Superresolution images reconstructed from aliased images

In this paper, we present a simple method to almost quadruple the spatial resolution of aliased images. From a set of four low resolution, undersampled and shifted images, a new image is constructed with almost twice the resolution in each dimension. The resulting image is aliasing-free. A small aliasing-free part of the frequency domain of the images is used to compute the exact subpixel shifts. When the relative image positions are known, a higher resolution image can be constructed using the Papoulis-Gerchberg algorithm. The proposed method is tested in a simulation where all simulation parameters are well controlled, and where the resulting image can be compared with its original. The algorithm is also applied to real, noisy images from a digital camera. Both experiments show very good results.

A Frequency Domain Approach to Registration of Aliased Images with Application to Super-Resolution

Sabine Süsstrunk, Patrick Vandewalle, Martin Vetterli

Super-resolution algorithms reconstruct a high resolution image from a set of low resolution images of a scene. Precise alignment of the input images is an essential part of such algorithms. If the low resolution images are undersampled and have aliasing artifacts, the performance of standard registration algorithms decreases. We propose a frequency domain technique to precisely register a set of aliased images, based on their low-frequency, aliasing-free part. A high resolution image is then reconstructed using cubic interpolation. Our algorithm is compared to other algorithms in simulations and practical experiments using real aliased images. Both show very good visual results and prove the attractivity of our approach in the case of aliased input images. A possible application is to digital cameras where a set of rapidly acquired images can be used to recover a higher resolution final image.

2006

Super-Resolution from Highly Undersampled Images

Luciano Sbaiz, Sabine Süsstrunk, Patrick Vandewalle, Martin Vetterli

Aliasing artifacts in images are visually very disturbing. Therefore, most imaging devices apply a low-pass filter before sampling. This removes all aliasing from the image, but it also creates a blurred image. Actually, all the image information above half the sampling frequency is removed. In this paper, we present a new method for the reconstruction of a high resolution image from a set of highly undersampled and thus aliased images. We use the information in the entire frequency spectrum, including the aliased part, to create a sharp, high resolution image. The unknown relative shifts between the images are computed using a subspace projection approach. We show that the projection can be decomposed into multiple projections onto smaller subspaces. This allows for a considerable reduction of the overall computational complexity of the algorithm. A high resolution image can then be reconstructed from the registered low resolution images. Simulation results show the validity of our algorithm.

2005

Super-resolution from unregistered aliased images

Patrick Vandewalle

Aliasing in images is often considered as a nuisance. Artificial low frequency patterns and jagged edges appear when an image is sampled at a too low frequency. However, aliasing also conveys useful information about the high frequency content of the image, which is exploited in super-resolution applications. We use a set of input images of the same scene to extract such high frequency information and create a higher resolution aliasing-free image. Typically, there is a small shift or more complex motion between the different images, such that they contain slightly different information about the scene. Super-resolution image reconstruction can be formulated as a multichannel sampling problem with unknown offsets. This results in a set of equations that are linear in the unknown signal coefficients but nonlinear in the offsets. This thesis concentrates on the computation of these offsets, as they are an essential prerequisite for an accurate high resolution reconstruction. If a part of the image spectra is free of aliasing, the planar shift and rotation parameters can be computed using only this low frequency information. In such a case, the images can be registered pairwise to a reference image. Such a method is not applicable if the images are undersampled by a factor of two or larger. A higher number of images needs to be registered jointly. Two subspace methods are discussed for such highly aliased images. The first approach is based on a Fourier description of the aliased signals as a sum of overlapping parts of the spectrum. It uses a rank condition to find the correct offsets. The second one uses a more general expansion in an arbitrary Hilbert space to compute the signal offsets. The sampled signal is represented as a linear combination of sampled basis functions. The offsets are computed by projecting the signal onto varying subspaces. Under certain conditions, in particular for bandlimited signals, the nonlinear super-resolution equations can be written as a set of polynomial equations. Using Buchberger's algorithm, the solution can then be computed as a Gröbner basis for the corresponding polynomial ideal. After a description of a standard algorithm, adaptations are made for the use with noisy measurements. The techniques presented in this thesis are tested in simulations and practical experiments. The experiments are performed on sets of real images taken with a digital camera. The results show the validity of the algorithms: registration parameters are computed with subpixel precision, and aliasing is accurately removed from the resulting high resolution image. This thesis is produced according to the concepts of reproducible research. All the results and examples used in this thesis are reproducible using the code and data available online.

EPFL2006

Super-resolution from unregistered aliased images

Patrick Vandewalle

EPFL2006