Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost.Comment: 30 page

Image interpolation using Shearlet based iterative refinement

This paper proposes an image interpolation algorithm exploiting sparse representation for natural images. It involves three main steps: (a) obtaining an initial estimate of the high resolution image using linear methods like FIR filtering, (b) promoting sparsity in a selected dictionary through iterative thresholding, and (c) extracting high frequency information from the approximation to refine the initial estimate. For the sparse modeling, a shearlet dictionary is chosen to yield a multiscale directional representation. The proposed algorithm is compared to several state-of-the-art methods to assess its objective as well as subjective performance. Compared to the cubic spline interpolation method, an average PSNR gain of around 0.8 dB is observed over a dataset of 200 images

Characterization of palmprints by wavelet signatures via directional context modeling

2003-2004 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Fully Scalable Video Coding Using Redundant-Wavelet Multihypothesis and Motion-Compensated Temporal Filtering

In this dissertation, a fully scalable video coding system is proposed. This system achieves full temporal, resolution, and fidelity scalability by combining mesh-based motion-compensated temporal filtering, multihypothesis motion compensation, and an embedded 3D wavelet-coefficient coder. The first major contribution of this work is the introduction of the redundant-wavelet multihypothesis paradigm into motion-compensated temporal filtering, which is achieved by deploying temporal filtering in the domain of a spatially redundant wavelet transform. A regular triangle mesh is used to track motion between frames, and an affine transform between mesh triangles implements motion compensation within a lifting-based temporal transform. Experimental results reveal that the incorporation of redundant-wavelet multihypothesis into mesh-based motion-compensated temporal filtering significantly improves the rate-distortion performance of the scalable coder. The second major contribution is the introduction of a sliding-window implementation of motion-compensated temporal filtering such that video sequences of arbitrarily length may be temporally filtered using a finite-length frame buffer without suffering from severe degradation at buffer boundaries. Finally, as a third major contribution, a novel 3D coder is designed for the coding of the 3D volume of coefficients resulting from the redundant-wavelet based temporal filtering. This coder employs an explicit estimate of the probability of coefficient significance to drive a nonadaptive arithmetic coder, resulting in a simple software implementation. Additionally, the coder offers the possibility of a high degree of vectorization particularly well suited to the data-parallel capabilities of modern general-purpose processors or customized hardware. Results show that the proposed coder yields nearly the same rate-distortion performance as a more complicated coefficient coder considered to be state of the art

Space-frequency quantization for image compression with directionlets

The standard separable 2-D wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to efficiently capture 1-D discontinuities, like edges or contours. These features, being elongated and characterized by geometrical regularity along different directions, intersect and generate many large magnitude wavelet coefficients. Since contours are very important elements in the visual perception of images, to provide a good visual quality of compressed images, it is fundamental to preserve good reconstruction of these directional features. In our previous work, we proposed a construction of critically sampled perfect reconstruction transforms with directional vanishing moments imposed in the corresponding basis functions along different directions, called directionlets. In this paper, we show how to design and implement a novel efficient space-frequency quantization (SFQ) compression algorithm using directionlets. Our new compression method outperforms the standard SFQ in a rate-distortion sense, both in terms of mean-square error and visual quality, especially in the low-rate compression regime. We also show that our compression method, does not increase the order of computational complexity as compared to the standard SFQ algorithm

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference