## Info

Medical Image Enhancement with Hybrid Filters

Wei Qian 1 Introduction 57

University of South Florida 2 Design of the Hybrid Filter 58

2.1 The Adaptive Multistage Nonlinear Filter • 2.2 The Multiresolution/Multiorientation Wavelet Transform

3 Experimental Results 62

3.1 Image Database • 3.2 Visual Evaluation of Enhanced Images • 3.3 MCC Detection

4 Discussions and Conclusions 64

References 65

### 1 Introduction

Image enhancement is usually performed by either suppressing the noise or increasing the image contrast [1-3]. The goal of enhancement techniques is to accentuate certain image features for subsequent analysis or display. Their properties should be noise reduction, detail preservation, and artifact-free images. In the early development of signal and image processing, linear filters were the primary tools. Their mathematical simplicity and the existence of some desirable properties made them easy to design and implement. Moreover, linear filters offered satisfactory performance in many applications. However, linear filters have poor performance in the presence of noise that is not additive as well as in problems where system nonlinearities or non-Gaussian statistics are encountered. In addition, various criteria, such as the maximum entropy criterion, lead to nonlinear solutions. In image processing applications, linear filters tend to blur the edges, do not remove impulsive noise effectively, and do not perform well in the presence of signal-dependent noise. Also, although the exact characteristics of our visual system are not well understood, experimental results indicate that the first processing levels of our visual system possess nonlinear characteristics. For such reasons, nonlinear filtering techniques for signal/image processing were considered as early as 1958 [1]. Nonlinear filtering has had a dynamic development since then. This is indicated by the amount of research presently published and the widespread use of nonlinear digital filters in a variety of applications, notably in telecommunications, image processing, and geophysical signal processing. Most of the currently available image processing software packages include nonlinear filters such as median filters and morphological filters.

In this chapter, the design of a hybrid filter combining an adaptive multistage nonlinear filter and a multiresolution/ multiorientation wavelet transform is presented and the application of the hybrid filter for image enhancement in medical imaging is illustrated. The specific clinical application used as an example is the enhancement of microcalcification clusters (MCCs) and mass in digitized mammograms. The hybrid enhancement technique is used to improve both their visualization and their detection using computer assisted diagnostic (CAD) methods. The enhancement of MCCs and masses is a good model for evaluating the hybrid nonlinear filter and wavelet transform because the detection of these structures presents a significant challenge to the performance of X-ray imaging sensors and image display monitors. Microcalcifications and masses vary in size, shape, signal intensity and contrast, and they may be located in areas of very dense parenchymal tissue, making their detection difficult [112]. The classification of MCCs and masses as benign or malignant requires their morphology and detail to be preserved as accurately as possible.

The implementation of direct digital X-ray sensors, as opposed to the conventional X-ray screen film method, will require the use of specialized high-luminance computer monitors for reading mammograms at either central or remote sites. These monitors must compete with conventional light box displays used for film interpretation, to allow a viable implementation of filmless radiology. Image enhancement of MCCs and mass in digitized mammograms should potentially

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improve visual diagnosis on a computer monitor and could also be used as a preprocessing algorithm for CAD methods being proposed as a "second opinion" in reading strategies [11,12]. Similarly, the improved response characteristics of either X-ray film digitizers or direct digital sensors of recent design, such as their spatial resolution and image contrast, place greater constraints on the design of image enhancement algorithms because image detail, such as small microcalcifications, must be preserved. Finally, the varying noise characteristics of these new sensors and the possible generation of image artifacts, particularly at high resolution, need to be accounted for in order to reduce the false positive detection rate of MCCs or masses.

Multiresolution/multiorientation methods, such as the wavelet transform, originally developed in the signal processing field [13], have been proposed for image enhancement, segmentation or edge detection in the field of digital mammo-graphy [12,14]. The motivation for the multiresolution/ multiorientation approaches is their inherent advantage over traditional filtering methods that primarily focus on the coupling between image pixels on a single scale and generally fail to preserve image details of important clinical features. For example, the use of traditional single-scale CAD algorithms for enhancement or detection of MCCs has generally resulted in a sensitivity (true positive, TP, detection rate) that does not exceed 85% with 1-4 false positives (FPs) per image [1-3].

The hybrid filter architecture includes first an adaptive multistage nonlinear filter (AMNF) used for both noise suppression and image enhancement by smoothing background structures surrounding the structures of interest. Second, a multiresolution/multiorientation wavelet transform (MMWT) is employed for further selective enhancement. The hybrid filter takes advantage of the image decomposition and reconstruction processes of the MMWT, where reconstruction of specific subimages is used to selectively enhance structures of interest and separate the background structures. Finally, the hybrid filter selectively combines the filtered and reconstructed images to provide further enhancement and selective removal of background tissue structures.

In this chapter, Section 2 presents the hybrid filter architecture and the theoretical basis of the AMNF and the MMWT, as well as the optimization of the filter parameters. Section 3 describes the evaluation of the visual interpretation of the enhanced images and the results for detection. Section 4 presents a discussion and conclusions.

### 2 Design of the Hybrid Filter

The hybrid filter evolved with earlier work for image noise suppression and the use of the wavelet transform, specifically for segmentation of MCCs and masses in digitized mammograms [11]. A multistage tree-structured filter (TSF), with fixed parameters, that demonstrated improved performance for noise suppression in digital mammograms compared to traditional single-stage filters was initially developed in Qian et al. [8]. Similarly, a two-channel multiresolution WT was successfully used for both decomposition and reconstruction, with selective reconstruction of different subimages to segment MCCs [10]. Cascaded implementation of the TSF and the WT resulted in a significant reduction in the FP rate for MCC detection in the analysis of both simulated images with varying noise content and analysis of digital mammograms with biopsy-proven MCCs. However, the image detail of the segmented MCCs and masses was not fully preserved, although results were better than single scale methods [5,9,10]. With the addition of the adaptive multistage nonlinear filter described in this chapter, better performance in noise suppression is obtained. The filter includes a criterion for selective enhancement of MCCs and masses while smoothing background parenchymal structures.

A block diagram of the hybrid filter architecture is shown in Fig. 1. The input mammographic image g(i, j) 1 < i < N 1 < j < M, is first filtered by the AMNF for enhancing desired features while suppressing image noise and smoothing the details of background tissue structures. The output image, expressed as gAMNF(i, j), is processed in two different ways. A weighting coefficient « is applied to the output image and the same output image is processed by MMWT, as shown in Fig. 1, which decomposes gAMNF(i, j) into a set of independent, spatially oriented frequency bands or lower-resolution subimages. The subimages are then classified into two categories, those that primarily contain the structures of interest and those that consist mainly of background. The subimages are then reconstructed by the MMWT into two images gw1(i, j) and gw2 (i, j) that contain the desired features and background features, respectively. Finally, the outputs of the reconstructed subimages weighted by coefficients a2 and a3, and the original weighted output image a1gAMNF(i, j), are combined as indicated in Fig. 1, to yield the output image go that further improves the enhancement:

go = «1 gAMNF (h j) + «2gw1(i, j) - «3gw2 (i> j) ■ (1)

A linear gray scaling is then used to scale the enhanced images.

2.1 The Adaptive Multistage Nonlinear Filter Basic Filter Structure

An image can be considered to consist of the sum of a low-frequency part and a high-frequency part. The low-frequency part may be dominant in homogeneous regions, whereas the high-frequency part may be dominant in edge regions. The two-component image model allows different treatment of the components, and it can be used for adaptive image filtering and enhancement [11]. The high-frequency part may be weighted with a signal-dependent weighting factor to achieve enhancement. The first stage of the AMNF includes multiple linear and nonlinear filters that are judged to be appropriate for the particular application. In this stage the input image is filtered with each of these filters and in the second stage, for each pixel, the output of only one filter is selected using an adaptive criterion. There is a wide choice of filters that can serve as the building blocks of the AMNF: Here we illustrate a first stage based on five different filters: a linear smoothing filter, three nonlinear a-trimmed mean filters [1] with different window sizes, and a tree-structured filter.

The a-trimmed mean filter is a good compromise between the median and moving average filter. For example, in a 3 x 3 window, it excludes the highest and lowest pixel values and computes the mean of the remaining 7 pixels. In this manner outliers are trimmed and averaging also is implemented.

The TSF is based on the central weighted median filter (CWMF), which provides a selectable compromise between noise removal and edge preservation in the operation of the conventional median filter. Consider an M xN window W with M and N odd, centered around a pixel x(i, j) in the input image The output y(i, j) of the CWMF is obtained by computing the median of pixels in the window augmented by 2K repetitions of x(i, j) [8], y(i, j) = median{x(i — m, j — n), 2K copies of x(i, j)}; m, ne W, where 2K is an even positive integer such that 0<2K <MN — 1. If K = 0, the CWMF is reduced to the standard median filter, and if 2K > MN — 1, then the CWMF becomes the identity filter. Larger values of K preserve more image detail to the expense of noise smoothing, compared to smaller values. In order to introduce directional sensitivity to the CWMF, we can use a string of pixels to serve as a window instead of the usual square window. Figure 2 shows a set of eight recommended linear and curved windows. The TSF is a multistage nonlinear filter that consists of multiple CWMFs organized in a tree structure. A three-stage TSF is illustrated in Fig. 3 where the first stage is made of 8 CWMFs using the linear and curved windows of Fig. 2. The second stage has two CWMFs without windows that process the outputs of the first stage and the input x(i, j). The third stage is a single CWMF that acts on three inputs and produces the output of the TSF.

The output of the AMNF shown in Fig. 4 is

SAMNF(i> j) = £AF (i> j) + b(i, j)(g (i> j) — gAF(h j)) (2)

where b(i, j) is a signal-dependent weighting factor that is a measure of the local signal activity and gAF (i, j) is the output of one of the five filters mentioned above selected for each pixel according to the value of b(i, j). The value of b(i, j) is obtained from the local statistics around the processed pixel as

FIGURE 4 Block diagram of the adaptive multistage nonlinear filter (AMNF) used for noise suppression and enhancement.

[Ci, C2, c3, c4, c5]T = [0, 0, 1, 0,0]T x2<b(i, j)<x3 (4)

The thresholds x1 to x4 have to be set by the user according to the application.

### Parameter Computation for the AMNF

The local mean g(i, j) and local variance og2(i, j) needed for Eqs. (1)-(4) can be calculated over a uniform moving average window of size (2r + 1) x (2s + 1) with

FIGURE 4 Block diagram of the adaptive multistage nonlinear filter (AMNF) used for noise suppression and enhancement.

b(i, j) = cy2(i, j)/(o/2(i, j) + ff„2(i, j)), where oy2 is the signal variance and o„2 is the noise variance. In flat regions of the input image, the signal-to-noise ratio is small, b(i, j) becomes small, and gAMNF(i, j) approaches gAF(i, j). On the other hand, around the edges in the image, the signal-to-noise ratio is large, b(i, j) gets close to 1, and gAMNF(i, j) approaches g(i, j). The operation of the filter therefore should preserve the edges in the image. The estimation of the parameters oy and o„ is described in a later subsection.

### Adaptive Operation

Noise suppression increases while the spatial resolution decreases with increasing window size. Linear filters smooth the edges, average the details with noise, and decrease greatly the spatial resolution. The AMNF selects the nonlinear filter with a small window (e.g., 3 x 3) in the areas containing small structures of interest such as microcalcifications, while a linear filter with a large window (e.g., 7 x 7 or 9 x 9) is used in areas without small structures, to achieve noise removal and background smoothing. During the enhancement process, the filter is automatically selected by the weighting factor fo(i, j). The outputs of the five filters in the first stage of Fig. 4 are subject to a binary weighting that selects one filter out of the five. Representing the outputs of the five filters as the vector gk, this adaptive process can be written with the vector notation g (', j)

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