The principal component analysis (PCA) is one of the procedures that have been a successful performance in signal processing and dimension reduction of the signals. However, a requirement in applying PCA to the images is converting images into a vector. This process leads to loss spatial locality information. To solve this problem, the two-dimensional PCA was proposed. Also, most recently the sparse principal component was introduced that not only keep the properties of standard PCA but also try to make a lot of elements of the basis vectors to zero. In this paper, inspired by the above two ideas, the two-dimensional sparse principal component analysis (2-D. SPCA) is proposed.
In this paper, the Least Angle Regression- Elastic Net formula, in addition, using l₁ and l₂ constraints is extended to two-dimensional model with a few minor changes in its input to approach 2-D. SPCA.
The two-dimensional sparse principal component analysis is evaluated in image compression. Before applying the algorithm, the image is divided into several blocks with resolution 8×8 and a database of these blocks is formed. Comparison the performance of 2-D. SPCA and Discrete Cosine transform, for the same number of elements that are necessary to save the image after the conversion shows the good performance of the proposed algorithm. In addition, the proposed algorithm is applied to 8×8 blocks of 60 images with different textures, and the resulted two-dimensional sparse principal components could be used for other test images with a suitable performance.