Related papers: Adjoint Method in PDE-based Image Compression

A finite-element method dependant adjoint-based procedure to determine the temperature field of structures based on measured displacements or strains and a set of standard loads is developed and tested. Given a series of force and…

A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…

We propose a PDE-constrained optimization approach for the determination of noise distribution in total variation (TV) image denoising. An optimization problem for the determination of the weights correspondent to different types of noise…

In this paper, we present a new image segmentation method based on the concept of sparse subset selection. Starting with an over-segmentation, we adopt local spectral histogram features to encode the visual information of the small segments…

This paper investigates a fully unsupervised statistical method for edge preserving image restoration and compression using a spatial decomposition scheme. Smoothed maximum likelihood is used for local estimation of edge pixels from mixture…

Image compression at extremely low bitrates (below 0.1 bits per pixel (bpp)) is a significant challenge due to substantial information loss. In this work, we propose a novel two-stage extreme image compression framework that exploits the…

Segmentation of microscopy images constitutes an ill-posed inverse problem due to measurement noise, weak object boundaries, and limited labeled data. Although deep neural networks provide flexible nonparametric estimators, unconstrained…

We propose a simple interpolation-based method for the efficient approximation of gradients in neural ODE models. We compare it with the reverse dynamic method (known in the literature as "adjoint method") to train neural ODEs on…

This paper presents a super-resolution method based on gradient-based adaptive interpolation. In this method, in addition to considering the distance between the interpolated pixel and the neighboring valid pixel, the interpolation…

Super-resolution is an important but difficult problem in image/video processing. If a video sequence or some training set other than the given low-resolution image is available, this kind of extra information can greatly aid in the…

We present a new nonlinear optimization approach for the sparse reconstruction of single-photon absorption and two-photon absorption coefficients in photoacoustic tomography (PAT). This framework comprises of minimizing an objective…

Point cloud is a crucial representation of 3D contents, which has been widely used in many areas such as virtual reality, mixed reality, autonomous driving, etc. With the boost of the number of points in the data, how to efficiently…

This paper focuses on the ultimate limit theory of image compression. It proves that for an image source, there exists a coding method with shapes that can achieve the entropy rate under a certain condition where the shape-pixel ratio in…

This paper describes a class of shape optimization problems for optical metamaterials comprised of periodic microscale inclusions composed of a dielectric, low-dimensional material suspended in a non-magnetic bulk dielectric. The shape…

Inpainting-based codecs store sparse selected pixel data and decode by reconstructing the discarded image parts by inpainting. Successful codecs (coders and decoders) traditionally use inpainting operators that solve partial differential…

The adjoint method allows efficient calculation of the gradient with respect to the design variables of a topology optimization problem. This method is almost exclusively used in combination with traditional Finite-Element-Analysis, whereas…

Existing customization methods require access to multiple reference examples to align pre-trained diffusion probabilistic models (DPMs) with user-provided concepts. This paper aims to address the challenge of DPM customization when the only…

We present an optimization framework for photo-acoustic tomography of brain based on a system of coupled equations that describe the propagation of sound waves in linear isotropic inhomogeneous and lossy elastic media with the absorption…

Learning-based image compression methods have emerged as state-of-the-art, showcasing higher performance compared to conventional compression solutions. These data-driven approaches aim to learn the parameters of a neural network model…

The search for image compression optimization techniques is a topic of constant interest both in and out of academic circles. One method that shows promise toward future improvements in this field is image colorization since image…