The quality of video sequences (e.g. old movies, webcam, TV broadcast) is often reduced by noise, usually
assumed white and Gaussian, being superimposed on the sequence. When denoising image sequences, rather
than a single image, the temporal dimension can be used for gaining in better denoising performance, as well
as in the algorithms' speed. This paper extends single image denoising method reported in to sequences.
This algorithm relies on sparse and redundant representations of small patches in the images. Three different
extensions are offered, and all are tested and found to lead to substantial benefits both in denoising quality and
algorithm complexity, compared to running the single image algorithm sequentially. After these modifications,
the proposed algorithm displays state-of-the-art denoising performance, while not relying on motion estimation.
Sparse and redundant representations − an emerging and powerful model for signals − suggests that a data source
could be described as a linear combination of few atoms from a pre-specified and over-complete dictionary. This
model has drawn a considerable attention in the past decade, due to its appealing theoretical foundations, and
promising practical results it leads to. Many of the applications that use this model are formulated as a mixture
of l2-lp (p ≤ 1) optimization expressions. Iterated Shrinkage algorithms are a new family of highly effective
numerical techniques for handling these optimization tasks, surpassing traditional optimization techniques. In
this paper we aim to give a broad view of this group of methods, motivate their need, present their derivation,
show their comparative performance, and most important of all, discuss their potential in various applications.
Theoretical and practical limitations usually constrain the achievable resolution of any imaging device. Super-Resolution (SR) methods are developed through the years to go beyond this limit by acquiring and fusing several low-resolution (LR) images of the same scene, producing a high-resolution (HR) image. The early works on SR,
although occasionally mathematically optimal for particular models of data and noise, produced poor results when applied to real images. In this paper, we discuss two of the main issues related to designing a practical SR system, namely reconstruction accuracy and computational efficiency. Reconstruction accuracy refers to the problem of designing a robust SR method applicable to images from different imaging systems. We study a general framework for optimal reconstruction of images from grayscale, color, or color filtered (CFA) cameras. The performance of our proposed method is boosted by using powerful priors and is robust to both measurement (e.g. CCD read out noise) and system noise (e.g. motion estimation error). Noting that the motion estimation is often considered a bottleneck in terms of SR performance, we introduce the concept of "constrained motions" for enhancing the quality of super-resolved images. We show that using such constraints will enhance the quality of the motion estimation and therefore results in more accurate reconstruction of the HR images. We also justify some practical assumptions that greatly reduce the computational complexity and memory requirements of the proposed methods. We use efficient approximation of the Kalman Filter (KF) and adopt a dynamic point of view to the SR problem. Novel methods for addressing these issues are accompanied by experimental results on real data.
The Morphological Component Analysis (MCA) is a a new method which allows us to separate features contained in an image when these features present different morphological aspects. We show that MCA can be very useful for decomposing images into texture and piecewise smooth (cartoon) parts or for inpainting applications. We extend MCA to a multichannel MCA (MMCA) for analyzing multispectral data and present a range of examples which illustrates the results.
In this work we investigate the image denoising problem. One common approach found in the literature involves manipulating the coefficients in the transform domain, e.g. shrinkage, followed by the inverse transform. Several advanced methods that model the inter-coefficient dependencies were developed recently, and were shown to
yield significant improvement. However, these methods operate on the transform domain error rather than on the image domain one. These errors are in general entirely different for redundant transforms. In this work we propose a novel denoising method, based on the Basis-Pursuit Denoising (BPDN). Our method combines the image domain error with the transform domain dependency structure, resulting in a general objective function, applicable for any wavelet-like transform. We focus here on the Contourlet Transform (CT) and on a redundant version of it, both relatively new transforms designed to sparsely represent images. The performance of our new method is compared favorably with the state-of-the-art method of Bayesian Least Squares Gaussian Scale Mixture (BLS-GSM), which we adapted to the CT as well, with further improvements still to come.
In recent years there is a growing interest in the study of sparse representation for signals. Using an overcomplete dictionary that contains prototype signal-atoms, signals are described as sparse linear combinations of these atoms. Recent activity in this field concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a given dictionary. Designing dictionaries to better fit the above model can be done by either selecting pre-specified transforms, or by adapting the dictionary to a set of training signals. Both these techniques have been considered in recent years, however this topic is largely still open. In this paper we address the latter problem of designing dictionaries, and introduce the K-SVD algorithm for this task. We show how this algorithm could be interpreted as a generalization of the K-Means clustering process, and demonstrate its behavior in both synthetic tests and in applications on real data. Finally, we turn to describe its generalization to nonnegative matrix factorization problem that suits signals generated under an additive model with positive atoms. We present a simple and yet efficient variation of the K-SVD that handles such extraction of non-negative dictionaries.
In the last two decades a variety of super-resolution (SR) methods have been proposed. These methods usually address the problem of fusing a set of monochromatic images to produce a single monochromatic image with higher spatial resolution. In this paper we address the dynamic and color SR problems of reconstructing a high-quality set of colored super-resolved images from low-quality mosaiced frames. Our approach includes a hybrid method for simultaneous SR and demosaicing, this way taking into account practical color measurements encountered in video sequences. For the case of translational motion and common space-invariant blur, the proposed method is based on a very fast and memory efficient approximation of the Kalman filter. Experimental results on both simulated and real data are supplied, demonstrating the presented algorithm, and its strength.
In the last two decades, two related categories of problems have been studied independently in the image restoration literature: super-resolution and demosaicing. A closer look at these problems reveals the relation between them, and as conventional color digital cameras suffer from both low-spatial resolution and color filtering, it is reasonable to address them in a unified context. In this paper, we propose a fast and robust hybrid method of super-resolution and demosaicing, based on a maximum a posteriori (MAP) estimation technique by minimizing a multi-term cost function. The L1 norm is used for measuring the difference between the projected estimate of the high-resolution image and each low-resolution image, removing outliers in the data and errors due to possibly inaccurate motion estimation. Bilateral regularization is used for regularizing the luminance component, resulting in sharp edges and forcing interpolation along the edges
and not across them. Simultaneously, Tikhonov regularization is used to smooth the chrominance component.
Finally, an additional regularization term is used to force similar edge orientation in different color channels.
We show that the minimization of the total cost function is relatively easy and fast. Experimental results on
synthetic and real data sets confirm the effectiveness of our method.
In this paper, we consider the compression of high-definition video sequences for bandwidth sensitive applications. We show that down-sampling the image sequence prior to encoding and then up-sampling the decoded frames increases compression efficiency. This is particularly true at lower bit-rates, as direct encoding of the high-definition sequence requires a large number of blocks to be signaled. We survey previous work that combines a resolution change and
compression mechanism. We then illustrate the success of our proposed approach through simulations. Both MPEG-2 and H.264 scenarios are considered. Given the benefits of the approach, we also interpret the results within the context of traditional spatial scalability.