Spatial Bias Removal in Microarray Images
1 Introduction Gene expression arrays are revolutionizing the field of molecular biology. The expression levels of thousands of genes can be measured in a single experiment. Already this technology has lead to new genetic disease identification and treatment [2], new cancer treatments [1][3], and a significant number of new findings in molecular biology. Each microarray, a type of gene expression array, consists of thousands of cDNA probes settled in a grid on an immobile substrate. The amount of mRNA bound to the probes would generally reflect the amount of mRNA transcribed in the sample, which in turn would provide information about the gene expression levels and protein production in the cell. A phosphorous version of the mRNA extracted from the tissue is bound to the probes on the microarray. Laser scanners then excite the dye, causing it to fluorescence and producing an image of the probes. A major obstacle in analyzing microarray data, and the focus of this paper , is the large amount of noise introduced to the gene expression measurements. This noise stems from multiple sources, such as background leakage, cross-hybridization, uneven sample washing, and scanner biasing. Here, we introduce a spatial bias removal strategy involving a high pass Gaussian filter. The filter is applied using a two dimensional Fourier transform on the image for computational efficiency. The filtering is performed on the log of the measured intensity values, as there is strong evidence to suggest that the bias is in the form of a multiplicative factor. 2 2 The spatial bias model An underlying assumption in our spatial bias removal is that the amount of mRNA bound to one probe of the microarray is independent of the probes around it. Since the probes are generally placed on the microarray in a random permutation, and not corresponding to their corresponding genes' placement in the genome sequence, this assumption is valid whether the microarray was designed to detect complete genes or specific exons in genes. Therefore, visually, the intensity measurements should be independent, and the image obtained should look like random noise. An inclusive model of all the factors that contribute to the intensity measurement at a certain probe can be written as: observed i = true i × bias i + noise i where we have termed the multiplicative noise as bias, to be distinguished from the additive noise. The bias is often found as a spatial gradient …