Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 536215, 9 pages

http://dx.doi.org/10.1155/2015/536215

## PCNN-Based Image Fusion in Compressed Domain

Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China

Received 8 October 2014; Revised 6 January 2015; Accepted 7 January 2015

Academic Editor: Yi-Kuei Lin

Copyright © 2015 Yang Chen and Zheng Qin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper addresses a novel method of image fusion problem for different application scenarios, employing compressive sensing (CS) as the image sparse representation method and pulse-coupled neural network (PCNN) as the fusion rule. Firstly, source images are compressed through scrambled block Hadamard ensemble (SBHE) for its compression capability and computational simplicity on the sensor side. Local standard variance is input to motivate PCNN and coefficients with large firing times are selected as the fusion coefficients in compressed domain. Fusion coefficients are smoothed by sliding window in order to avoid blocking effect. Experimental results demonstrate that the proposed fusion method outperforms other fusion methods in compressed domain and is effective and adaptive in different image fusion applications.

#### 1. Introduction

Image fusion is the processing of combining the complementary information from multiple source images into a fused image which provides more accuracy than any of the source images. Image fusion is widely used in civil, military, and medical image processing. For example, fusion of multifocus images [1, 2] can provide a better view for human or machine perception. Fusion of infrared and visible light [3, 4] can provide a strong ability of discovering important targets with detailed texture expression. In addition, fusion of computed tomography (CT) image and magnetic resonance imaging (MRI) images [5, 6] can provide detailed information on bones structures and soft tissue for diagnosis.

Many image fusion methods have been proposed and they can be classified into three levels of information representation, namely, pixel level [7, 8], feature level [9], and decision level [10]. Among these categories of image fusion, the pixel level image fusion is the most effective in terms of conveying more information from multimodal images. Particularly, multiscale transform based methods are the most widely used, such as pyramid [11], gradient [12], wavelet [13–15], and contourlet [16–18].

In recent years, CS [19, 20] has become a much preferred algorithm for image fusion and other image processings due to its compression capability in the sampling procedure on the sensor side. Sampling is performed on source images to obtain their linear measurements in the compressed domain. There are different CS sampling patterns addressed in previous CS literature [20–23], such as discrete cosine transform (DCT) [21], star shape, double-star shape, star-circle shape [22], and scrambled block Hadamard ensemble (SBHE) [24]. In the fusion rules of compressive image fusion, weighted fusion factors are calculated by mathematical combinations of image channels. The calculation rules of fusion weighted factors are mainly based on average [25], mean, variance, PCA [26, 27], and mutual information [28, 29]. In addition, fused image in compressed domain can be reconstructed from the measurement according to a recovery algorithm such as gradient projection for sparse reconstruction (GPSR) [30], basis pursuit [31], total variation minimization [32], orthogonal matching pursuit [33], and L1-norm minimization [34, 35].

Different from existed compressive image fusion methods, this paper addresses a novel image fusion method by using PCNN in compressed domain. PCNN is a biologically inspired neural network algorithm developed by Eckhorn et al. [36], which has been used in image segmentation, image fusion [2], image enhancement, and pattern recognition. It is characterized by the global coupling and pulse synchronization of neurons. These characteristics benefit image fusion which makes use of local image information. Generally, humans are sensitive to edges or salient information. Therefore, local standard variance, which stands for gradient activity in the local neighbourhood, is used to motivate PCNN neurons in this paper.

The remainder of the paper is organized as follows. Section 2 provides a brief description of compressive sensing theory. Proposed image fusion methods in compressed domain are illustrated in Section 3. Experimental results and discussions are presented in Section 4 and conclusions are provided in Section 5.

#### 2. Compressive Sensing and Sampling Pattern

Compressive sensing theory [19, 20] enables a sparse or compressible signal to be reconstructed from a small number of nonadaptive linear projections, thus significantly reducing the sampling and computation costs.

##### 2.1. Background on Compressive Sensing

Consider an unknown signal ; it is expressed in the following form on the orthogonal base: . For the coefficient vector , if only elements are not zero, we say is sparse when is in the substrate . After the measurement matrix projection, there is . Since , the projection process combines the traditional signal sampling and compression process. Through and , direct recovery of is morbid inverse problem. But sparse theory suggests that this problem can be transformed into an optimization problem of sparse vectors to be solved: where represents norm. Thus the signal can be restored from the formula .

Subsequently, measurement matrix is required to satisfy the following properties (RIP) criterion in order to recover signal accurately: where , represents norm. is a dimensional vector with strictly sparseness. That is to say, matrix and substrate are not related.

##### 2.2. SBHE Sampling

In the block CS, an image is divided into small blocks with the size of . Sampling operator with size of is formed by the partial block Hadamard transform with its columns randomly permuted as SBHE operator [24]. The sampling operator is a block diagonal matrix, which is expressed as where represents the Hadamard matrices of . Let denote the vectorized signal of the th block. The corresponding measurement output vector is expressed as Then, the measurement output vector of the entire image is determined by

SBHE is adopted as the sampling pattern in this paper, which has been shown to satisfy the five requirements, including near optimal performance, university, fast computation, being memory efficient, and being Hardware friendly.

#### 3. Proposed Medical Image Fusion Method

##### 3.1. Image Fusion Framework in Compressed Domain

In image fusion, pixel level image fusion offers effective fused information at the cost of higher computational complexity. Compressed domain approaches, on the other hand, are more promising due to their compression capability and computational simplicity on the sensor side. Thus, it is important to explore the compressive image fusion method, and the flowchart of image fusion in compressed domain is illustrated as Figure 1.