Step-edge reconstruction using 2D finite rate of innovation principle

Parametric signals that have a finite number of degrees of freedom per unit of time are defined as signals with Finite Rate of Innovation (FRI). Sampling and reconstruction schemes have been developed based on the 1D FRI principle and applied to reconstructing step edge images on a row by row basis. In this paper, we derive the 2D FRI principle by exploiting the separability of the B-spline sampling kernel. The proposed 2D FRI principle regards the sampling and reconstruction as block by block operations. The step-edge parameters can be retrieved in high accuracy with no post-processing. The performance on synthetic images shows that our proposed technique is more precise than the row by row approaches on Signal-to-Noise Ratio (SNR) levels larger than 4 dB. Experimental results on real images demonstrate that the proposed method can reconstruct the step-edge precisely under noisy and practical sampling conditions.