Image restoration from a downsampled image by using the DCT

• Published in: Signal processing Vol. 87; no. 10; pp. 2370 - 2380
• Main Authors: Abe, Yoshinori, Iiguni, Youji
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.10.2007; Elsevier Science
• Subjects: Applied sciences; Discrete cosine transform; Exact sciences and technology; High resolution image restoration; Image processing; Information, signal and communications theory; Lagrange multiplier method; Miscellaneous; Signal processing; Similar transformation; Telecommunications and information theory; High resolution image restoration; Lagrange multiplier method; Similar transformation; Discrete cosine transform; Additive noise; Performance evaluation; High resolution; Computer simulation; Image processing; Low resolution; Image restoration; Spline approximation; Cubic spline; Lagrange multiplier; Sparse matrix; Signal processing; Matrix method; Sparse representation; Discrete cosine transforms
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2007.03.010

The high-resolution (HR) image restoration from a downsampled low-resolution (LR) image by using the discrete cosine transform (DCT) is proposed. The downsampling process is modeled in matrix form and the DCT is applied to the downsampling matrix to obtain the sparse matrix representation. The restored HR image is then efficiently computed from the LR image by using the sparsity. The distortion caused by the observation noise is theoretically analyzed, and the power of distortion is shown to be closely equal to the variance of the observation noise. Computer simulations show that the proposed method is superior to the cubic spline interpolation in the HR image restoration performance as far as the amount of the additive noise is small.