Many signal and image estimation problems such as maximum entropy reconstruction and positron emission tomography, require the minimization of a criterion containing a barrier function i.e., an unbounded function at the boundary of the feasible solution domain. This function has to be carefully handled in the optimization algorithm. When an iterative descent method is used for the minimization, a search along the line supported by the descent direction is usually performed at each iteration. However, standard line search strategies tend to be inefficient in this context. In this paper, we propose an original line search algorithm based on the majorize-minimize principle. A tangent majorant function is built to approximate a scalar criterion containing a barrier function. This leads to a simple line search ensuring the convergence of several classical descent optimization strategies, including the most classical variants of nonlinear conjugate gradient. The practical efficiency of the proposal scheme is illustrated by means of two examples of signal and image reconstruction. 1.

Distances in the well known fuzzy c-means algorithm of Bezdek (1973) are measured by the squared Euclidean distance. Other distances have been used as well in fuzzy clustering. For example, Jajuga (1991) proposed to use the L1-distance and Bobrowski and Bezdek (1991) also used the L∞-distance. For the more general case of Minkowski distance and the case of using a root of the squared Minkowski distance, Groenen and Jajuga (2001) introduced a majorization algorithm to minimize the error. One of the advantages of iterative majorization is that it is a guaranteed descent algorithm, so that every iteration reduces the error until convergence is reached. However, their algorithm was limited to the case of Minkowski parameter between 1 and 2, that is, between the L1-distance and the Euclidean distance. Here, we extend their majorization algorithm to any Minkowski distance with Minkowski parameter greater than (or equal to) 1. This extension also includes the case of the L∞-distance. We also investigate how well this algorithm performs and present an empirical application.

A wavelet inpainting problem refers to the problem of filling in missing wavelet coefficients in an image. A variational approach was used in Chan, Shen and Zhou (Total variation wavelet inpainting, J. Math. Imaging Vision, 25(1):107–125, 2006). The resulting functional was minimized by the gradient descent method. In this paper, we use an optimization transfer technique which involves replacing their univariate functional by a bivariate functional by adding an auxiliary variable. Our bivariate functional can be minimized easily by alternating minimization: for the auxiliary variable, the minimum has a closed form solution; and for the original variable, the minimization problem can be formulated as a classical total variation (TV) denoising problem, and hence can be solved efficiently using a dual formulation. We show that our bivariate functional is equivalent to the original univariate functional. We also show that our alternating minimization is convergent. Numerical results show that the proposed algorithm is very efficient and outperforms that in Chan, Shen and Zhou.

The JPEG standard is one of the most prevalent image compression schemes in use today. While JPEG was designed for use with natural images, it is also widely used for the encoding of raster documents. Unfortunately, JPEG’s characteristic blocking and ringing artifacts can severely degrade the quality of text and graphics in complex documents. We propose a JPEG decompression algorithm which is designed to produce substantially higher quality images from the same standard JPEG encodings. The method works by incorporating a document image model into the decoding process which accounts for the wide variety of content in modern complex color documents. The method works by first segmenting the JPEG encoded document into regions corresponding to background, text, and picture content. The regions corresponding to text and background are then decoded using maximum a posteriori (MAP) estimation. Most importantly, the MAP reconstruction of the text regions uses a model which accounts for the spatial characteristics of text and graphics. Our experimental comparisons to the baseline JPEG decoding as well as to three other decoding schemes, demonstrate that our method substantially improves the quality of decoded images, both visually and as measured by PSNR. I.

Modeling gene expression regulatory networks with the sparse vector autoregressive model

Abstract—The JPEG standard is one of the most prevalent image compression schemes in use today. While JPEG was designed for use with natural images, it is also widely used for the encoding of raster documents. Unfortunately, JPEG’s characteristic blocking and ringing artifacts can severely degrade the quality of text and graphics in complex documents. We propose a JPEG decompression algorithm which is designed to produce substantially higher quality images from the same standard JPEG encodings. The method works by incorporating a document image model into the decoding process which accounts for the wide variety of content in modern complex color documents. The method works by first segmenting the JPEG encoded document into regions corresponding to background, text, and picture content. The regions corresponding to text and background are then decoded using maximum a posteriori (MAP) estimation. Most importantly, the MAP reconstruction of the text regions uses a model which accounts for the spatial characteristics of text and graphics. Our experimental comparisons to the baseline JPEG decoding as well as to three other decoding schemes, demonstrate that our method substantially improves the quality of decoded images, both visually and as measured by PSNR. Index Terms—Decoding, document image processing, image enhancement, image reconstruction, image segmentation, JPEG. I.

Abstract—This paper introduces a new self-calibration destriping technique for pushbroom-type satellite imaging systems. Selfcalibration means that no specific training data are required. It is based on the statistical estimation of each detector gain from the observed image, assuming a linear response. Both theoretical and practical behaviors are studied. Our technique is shown to outperform simpler techniques based on column averages in terms of gain estimation precision while keeping the computational cost within admissible limits. Index Terms—Calibration, estimation, gain measurement, image restoration, image sensors, radiometry. Hervé Carfantan, Member, IEEE, and Jérôme Idier © 2010 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. I.

Techniques based on sparse and redundant representations are at the heart of many state of the art denoising and deconvolution algorithms. A very sparse representation of piecewise polynomial images can be obtained by using a quadtree decomposition to adaptively select a basis. We have recently exploited this to restore images of this form, however the same model can also provide very good sparse approximations of real world images. In this paper we take advantage of this to develop both image denoising and deconvolution algorithms suitable for real world images. We present results on the cameraman image showing comparable performance with soft thresholding using the undecimated wavelet transform in the denoising case and iterative soft thresholding using the undecimated wavelet transform in the deconvolution case. Index Terms — Image restoration, piecewise polynomial approximation, quadtrees, sparse matrices.

Tensors are multi-way arrays, and the CANDECOMP/PARAFAC (CP) tensor factorization has found application in many different domains. The CP model is typically fit using a least squares objective function, which is a maximum likelihood estimate under the assumption of i.i.d. Gaussian noise. We demonstrate that this loss function can actually be highly sensitive to non-Gaussian noise. Therefore, we propose a loss function based on the 1-norm because it can accommodate both Gaussian and grossly non-Gaussian perturbations. We also present an alternating majorization-minimization algorithm for fitting a CP model using our proposed loss function. 1

Simultaneous localization and tracking (SLAT) in sensor networks aims to determine the positions of sensor nodes and a moving target in a network, given incomplete and inaccurate range measurements. One of the established methods for achieving this goal is to maximize a likelihood function (ML), which requires initialization with an approximate solution to avoid convergence towards local extrema. In this paper a Euclidean Distance Matrix (EDM) completion problem is solved to obtain initial sensor/target positions. The likelihood function is then iteratively optimized through either a Majorization-Minimization (MM) or Newton method. To reduce the computational load, an incremental scheme is proposed whereby each new target position is estimated from range measurements, providing additional initialization for ML without the need for solving an expanded EDM completion problem. The performance of these methods is assessed through simulation. 1.