Related papers: Geometric kernel smoothing of tensor fields
A method to estimate an acoustic field from discrete microphone measurements is proposed. A kernel-interpolation-based method using the kernel function formulated for sound field interpolation has been used in various applications. The…
The main purpose of this paper is providing a systematic study and classification of non-scalar kernels for Reproducing Kernel Hilbert Spaces (RKHS), to be used in the analysis of deformation in shape spaces endowed with metrics induced by…
This paper describes the many image decomposition models that allow to separate structures and textures or structures, textures, and noise. These models combined a total variation approach with different adapted functional spaces such as…
Tensors in the form of multilinear arrays are ubiquitous in data science applications. Captured real-world data, including video, hyperspectral images, and discretized physical systems, naturally occur as tensors and often come with…
Gaussian noise removal is an interesting area in digital image processing not only to improve the visual quality, but for its impact on other post-processing algorithms like image registration or segmentation. Many presented…
We discuss decrease of coherence in a massive system due to the emission of gravitational waves. In particular we investigate environmental gravitational decoherence in the context of an interference experiment. The time-evolution of the…
Large deformation analysis in geomechanics plays an important role in understanding the nature of post-failure flows and hazards associated with landslides under different natural calamities. In this study, a SPH framework is proposed for…
We present TensoRF, a novel approach to model and reconstruct radiance fields. Unlike NeRF that purely uses MLPs, we model the radiance field of a scene as a 4D tensor, which represents a 3D voxel grid with per-voxel multi-channel features.…
The expected number of false inflection points of kernel smoothers is evaluated. To obtain the small noise limit, we use a reformulation of the Leadbetter-Cryer integral for the expected number of zero crossings of a differentiable Gaussian…
The denoising process of diffusion models can be interpreted as an approximate projection of noisy samples onto the data manifold. Moreover, the noise level in these samples approximates their distance to the underlying manifold. Building…
For signals belonging to balls in smoothness classes and noise with enough moments, the asymptotic behavior of the minimax quadratic risk among soft-threshold estimates is investigated. In turn, these results, combined with a median…
Denoising is intuitively related to projection. Indeed, under the manifold hypothesis, adding random noise is approximately equivalent to orthogonal perturbation. Hence, learning to denoise is approximately learning to project. In this…
Statisticians, as well as machine learning and computer vision experts, have been studying image reconstitution through denoising different domains of photography, such as textual documentation, tomographic, astronomical, and low-light…
The present paper provides a comprehensive study of de-noising properties of frames and, in particular, tight frames, which constitute one of the most popular tools in contemporary signal processing. The objective of the paper is to bridge…
We propose a linear algebraic framework for performing density estimation. It consists of three simple steps: convolving the empirical distribution with certain smoothing kernels to remove the exponentially large variance; compressing the…
We address voice activity detection in acoustic environments of transients and stationary noises, which often occur in real life scenarios. We exploit unique spatial patterns of speech and non-speech audio frames by independently learning…
This paper studies the statistical complexity of kernel hyperparameter tuning in the setting of active regression under adversarial noise. We consider the problem of finding the best interpolant from a class of kernels with unknown…
In this paper, a filtering approach for the 3D magnetic resonance imaging (MRI) assuming a Rician model for noise is addressed. Our denoising method is based on the Conventional Approach (CA) proposed to deal with the noise issue in the…
Under the assumption that data lie on a compact (unknown) manifold without boundary, we derive finite sample bounds for kernel smoothing and its (first and second) derivatives, and we establish asymptotic normality through Berry-Esseen type…
Denoising diffusion models are a class of generative models which have recently achieved state-of-the-art results across many domains. Gradual noise is added to the data using a diffusion process, which transforms the data distribution into…