Biomedical subjects

Michael Elad

Publications and source records attributed to Michael Elad.

5 recordsLinked to original sources

PubMed2006

Multiframe demosaicing and super-resolution of color images.

In the last two decades, two related categories of problems have been studied independently in 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 posteron estimation technique by minimizing a multiterm 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 spatially 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 components. Finally, an additional regularization term is used to force similar edge location and 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.

Algorithms↗

PubMed2005

Space-dependent color gamut mapping: a variational approach.

Gamut mapping deals with the need to adjust a color image to fit into the constrained color gamut of a given rendering medium. A typical use for this tool is the reproduction of a color image prior to its printing, such that it exploits best the given printer/medium color gamut, namely the colors the printer can produce on the given medium. Most of the classical gamut mapping methods involve a pixel-by-pixel mapping and ignore the spatial color configuration. Recently proposed spatial-dependent approaches for gamut mapping are either based on heuristic assumptions or involve a high computational cost. In this paper, we present a new variational approach for space-dependent gamut mapping. Our treatment starts with the presentation of a new measure for the problem, closely related to a recent measure proposed for Retinex. We also link our method to recent measures that attempt to couple spectral and spatial perceptual measures. It is shown that the gamut mapping problem leads to a quadratic programming formulation, guaranteed to have a unique solution if the gamut of the target device is convex. An efficient numerical solution is proposed with promising results.

Algorithms↗

PubMed2005

Image decomposition via the combination of sparse representations and a variational approach.

The separation of image content into semantic parts plays a vital role in applications such as compression, enhancement, restoration, and more. In recent years, several pioneering works suggested such a separation be based on variational formulation and others using independent component analysis and sparsity. This paper presents a novel method for separating images into texture and piecewise smooth (cartoon) parts, exploiting both the variational and the sparsity mechanisms. The method combines the basis pursuit denoising (BPDN) algorithm and the total-variation (TV) regularization scheme. The basic idea presented in this paper is the use of two appropriate dictionaries, one for the representation of textures and the other for the natural scene parts assumed to be piecewise smooth. Both dictionaries are chosen such that they lead to sparse representations over one type of image-content (either texture or piecewise smooth). The use of the BPDN with the two amalgamed dictionaries leads to the desired separation, along with noise removal as a by-product. As the need to choose proper dictionaries is generally hard, a TV regularization is employed to better direct the separation process and reduce ringing artifacts. We present a highly efficient numerical scheme to solve the combined optimization problem posed by our model and to show several experimental results that validate the algorithm's performance.

Algorithms↗

PubMed2004

Fast and robust multiframe super resolution.

Super-resolution reconstruction produces one or a set of high-resolution images from a set of low-resolution images. In the last two decades, a variety of super-resolution methods have been proposed. These methods are usually very sensitive to their assumed model of data and noise, which limits their utility. This paper reviews some of these methods and addresses their short-comings. We propose an alternate approach using L1 norm minimization and robust regularization based on a bilateral prior to deal with different data and noise models. This computationally inexpensive method is robust to errors in motion and blur estimation and results in images with sharp edges. Simulation results confirm the effectiveness of our method and demonstrate its superiority to other super-resolution methods.

Algorithms↗

PubMed2003

Optimally sparse representation in general (nonorthogonal) dictionaries via l minimization.

Given a dictionary D = {d(k)} of vectors d(k), we seek to represent a signal S as a linear combination S = summation operator(k) gamma(k)d(k), with scalar coefficients gamma(k). In particular, we aim for the sparsest representation possible. In general, this requires a combinatorial optimization process. Previous work considered the special case where D is an overcomplete system consisting of exactly two orthobases and has shown that, under a condition of mutual incoherence of the two bases, and assuming that S has a sufficiently sparse representation, this representation is unique and can be found by solving a convex optimization problem: specifically, minimizing the l(1) norm of the coefficients gamma. In this article, we obtain parallel results in a more general setting, where the dictionary D can arise from two or several bases, frames, or even less structured systems. We sketch three applications: separating linear features from planar ones in 3D data, noncooperative multiuser encoding, and identification of over-complete independent component models.

Journal Article↗