Brendt Wohlberg

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Replacing the lscr<sup>2</sup> data fidelity term of the standard total variation (TV) functional with an lscr<sup>1</sup> data fidelity term has been found to offer a number of theoretical and practical benefits. Efficient algorithms for minimizing this lscr<sup>1</sup>-TV functional have only recently begun to be developed, the fastest of which exploit(More)
Model-based reconstruction is a powerful framework for solving a variety of inverse problems in imaging. In recent years, enormous progress has been made in the problem of denoising, a special case of an inverse problem where the forward model is an identity operator. Similarly, great progress has been made in improving model-based inversion when the(More)
This report discusses methods for estimating linear motion blur. The blurred image is modeled as a convolution between the original image and an unknown point-spread function. The angle of motion blur is estimated using three different approaches. The first employs the cepstrum, the second a Gaussian filter, and the third the Radon transform. To estimate(More)
Fractal image compression is a technique based on the representation of an image by a contractive transform, on the space of images, for which the fixed point is close to the original image. This broad principle encompasses a very wide variety of coding schemes, many of which have been explored in the rapidly growing body of published research. While(More)
Total variation (TV) regularization has become a popular method for a wide variety of image restoration problems, including denoising and deconvolution. A number of authors have recently noted the advantages of replacing the standard lscr<sup>2</sup>data fidelity term with an lscr<sup>1</sup> norm. We propose a simple but very flexible method for solving a(More)
When applying sparse representation techniques to images, the standard approach is to independently compute the representations for a set of overlapping image patches. This method performs very well in a variety of applications, but results in a representation that is multi-valued and not optimized with respect to the entire image. An alternative(More)
Many material and biological samples in scientific imaging are characterized by nonlocal repeating structures. These are studied using scanning electron microscopy and electron tomography. Sparse sampling of individual pixels in a two-dimensional image acquisition geometry, or sparse sampling of projection images with large tilt increments in a tomography(More)
Video background modeling is an important preprocessing step in many video analysis systems. Principal component pursuit (PCP), which is currently considered to be the state-of-the-art method for this problem, has a high computational cost, and processes a large number of video frames at a time, resulting in high memory usage and constraining the(More)
When applying sparse representation techniques to images, the standard approach is to independently compute the representations for a set of overlapping image patches. This method performs very well in a variety of applications, but the independent sparse coding of each patch results in a representation that is not optimal for the image as a whole. A recent(More)
We propose a simple alternating minimization algorithm for solving a minor variation on the original Principal Component Pursuit (PCP) functional. In computational experiments in the video background modeling problem, the proposed algorithm is able to deliver a consistent sparse approximation even after the first outer loop, (taking approximately 12 seconds(More)