Even though image signals are typically defined on a regular 2D grid, there also exist many scenarios where this is not the case and the amplitude of the image signal only is available for a non-regular subset of pixel positions. In such a case, a resampling of the image to a regular grid has to be carried out. This is necessary since almost all algorithms and technologies for processing, transmitting or displaying image signals rely on the samples being available on a regular grid. Thus, it is of great importance to reconstruct the image on this regular grid, so that the reconstruction comes closest to the case that the signal has been originally acquired on the regular grid. In this paper, Frequency Selective Reconstruction is introduced for solving this challenging task. This algorithm reconstructs image signals by exploiting the property that small areas of images can be represented sparsely in the Fourier domain. By further considering the basic properties of the optical transfer function of imaging systems, a sparse model of the signal is iteratively generated. In doing so, the proposed algorithm is able to achieve a very high reconstruction quality, in terms of peak signal-to-noise ratio (PSNR) and structural similarity measure as well as in terms of visual quality. The simulation results show that the proposed algorithm is able to outperform state-of-the-art reconstruction algorithms and gains of more than 1 dB PSNR are possible.

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High resolution images can be acquired using a non-regular sampling sensor which consists of an underlying low resolution sensor that is covered with a non-regular sampling mask. The reconstructed high resolution image is then obtained during post-processing. Recently, it has been shown that the temporal correlation between neighboring frames can be exploited in order to enhance the reconstruction quality of non-regularly sampled video data. In this paper, a new recursive multi-frame reconstruction approach is proposed in order to further increase the reconstruction quality. By using a new reference order, previously reconstructed frames can be used for the subsequent motion estimation and a new weighting function allows for the incorporation of multiple pixels projected onto the same position. With the new recursive multi-frame approach, a visually noticeable average gain in PSNR of up to 1.13 dB with respect to a state-of-the-art single-frame reconstruction approach can be achieved. Compared to the existing multi-frame approach, a gain of 0.31 dB is possible. SSIM results show the same behavior as PSNR results. Additionally, the pre-reconstruction step of the existing multi-frame approach can be avoided and the new algorithm is, in general, capable of real-time processing.

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Increasing spatial image resolution is an often required, yet challenging task in image acquisition. Recently, it has been shown that it is possible to obtain a high resolution image by covering a low resolution sensor with a non-regular sampling mask. Due to the masking, however, some pixel information in the resulting high resolution image is not available and has to be reconstructed by an efficient image reconstruction algorithm in order to get a fully reconstructed high resolution image. In this paper, the influence of different sampling masks with a reduced randomness of the non-regularity on the image reconstruction process is evaluated. Simulation results show that it is sufficient to use sampling masks that are non-regular only on a smaller scale. These sampling masks lead to a visually noticeable gain in PSNR compared to arbitrary chosen sampling masks which are non-regular over the whole image sensor size. At the same time, they simplify the manufacturing process and allow for efficient storage.

Recently, it has been shown that a high resolution image can be obtained without the usage of a high resolution sensor. The main idea has been that a low resolution sensor is covered with a nonregular sampling mask followed by a reconstruction of the incomplete high resolution image captured this way. In this paper, a multi-frame reconstruction approach is proposed where a video is taken by a nonregular sampling sensor and fully reconstructed afterwards. By utilizing the temporal correlation between neighboring frames, the reconstruction quality can be further enhanced. Compared to a state-of-the-art singleframe reconstruction approach, this leads to a visually noticeable gain in PSNR of up to 1.19 dB on average.

Multi-view image acquisition systems with two or more cameras can be rather costly due to the number of high resolution image sensors that are required. Recently, it has been shown that by covering a low resolution sensor with a non-regular sampling mask and by using an efficient algorithm for image reconstruction, a high resolution image can be obtained. In this paper, a stereo image reconstruction setup for multi-view scenarios is proposed. A scene is captured by a pair of non-regular sampling sensors and by incorporating information from the adjacent view, the reconstruction quality can be increased. Compared to a state-of-the-art single-view reconstruction algorithm, this leads to a visually noticeable average gain in PSNR of 0.74 dB.

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