Adaptive frequency prior for frequency selective reconstruction of images from non-regular subsampling

Abstract: Image signals typically are defined on a rectangular two-dimensional grid. However, there exist scenarios where this is not fulfilled and where the image information only is available for a non-regular subset of pixel position. For processing, transmitting or displaying such an image signal, a re-sampling to a regular grid is required. Recently, Frequency Selective Reconstruction (FSR) has been proposed as a very effective sparsity-based algorithm for solving this under-determined problem. For this, FSR iteratively generates a model of the signal in the Fourier-domain. In this context, a fixed frequency prior inspired by the optical transfer function is used for favoring low-frequency content. However, this fixed prior is often too strict and may lead to a reduced reconstruction quality. To resolve this weakness, this paper proposes an adaptive frequency prior which takes the local density of the available samples into account. The proposed adaptive prior allows for a very high reconstruction quality, yielding gains of up to 0.6 dB PSNR over the fixed prior, independently of the density of the available samples. Compared to other state-of-the-art algorithms, visually noticeable gains of several dB are possible.