Nikolas P. Galatsanos

A support vector machine approach for detection of microcalcifications

We investigate an approach based on support vector machines (SVMs) for detection of microcalcification (MC) clusters in digital mammograms, and propose a successive enhancement learning scheme for improved performance. SVM is a machine-learning method, based on the principle of structural risk minimization, which performs well when applied to data outside the training set. We formulate MC detection as a supervised-learning problem and apply SVM to develop the detection algorithm. We use the SVM to detect at each location in the image whether an MC is present or not. We tested the proposed method using a database of 76 clinical mammograms containing 1120 MCs. We use free-response receiver operating characteristic curves to evaluate detection performance, and compare the proposed algorithm with several existing methods. In our experiments, the proposed SVM framework outperformed all the other methods tested. In particular, a sensitivity as high as 94% was achieved by the SVM method at an error rate of one false-positive cluster per image. The ability of SVM to outperform several well-known methods developed for the widely studied problem of MC detection suggests that SVM is a promising technique for object detection in a medical imaging application.

Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation

The application of regularization to ill-conditioned problems necessitates the choice of a regularization parameter which trades fidelity to the data with smoothness of the solution. The value of the regularization parameter depends on the variance of the noise in the data. The problem of choosing the regularization parameter and estimating the noise variance in image restoration is examined. An error analysis based on an objective mean-square-error (MSE) criterion is used to motivate regularization. Two approaches for choosing the regularization parameter and estimating the noise variance are proposed. The proposed and existing methods are compared and their relationship to linear minimum-mean-square-error filtering is examined. Experiments are presented that verify the theoretical results.

Regularized reconstruction to reduce blocking artifacts of block discrete cosine transform compressed images

The reconstruction of images from incomplete block discrete cosine transform (BDCT) data is examined. The problem is formulated as one of regularized image recovery. According to this formulation, the image in the decoder is reconstructed by using not only the transmitted data but also prior knowledge about the smoothness of the original image, which complements the transmitted data. Two methods are proposed for solving this regularized recovery problem. The first is based on the theory of projections onto convex sets (POCS) while the second is based on the constrained least squares (CLS) approach. For the POCS-based method, a new constraint set is defined that conveys smoothness information not captured by the transmitted BDCT coefficients, and the projection onto it is computed. For the CLS method an objective function is proposed that captures the smoothness properties of the original image. Iterative algorithms are introduced for its minimization. Experimental results are presented. >

Projection-based spatially adaptive reconstruction of block-transform compressed images

At the present time, block-transform coding is probably the most popular approach for image compression. For this approach, the compressed images are decoded using only the transmitted transform data. We formulate image decoding as an image recovery problem. According to this approach, the decoded image is reconstructed using not only the transmitted data but, in addition, the prior knowledge that images before compression do not display between-block discontinuities. A spatially adaptive image recovery algorithm is proposed based on the theory of projections onto convex sets. Apart from the data constraint set, this algorithm uses another new constraint set that enforces between-block smoothness. The novelty of this set is that it captures both the local statistical properties of the image and the human perceptual characteristics. A simplified spatially adaptive recovery algorithm is also proposed, and the analysis of its computational complexity is presented. Numerical experiments are shown that demonstrate that the proposed algorithms work better than both the JPEG deblocking recommendation and our previous projection-based image decoding approach.

A similarity learning approach to content-based image retrieval: application to digital mammography

In this paper, we describe an approach to content-based retrieval of medical images from a database, and provide a preliminary demonstration of our approach as applied to retrieval of digital mammograms. Content-based image retrieval (CBIR) refers to the retrieval of images from a database using information derived from the images themselves, rather than solely from accompanying text indices. In the medical-imaging context, the ultimate aim of CBIR is to provide radiologists with a diagnostic aid in the form of a display of relevant past cases, along with proven pathology and other suitable information. CBIR may also be useful as a training tool for medical students and residents. The goal of information retrieval is to recall from a database information that is relevant to the users query. The most challenging aspect of CBIR is the definition of relevance (similarity), which is used to guide the retrieval machine. In this paper, we pursue a new approach, in which similarity is learned from training examples provided by human observers. Specifically, we explore the use of neural networks and support vector machines to predict the users notion of similarity. Within this framework we propose using a hierarchal learning approach, which consists of a cascade of a binary classifier and a regression module to optimize retrieval effectiveness and efficiency. We also explore how to incorporate online human interaction to achieve relevance feedback in this learning framework. Our experiments are based on a database consisting of 76 mammograms, all of which contain clustered microcalcifications (MCs). Our goal is to retrieve mammogram images containing similar MC clusters to that in a query. The performance of the retrieval system is evaluated using precision-recall curves computed using a cross-validation procedure. Our experimental results demonstrate that: 1) the learning framework can accurately predict the perceptual similarity reported by human observers, thereby serving as a basis for CBIR; 2) the learning-based framework can significantly outperform a simple distance-based similarity metric; 3) the use of the hierarchical two-stage network can improve retrieval performance; and 4) relevance feedback can be effectively incorporated into this learning framework to achieve improvement in retrieval precision based on online interaction with users; and 5) the retrieved images by the network can have predicting value for the disease condition of the query.

Digital watermarking robust to geometric distortions

In this paper, we present two watermarking approaches that are robust to geometric distortions. The first approach is based on image normalization, in which both watermark embedding and extraction are carried out with respect to an image normalized to meet a set of predefined moment criteria. We propose a new normalization procedure, which is invariant to affine transform attacks. The resulting watermarking scheme is suitable for public watermarking applications, where the original image is not available for watermark extraction. The second approach is based on a watermark resynchronization scheme aimed to alleviate the effects of random bending attacks. In this scheme, a deformable mesh is used to correct the distortion caused by the attack. The watermark is then extracted from the corrected image. In contrast to the first scheme, the latter is suitable for private watermarking applications, where the original image is necessary for watermark detection. In both schemes, we employ a direct-sequence code division multiple access approach to embed a multibit watermark in the discrete cosine transform domain of the image. Numerical experiments demonstrate that the proposed watermarking schemes are robust to a wide range of geometric attacks.

Multiple-image radiography

Conventional radiography produces a single image of an object by measuring the attenuation of an x-ray beam passing through it. When imaging weakly absorbing tissues, x-ray attenuation may be a suboptimal signature of disease-related information. In this paper we describe a new phase-sensitive imaging method, called multiple-image radiography (MIR), which is an improvement on a prior technique called diffraction-enhanced imaging (DEI). This paper elaborates on our initial presentation of the idea in Wernick et al (2002 Proc. Int. Symp. Biomed. Imaging pp 129-32). MIR simultaneously produces several images from a set of measurements made with a single x-ray beam. Specifically, MIR yields three images depicting separately the effects of refraction, ultra-small-angle scatter and attenuation by the object. All three images have good contrast, in part because they are virtually immune from degradation due to scatter at higher angles. MIR also yields a very comprehensive object description, consisting of the angular intensity spectrum of a transmitted x-ray beam at every image pixel, within a narrow angular range. Our experiments are based on data acquired using a synchrotron light source; however, in preparation for more practical implementations using conventional x-ray sources, we develop and evaluate algorithms designed for Poisson noise, which is characteristic of photon-limited imaging. The results suggest that MIR is capable of operating at low photon count levels, therefore the method shows promise for use with conventional x-ray sources. The results also show that, in addition to producing new types of object descriptions, MIR produces substantially more accurate images than its predecessor, DEI. MIR results are shown in the form of planar images of a phantom and a biological specimen. A preliminary demonstration of the use of MIR for computed tomography is also presented.

Least squares restoration of multichannel images

Multichannel restoration using both within- and between-channel deterministic information is considered. A multichannel image is a set of image planes that exhibit cross-plane similarity. Existing optimal restoration filters for single-plane images yield suboptimal results when applied to multichannel images, since between-channel information is not utilized. Multichannel least squares restoration filters are developed using the set theoretic and the constrained optimization approaches. A geometric interpretation of the estimates of both filters is given. Color images (three-channel imagery with red, green, and blue components) are considered. Constraints that capture the within- and between-channel properties of color images are developed. Issues associated with the computation of the two estimates are addressed. A spatially adaptive, multichannel least squares filter that utilizes local within- and between-channel image properties is proposed. Experiments using color images are described. >

A spatially constrained mixture model for image segmentation

Gaussian mixture models (GMMs) constitute a well-known type of probabilistic neural networks. One of their many successful applications is in image segmentation, where spatially constrained mixture models have been trained using the expectation-maximization (EM) framework. In this letter, we elaborate on this method and propose a new methodology for the M-step of the EM algorithm that is based on a novel constrained optimization formulation. Numerical experiments using simulated images illustrate the superior performance of our method in terms of the attained maximum value of the objective function and segmentation accuracy compared to previous implementations of this approach.

Regularized constrained total least squares image restoration

In this paper, the problem of restoring an image distorted by a linear space-invariant (LSI) point-spread function (PSF) that is not exactly known is formulated as the solution of a perturbed set of linear equations. The regularized constrained total least-squares (RCTLS) method is used to solve this set of equations. Using the diagonalization properties of the discrete Fourier transform (DFT) for circulant matrices, the RCTLS estimate is computed in the DFT domain. This significantly reduces the computational cost of this approach and makes its implementation possible even for large images. An error analysis of the RCTLS estimate, based on the mean-squared-error (MSE) criterion, is performed to verify its superiority over the constrained total least-squares (CTLS) estimate. Numerical experiments for different errors in the PSF are performed to test the RCTLS estimator. Objective and visual comparisons are presented with the linear minimum mean-squared-error (LMMSE) and the regularized least-squares (RLS) estimator. Our experiments show that the RCTLS estimator reduces significantly ringing artifacts around edges as compared to the two other approaches.