**1. Introduction**

It is well known that the deoxyribonucleic acid (DNA) of a genome essential for human life often demonstrates structural changes [1–3] called genome copy number alterations (CNAs) [4–6], which are associated with disease such as cancer [7]. Analysis of the breakpoint locations in the CAN structure is still an important issue because it helps detecting structural alterations, load

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of alterations in the tumor genome, and absolute segment copy numbers. Thus, efficient estimators are required to extract information about the breakpoints with accuracy acceptable for medical needs. To produce CNA profile, several technologies have been developed such as comparative genomic hybridization (CGH) [8], high‐resolution CGH (HR‐CGH) [9], whole genome sequencing [10], and most recently single‐nucleotide polymorphism (SNP) [11]. The HR‐CGH technology is still used widely in spite of its low resolution [12]. It has been reported in [13] that the HR‐CGH arrays are accurate to detect structural variations (SVs) at the resolu‐ tion of 200 bp (*base pairs*). Most recently, the single‐nucleotide polymorphism technology was developedinthestudyofWangetal.[11]toprovidehigh‐resolutionmeasurementsoftheCNAs. In spite of their high resolution, the modern methods still demonstrate the inability in obtain‐ ing good estimates of the breakpoint locations because of the following factors: (1) the nature of biological material (tumor is contaminated by normal tissue, relative values, and unknown baseline for copy number estimation), (2) technological biases (quality of material and hybrid‐ ization/sequencing), and (3) intensive random noise. The HR‐CGH and SNP profiles have demonstrated deficiency in detecting the CNAs, but noise in the detected changes still re‐ mains at a high level [14] and accurate estimators are required to extract information about structural changes.

In the HR‐CGH microarray technique, the CNAs are often normalized and plotted as log2*R* / *G* =log<sup>2</sup> ratio, where *R* and *G* are the fluorescent Red and Green intensities, respectively [12]. The CNA measurements using SNP technologies are represented by the Log‐*R* ratios (LRRs), which are the log‐transformed ratios of experimental and normal reference SNP intensities centered at zero for each sample [14]. From the standpoint of signal processing, the following properties of the CNA function are of importance [15]:


The CNA estimation problem is thus to predict the breakpoint locations and the segmental levels with a maximum possible accuracy and precision acceptable for medical applications. In this work, we developed our methods to two types of cancer: B‐cell chronic lymphocytic leukemia (B‐CLL) and BLC primary breast carcinoma. Nevertheless, the methods were designed to any samples of cancer with the characteristics described above.
