technique, which minimizes potential estimation errors. The effectiveness of the proposed M-band decomposition is demonstrated via denoising comparisons on several image types (natural, texture, seismics), with various M-band wavelets and thresholding strategies. Significant improvements in terms of both overall noise reduction and direction preservation are observed.