Konstantin Dragomiretskiy

Bio: Konstantin Dragomiretskiy is an academic researcher from University of California, Los Angeles. The author has contributed to research in topics: Compressed sensing & Hilbert–Huang transform. The author has an hindex of 6, co-authored 7 publications receiving 2337 citations.

Variational Mode Decomposition

Abstract: During the late 1990s, Huang introduced the algorithm called Empirical Mode Decomposition, which is widely used today to recursively decompose a signal into different modes of unknown but separate spectral bands. EMD is known for limitations like sensitivity to noise and sampling. These limitations could only partially be addressed by more mathematical attempts to this decomposition problem, like synchrosqueezing, empirical wavelets or recursive variational decomposition. Here, we propose an entirely non-recursive variational mode decomposition model, where the modes are extracted concurrently. The model looks for an ensemble of modes and their respective center frequencies, such that the modes collectively reproduce the input signal, while each being smooth after demodulation into baseband. In Fourier domain, this corresponds to a narrow-band prior. We show important relations to Wiener filter denoising. Indeed, the proposed method is a generalization of the classic Wiener filter into multiple, adaptive bands. Our model provides a solution to the decomposition problem that is theoretically well founded and still easy to understand. The variational model is efficiently optimized using an alternating direction method of multipliers approach. Preliminary results show attractive performance with respect to existing mode decomposition models. In particular, our proposed model is much more robust to sampling and noise. Finally, we show promising practical decomposition results on a series of artificial and real data.

Two-Dimensional Variational Mode Decomposition

Abstract: In this paper we propose a variational method to adaptively decompose an image into few different modes of separate spectral bands, which are unknown before. A popular method for recursive one dimensional signal decomposition is the Empirical Mode Decomposition algorithm, introduced by Huang in the nineties. This algorithm, as well as its 2D extension, though extensively used, suffers from a lack of exact mathematical model, interpolation choice, and sensitivity to both noise and sampling. Other state-of-the-art models include synchrosqueezing, the empirical wavelet transform, and recursive variational decomposition into smooth signals and residuals. Here, we have created an entirely non-recursive 2D variational mode decomposition (2D-VMD) model, where the modes are extracted concurrently. The model looks for a number of 2D modes and their respective center frequencies, such that the bandlimited modes reproduce the input image (exactly or in least-squares sense). Preliminary results show excellent performance on both synthetic and real images. Running this algorithm on a peptide microscopy image yields accurate, timely, and autonomous segmentation - pertinent in the fields of biochemistry and nanoscience.

Two-Dimensional Compact Variational Mode Decomposition

Abstract: Decomposing multidimensional signals, such as images, into spatially compact, potentially overlapping modes of essentially wavelike nature makes these components accessible for further downstream analysis. This decomposition enables space---frequency analysis, demodulation, estimation of local orientation, edge and corner detection, texture analysis, denoising, inpainting, or curvature estimation. Our model decomposes the input signal into modes with narrow Fourier bandwidth; to cope with sharp region boundaries, incompatible with narrow bandwidth, we introduce binary support functions that act as masks on the narrow-band mode for image recomposition. $$L^1$$L1 and TV terms promote sparsity and spatial compactness. Constraining the support functions to partitions of the signal domain, we effectively get an image segmentation model based on spectral homogeneity. By coupling several submodes together with a single support function, we are able to decompose an image into several crystal grains. Our efficient algorithm is based on variable splitting and alternate direction optimization; we employ Merriman---Bence---Osher-like threshold dynamics to handle efficiently the motion by mean curvature of the support function boundaries under the sparsity promoting terms. The versatility and effectiveness of our proposed model is demonstrated on a broad variety of example images from different modalities. These demonstrations include the decomposition of images into overlapping modes with smooth or sharp boundaries, segmentation of images of crystal grains, and inpainting of damaged image regions through artifact detection.

Mapping Buried Hydrogen-Bonding Networks.

Abstract: We map buried hydrogen-bonding networks within self-assembled monolayers of 3-mercapto-N-nonylpropionamide on Au{111}. The contributing interactions include the buried S-Au bonds at the substrate surface and the buried plane of linear networks of hydrogen bonds. Both are simultaneously mapped with submolecular resolution, in addition to the exposed interface, to determine the orientations of molecular segments and directional bonding. Two-dimensional mode-decomposition techniques are used to elucidate the directionality of these networks. We find that amide-based hydrogen bonds cross molecular domain boundaries and areas of local disorder.

Variational Destriping in Remote Sensing Imagery: Total Variation with L1 Fidelity

Abstract: This paper introduces a variational method for destriping data acquired by pushbroom-type satellite imaging systems. The model leverages sparsity in signals and is based on current research in sparse optimization and compressed sensing. It is based on the basic principles of regularization and data fidelity with certain constraints using modern methods in variational optimization, namely, total variation (TV), L 1 fidelity, and the alternating direction method of multipliers (ADMM). The proposed algorithm, TV– L 1 , uses sparsity-promoting energy functionals to achieve two important imaging effects. The TV term maintains boundary sharpness of the content in the underlying clean image, while the L 1 fidelity allows for the equitable removal of stripes without over- or under-penalization, providing a more accurate model of presumably independent sensors with an unspecified and unrestricted bias distribution. A comparison is made between the TV– L 2 model and the proposed TV– L 1 model to exemplify the qualitative efficacy of an L 1 striping penalty. The model makes use of novel minimization splittings and proximal mapping operators, successfully yielding more realistic destriped images in very few iterations.