Multiscale Wavelet Representation Research Articles

MWG-Net: Multiscale Wavelet Guidance Network for COVID-19 Lung Infection Segmentation From CT Images

Recently, accurate segmentation of COVID-19 infection from computed tomography (CT) scans is critical for the diagnosis and treatment of COVID-19. However, infection segmentation is a challenging task due to various textures, sizes and locations of infections, low contrast, and blurred boundaries. To address these problems, we propose a novel Multi-scale Wavelet Guidance Network (MWG-Net) for COVID-19 lung infection by integrating the multi-scale information of wavelet domain into the encoder and decoder of the convolutional neural network (CNN). In particular, we propose the Wavelet Guidance Module (WGM) and Wavelet & Edge Guidance Module (WEGM). Among them, the WGM guides the encoder to extract infection details through the multi-scale spatial and frequency features in the wavelet domain, while the WEGM guides the decoder to recover infection details through the multi-scale wavelet representations and multi-scale infection edge information. Besides, a Progressive Fusion Module (PFM) is further developed to aggregate and explore multi-scale features of the encoder and decoder. Notably, we establish a COVID-19 segmentation dataset (named COVID-Seg-100) containing 5800+ annotated slices for performance evaluation. Furthermore, we conduct extensive experiments to compare our method with other state-of-the-art approaches on our COVID-19-Seg-100 and two publicly available datasets, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e</i> ., MosMedData and COVID-SemiSeg. The results show that our MWG-Net outperforms state-of-the-art methods on different datasets and can achieve more accurate and promising COVID-19 lung infection segmentation.

A novel multi-branch wavelet neural network for sparse representation based object classification

Recent advances in acquisition and display technologies have led to an enormous amount of visual data, which requires appropriate storage and management tools. One of the fundamental needs is the design of efficient image classification and recognition solutions. In this paper, we propose a wavelet neural network approach for sparse representation-based object classification. The proposed approach aims to exploit the advantages of sparse coding, multi-scale wavelet representation as well as neural networks. More precisely, a wavelet transform is firstly applied to the image datasets. The generated approximation and detail wavelet subbands are then fed into a multi-branch neural network architecture. This architecture produces multiple sparse codes that are efficiently combined during the classification stage. Extensive experiments, carried out on various types of standard object datasets, have shown the efficiency of the proposed method compared to the existing sparse coding and deep learning-based methods.

Wavelet-based approximations of pointwise bound constraints in Lebesgue and Sobolev spaces

Abstract Many problems in optimal control, PDE-constrained optimization and constrained variational problems include pointwise bound constraints on the feasible controls and state variables. Most well-known approaches for treating such pointwise inequality constraints in numerical methods rely on finite element discretizations and interpolation arguments. We propose an alternative means of discretizing pointwise bound constraints using a wavelet-based discretization. The main results show that the discrete, approximating sets converge in the sense of Mosco to the original sets. In situations of higher regularity, convergence rates follow immediately from the underlying wavelet theory. The approach exploits the fact that one can easily transform between a given multiscale wavelet representation and single-scale representation with linear complexity. This allows, for example, a direct treatment of variational problems involving fractional operators, without the need for lifting techniques. We demonstrate this fact with several numerical examples of fractional obstacle problems.

Monitoring of mineral processing systems by using textural image analysis

In the last few decades, developments in machine vision technology have led to innovative approaches to the control and monitoring of mineral processing systems. Image representation plays an important role in the performance of the recognition systems used in these approaches, where the use of feature representations based on second-order statistics of the image pixels have predominated. However, these representations may not adequately capture or express the visual textural structure associated with the observed patterns in images. In this study, the use of texton and complex multiscale wavelet representations (steerable pyramids) that exploit higher-order statistical regularities, is investigated. These techniques are applied to two image data sets: industrial platinum group metals froth flotation, and coal particles on a conveyor belt. Compared to grey level co-occurrence matrix and classical wavelet representations, these are observed to improve performance when used as input in the pattern recognition phase.

Detecting fine scratches on smooth surfaces with multiscale wavelet representation

This paper presents a set of image-processing algorithms for automatic detection of fine scratches on smooth surfaces, such as automobile paint surfaces. The scratches to be detected have random directions, inconspicuous gray levels and background noise. The multiscale wavelet transform was used to extract texture features, and a controlled edge fusion model was employed to merge the detailed (horizontal, vertical and diagonal) wavelet coefficient maps. Based on the fused detail map, multivariate statistics were applied to synthesize features in multiple scales and directions, and an optimal threshold was set to separate scratches from the background. The experimental results of 24 automobile paint surface showed that the presented algorithms can effectively suppress background noise and detect scratches accurately.

Anomaly subspace detection based on a multi-scale Markov random field model

In this paper we introduce a multi-scale Gaussian Markov random field (GMRF) model and a corresponding anomaly subspace detection algorithm. Natural clutter images, often appear to have several periodical patterns of various period lengths. In such cases, the GMRF model may not sufficiently describe the clutter image. The proposed model is based on a multi-scale wavelet representation of the image, independent component analysis, and modeling each independent component as a GMRF. Anomaly detection is subsequently carried out by applying a matched subspace detector to the innovations process generated by the presumed model. The robustness of the proposed approach is demonstrated with application to automatic target detection in synthetic and real imagery. A quantitative performance analysis and experimental results demonstrate the advantage of the proposed method in comparison to competing methods.

Application of Imaging Techniques to Geometry Analysis of Aggregate Particles

This paper presents image analysis techniques by which to characterize the texture, angularity, and form of aggregate particles used in highway construction and geotechnical applications. For texture analysis, wavelet decomposition in gray scale images of particles is performed. The results demonstrate that multiscale wavelet representation is a powerful tool by which to capture the texture and to differentiate true texture from false texture caused by variations of natural color on a particle surface. Angularity and form analyses of particles are done using binary images. A gradient-based method is employed to describe angularity. This method is shown to differentiate between particles with different angularity characteristics. Form analysis of the particles includes computing the shape factor and sphericity index, which are based on measurements of the shortest, intermediate, and longest axis of the particle. Particle thickness is measured using the feature of an autofocus microscope. The width and length are calculated by an eigenvalue decomposition method of two-dimensional particle projections. Details of an interactive software developed to compute the different aggregate shape factors are discussed. The results indicate that these calculated values of the particle dimensions match very closely the values measured manually using a digital caliper.

Are global methods appropriate for fMRI data analysis? An in vivo fMRI study of the spatio-temporal heterogeneity of fMRI data

We propose a two-stage, data-driven exploratory approach to analyze the heterogeneity of null hypothesis (i.e. no task) fMRI data. In particular, we used a screening stage followed by (local) temporal clustering. Our analysis confirms that fMRI data are extremely heterogeneous. The physiological noise varies throughout the neuroscientifically interesting regions; this poses an extreme challenge for models used for the analysis. We conclude that local, data-driven approaches such as clustering should be carried out as a mandatory first step in fMRI data analysis, since they provide important insights for the development of more flexible, locally adaptive model-based methods based on e.g,, multiscale wavelet representations or local regularization techniques. The combination of data-driven and model-driven approaches should be the strategy adopted for the analysis of fMRI data.

A shift-invariant discrete wavelet transform

This article presents a unifying approach to the derivation and implementation of a shift-invariant wavelet transform of one- and two-dimensional (1-D and 2-D) discrete signals. Starting with Mallat's (1989) multiresolution wavelet representation (MRWAR), it presents an analytical process through which a shift-invariant, orthogonal, discrete wavelet transform called the multiscale wavelet representation (MSWAR) is obtained. The coefficients in the MSWAR are shown to be inclusive of those in the MRWAR with the implication that the derived representation is invertible. The computational complexity of the MSWAR is quantified in terms of the required convolutions, and its implementation is shown to be equivalent to the filter upsampling technique.