ABSTRACT:We propose a single-frame, learning-based super-resolution restoration technique by using the wavelet domain to define a constraint on the solution. Wavelet coefficients at finer scales of the unknown high-resolution image are learned from a set of high-resolution training images and the learned image in the wavelet domain is used for further regularization while super-resolving the picture. We use an appropriate smoothness prior with discontinuity preservation in addition to the wavelet-based constraint to estimate the superresolved image. The smoothness term ensures the spatial correlation among the pixels, whereas the learning term chooses the best edges from the training set. Because this amounts to extrapolating the high-frequency components, the proposed method does not suffer from oversmoothing effects. The results demonstrate the effectiveness of the proposed approach.

We propose a learning-based, single-image super-resolution reconstruction technique using the contourlet transform, which is capable of capturing the smoothness along contours making use of directional decompositions. The contourlet coefficients at finer scales of the unknown high-resolution image are learned locally from a set of high-resolution training images, the inverse contourlet transform of which recovers the super-resolved image. In effect, we learn the high-resolution representation of an oriented edge primitive from the training data. Our experiments show that the proposed approach outperforms standard interpolation techniques as well as a standard (Cartesian) wavelet-based learning both visually and in terms of the PSNR values, especially for images with arbitrarily oriented edges.

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In this paper we study the possibility of removing aliasing in a scene from a single observation by designing an alias-free upsampling scheme. We generate the unknown high frequency components of the given partially aliased (low resolution) image by minimizing the total variation of the interpolant subject to the constraint that part of unaliased spectral components in the low resolution observation are known precisely and under the assumption of sparsity in the data. This provides a mathematical basis for exact reproduction of high frequency components with probability approaching one, from their aliased observation. The primary application of the given approach would be in super-resolution imaging.