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This paper introduces a novel variational approach for image compression motivated by recent PDE-based approaches combining edge detection and Laplacian inpainting. The essential feature is to encode the image via a sparse vector field,…
Recently sparse coding have been highly successful in image classification mainly due to its capability of incorporating the sparsity of image representation. In this paper, we propose an improved sparse coding model based on linear spatial…
Optical flow is the pattern of apparent motion of objects in a scene. The computation of optical flow is a critical component in numerous computer vision tasks such as object detection, visual object tracking, and activity recognition.…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…
In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The…
Sparse representation of images under certain transform domain has been playing a fundamental role in image restoration tasks. One such representative method is the widely used wavelet tight frame systems. Instead of adopting fixed filters…
In-network distributed estimation of sparse parameter vectors via diffusion LMS strategies has been studied and investigated in recent years. In all the existing works, some convex regularization approach has been used at each node of the…
The data-driven sparse methods such as synthesis dictionary learning (e.g., K-SVD) and sparsifying transform learning have been proven effective in image denoising. However, they are intrinsically single-scale which can lead to suboptimal…
We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularisation, exploiting sparsity in both axisymmetric and directional scale-discretised wavelet space. Denoising, inpainting, and deconvolution problems,…
The L1 norm regularized least squares method is often used for finding sparse approximate solutions and is widely used in 1-D signal restoration. Basis pursuit denoising (BPD) performs noise reduction in this way. However, the shortcoming…
Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many…
Learned data models based on sparsity are widely used in signal processing and imaging applications. A variety of methods for learning synthesis dictionaries, sparsifying transforms, etc., have been proposed in recent years, often imposing…
This paper develops a Statics Preserving Sparse Radon transform (SPSR) algorithm.The de-coloration power of Radon basis functions depends on different factors. The most important one is statics. Statics decrease the sparsity of Radon…
Features based on sparse representation, especially using the synthesis dictionary model, have been heavily exploited in signal processing and computer vision. However, synthesis dictionary learning typically involves NP-hard sparse coding…
Application of deconvolution algorithms to astronomical images is often limited by variations in PSF structure over the domain of the images. One major difficulty is that Fourier methods can no longer be used for fast convolutions over the…
Synthetic aperture sonar (SAS) image resolution is constrained by waveform bandwidth and array geometry. Specifically, the waveform bandwidth determines a point spread function (PSF) that blurs the locations of point scatterers in the…
In a recent article series, the authors have promoted convex optimization algorithms for radio-interferometric imaging in the framework of compressed sensing, which leverages sparsity regularization priors for the associated inverse problem…
We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transform. Our key…
Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…
Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…