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In this letter, a new method for Kennaugh matrix decomposition is proposed, and a new norm for the Kennaugh matrix is defined. The Kennaugh matrix is decomposed into two parts: The first is a coherent target matrix, and the second is a residual matrix with minimum norm. The properties of the extracted coherent target are discussed, and an application of the extracted coherent target is implemented. In this application, an incoherent image is converted into a coherent image. Single-look sphere-diplane-helix decomposition is then performed. An experiment on Airborne SAR polarimetric data over San Francisco has been carried out, thus demonstrating the effectiveness of the application.