Compression of frontal facial images is an appealing and important application. Recent work has shown that specially tailored algorithms for this task can lead to performance far exceeding JPEG2000. This letter proposes a novel such compression algorithm, exploiting our recently developed redundant tree-based wavelet transform. Originally meant for functions defined on graphs and cloud of points, this new transform has been shown to be highly effective as an image adaptive redundant and multi-scale decomposition. The key concept behind this method is reordering of the image pixels so as to form a highly smooth 1D signal that can be sparsified by a regular wavelet. In this work we bring this image adaptive transform to the realm of compression of aligned frontal facial images. Given a training set of such images, the transform is designed to best sparsify the whole set using a common feature-ordering. Our compression scheme consists of sparse coding using the transform, followed by entropy coding of the obtained coefficients. The inverse transform and a post-processing stage are used to decode the compressed image. We demonstrate the performance of the proposed scheme and compare it to other competing algorithms.

In our previous work [1] we have introduced a redundant tree-based wavelet transform (RTBWT), originally designed to represent functions defined on high dimensional data clouds and graphs. We have further shown that RTBWT can be used as a highly effective image-adaptive redundant transform that operates on an image using orderings of its overlapped patches. The resulting transform is robust to corruptions in the image, and thus able to efficiently represent the unknown target image even when it is calculated from its corrupted version. In this paper, we utilize this redundant transform as a powerful sparsity-promoting regularizer in inverse problems in image processing. We show that the image representation obtained with this transform is a frame expansion, and derive the analysis and synthesis operators associated with it. We explore the use of this frame operators to image denoising and deblurring, and demonstrate in both these cases state-of-the-art results.

In our recent work we proposed an image denoising scheme based on reordering of the noisy image pixels to a one dimensional (1D) signal, and applying linear smoothing filters on it. This algorithm had two main limitations: It did not take advantage of the distances between the noisy image patches, which were used in the reordering process; and the smoothing filters required a separate training set to be learned from. In this work, we propose an image denoising algorithm, which applies similar permutations to the noisy image, but overcomes the above two shortcomings. We eliminate the need for learning filters by employing the nonlocal means (NL-means) algorithm. We estimate each pixel as a weighted average of noisy pixels in union of neighborhoods obtained from different global pixel permutations, where the weights are determined by distances between the patches. We show that the proposed scheme achieves results which are close to the state-of-the-art.

We propose an image processing scheme based on reordering of its patches. For a given corrupted image, we extract all patches with overlaps, refer to these as coordinates in high-dimensional space, and order them such that they are chained in the "shortest possible path," essentially solving the traveling salesman problem. The obtained ordering applied to the corrupted image implies a permutation of the image pixels to what should be a regular signal. This enables us to obtain good recovery of the clean image by applying relatively simple one-dimensional smoothing operations (such as filtering or interpolation) to the reordered set of pixels. We explore the use of the proposed approach to image denoising and inpainting, and show promising results in both cases.

In this paper, we propose a new redundant wavelet transform applicable to scalar functions defined on high dimensional coordinates, weighted graphs and networks. The proposed transform utilizes the distances between the given data points to construct tree-like structures. We modify the filter-bank decomposition scheme of the redundant wavelet transform by adding in each decomposition level operators that reorder the approximation coefficients. These reordering operators are derived by organizing the tree-node features so as to shorten the path that passes through these points. We explore the use of the proposed transform for the recovery of labels defined on point clouds and to image denoising, and show that in both cases the results are promising.