Mathematics behind a Class of Image Restoration Algorithms

The restoration techniques are usually oriented toward modeling the type of degradation in order to infer the inverse process for recovering the given image. This approach usually involves the option for a criterion to numerically evaluate the quality of the resulted image and consequently the restoration process can be expressed in terms of an optimization problem. Most of the approaches are essentially based on additional hypothesis concerning the statistical properties of images. However, in real life applications, there is no enough information to support a certain particular image model, and consequently model-free developments have to be used instead. In our approaches the problem of image denoising/restoration is viewed as an information transmission/processing system, where the signal representing a certain clean image is transmitted through a noisy channel and only a noise-corrupted version is available. The aim is to recover the available signal as much as possible by using different noise removal techniques that is to build an accurate approximation of the initial image. Unfortunately, a series of image qualities, as for instance clarity, brightness, contrast, are affected by the noise removal techniques and consequently there is a need to partially restore them on the basis of information extracted exclusively from data. Following a brief description of the image restoration framework provided in the introductory part, a PCA-based methodology is presented in the second section of the paper. The basics of a new informational-based development for image restoration purposes and scatter matrix-based methods are given in the next two sections. The final section contains concluding remarks and suggestions for further work

Lossy compression of multidimensional medical images using sinusoidal activation networks: an evaluation study

In this work, we evaluate how neural networks with periodic activation functions can be leveraged to reliably compress large multidimensional medical image datasets, with proof-of-concept application to 4D diffusion-weighted MRI (dMRI). In the medical imaging landscape, multidimensional MRI is a key area of research for developing biomarkers that are both sensitive and specific to the underlying tissue microstructure. However, the high-dimensional nature of these data poses a challenge in terms of both storage and sharing capabilities and associated costs, requiring appropriate algorithms able to represent the information in a low-dimensional space. Recent theoretical developments in deep learning have shown how periodic activation functions are a powerful tool for implicit neural representation of images and can be used for compression of 2D images. Here we extend this approach to 4D images and show how any given 4D dMRI dataset can be accurately represented through the parameters of a sinusoidal activation network, achieving a data compression rate about 10 times higher than the standard DEFLATE algorithm. Our results show that the proposed approach outperforms benchmark ReLU and Tanh activation perceptron architectures in terms of mean squared error, peak signal-to-noise ratio and structural similarity index. Subsequent analyses using the tensor and spherical harmonics representations demonstrate that the proposed lossy compression reproduces accurately the characteristics of the original data, leading to relative errors about 5 to 10 times lower than the benchmark JPEG2000 lossy compression and similar to standard pre-processing steps such as MP-PCA denosing, suggesting a loss of information within the currently accepted levels for clinical application

A Decade of Neural Networks: Practical Applications and Prospects

The Jet Propulsion Laboratory Neural Network Workshop, sponsored by NASA and DOD, brings together sponsoring agencies, active researchers, and the user community to formulate a vision for the next decade of neural network research and application prospects. While the speed and computing power of microprocessors continue to grow at an ever-increasing pace, the demand to intelligently and adaptively deal with the complex, fuzzy, and often ill-defined world around us remains to a large extent unaddressed. Powerful, highly parallel computing paradigms such as neural networks promise to have a major impact in addressing these needs. Papers in the workshop proceedings highlight benefits of neural networks in real-world applications compared to conventional computing techniques. Topics include fault diagnosis, pattern recognition, and multiparameter optimization

An autoencoder compression approach for accelerating large-scale inverse problems

PDE-constrained inverse problems are some of the most challenging and computationally demanding problems in computational science today. Fine meshes that are required to accurately compute the PDE solution introduce an enormous number of parameters and require large scale computing resources such as more processors and more memory to solve such systems in a reasonable time. For inverse problems constrained by time dependent PDEs, the adjoint method that is often employed to efficiently compute gradients and higher order derivatives requires solving a time-reversed, so-called adjoint PDE that depends on the forward PDE solution at each timestep. This necessitates the storage of a high dimensional forward solution vector at every timestep. Such a procedure quickly exhausts the available memory resources. Several approaches that trade additional computation for reduced memory footprint have been proposed to mitigate the memory bottleneck, including checkpointing and compression strategies. In this work, we propose a close-to-ideal scalable compression approach using autoencoders to eliminate the need for checkpointing and substantial memory storage, thereby reducing both the time-to-solution and memory requirements. We compare our approach with checkpointing and an off-the-shelf compression approach on an earth-scale ill-posed seismic inverse problem. The results verify the expected close-to-ideal speedup for both the gradient and Hessian-vector product using the proposed autoencoder compression approach. To highlight the usefulness of the proposed approach, we combine the autoencoder compression with the data-informed active subspace (DIAS) prior to show how the DIAS method can be affordably extended to large scale problems without the need of checkpointing and large memory