Variational Bayesian image restoration with group-sparse modeling of wavelet coefficients

In this work, we present a recent wavelet-based image restoration framework based on a group-sparse Gaussian scale mixture model. A hierarchical Bayesian estimation is derived using a combination of variational Bayesian inference and a subband-adaptive majorization–minimization method that simplifies computation of the posterior distribution. We show that both of these iterative methods can converge together without needing nested loops, and thus good solutions can be found rapidly in the non-convex search space. We also integrate our method, variational Bayesian with majorization minimization (VBMM), with tree-structured modeling of the wavelet coefficients. This extension achieves significant gains in performance over the coefficient-sparse version of the algorithm. The experimental results demonstrate that the proposed method and its tree-structured extensions are effective for various imaging applications such as image deconvolution, image superresolution and compressive sensing magnetic resonance imaging (MRI) reconstruction, and that they outperform more conventional sparsity-inducing methods based on the _l1-norm.This is the author accepted manuscript. The final version is available from Elsevier at http://www.sciencedirect.com/science/article/pii/S1051200415001438

Ehdolliset normalisoivat virtaukset kuvien käänteisongelmissa

Learning-based methods have provided powerful tools for solving classification and regression -related problems yielding far superior results to classical handcrafted rule-based models. These models have proven to be efficient in multiple domains in many different fields. However, many common problems are inherently illposed and lack a unique answer hence requiring a regularization pass or alternatively a probabilistic framework for successful modeling. While many different families of models capable of learning distributions given samples exist, they commonly resort to approximations or surrogate training objectives. In this thesis we solve image-related inverse problems with a family of probabilistic models known as conditional normalizing flows. A normalizing flow consists of repeated applications of invertible transformations on a simple prior distribution rendering it into a more complex distribution with direct and tractable probability density evaluation and efficient sampling. We show that a conditional normalizing flow is able to provide plausible, high-quality samples with visible benign variance from a conditional distribution in image super resolution, denoising and colorization tasks. We quantify the success of the model as well as its shortcomings and inspect how it internally addresses the conversion of white noise into a realistic image.Havainnoista oppimiseen optimoinnin avulla perustuvat mallit kykenevät ratkaisemaan monia ongelmia huomattavasti tehokkaammin, kuin klassiset staattisiin päätössääntöihin perustuvat mallit. Perinteisesti mallit antavat yleensä kuitenkin vain yhden vastauksen, vaikka useilla ongelmilla saattaa olla monta keskenään yhtä hyväksyttävää vastausta. Tämän takia on tarkoituksenmukaista mallintaa todennäköisyysjakaumaa kaikista mahdollisista vastauksista yksittäisen vastauksen sijaan. Tässä diplomityössä tutkitaan normalisoivien virtausten malliluokan soveltamista digitaalisiin kuviin liittyviin käänteisongelmiin. Normalisoiva virtaus muuntaa yksinkertaisen todennäköisyysjakauman neuroverkoilla parametrosoiduilla kääntyvillä funktioilla monimutkaisemmaksi jakaumaksi, siten että havaintojen uskottavuudesta saadaan kuitenkin tarkka numeerinen arvo. Normalisoivat virtaukset mahdollistavat myös tehokkaan näytteiden ottamisen niiden mallintamasta monimutkaisesta todennäköisyysjakaumasta. Työssä määritetään, kuinka hyvin virtausmallit onnistuvat tehtävässään ja kuinka ne muodostavat uskottavia kuvia kohinasta. Työssä todetaan, että ehdollisten normalisoivien virtausten avulla voidaan tuottaa korkealaatuisia näytteitä useissa kuviin liittyvissä käänteisongelmissa

Unraveling the Thousand Word Picture: An Introduction to Super-Resolution Data Analysis

Super-resolution microscopy provides direct insight into fundamental biological processes occurring at length scales smaller than light’s diffraction limit. The analysis of data at such scales has brought statistical and machine learning methods into the mainstream. Here we provide a survey of data analysis methods starting from an overview of basic statistical techniques underlying the analysis of super-resolution and, more broadly, imaging data. We subsequently break down the analysis of super-resolution data into four problems: the localization problem, the counting problem, the linking problem, and what we’ve termed the interpretation problem

Statistical Models for Single Molecule Localization Microscopy

Single-molecule localization microscopy (SMLM) has revolutionized the field of cell biology. It allowed scientists to break the Abbe diffraction limit for fluorescence microscopy and got it closer to the electron microscopy resolution but still it faced some serious challenges. Two of the most important of these are the sample drift and the measurement noise problems that result in lower resolution images. Both of these problems are generally unavoidable where the sample drift is a natural mechanical phenomenon that occurs during the long time of image acquisition required for SMLM (Geisler et al. 2012) while the measurement noise, which arises from combining localization uncertainty and counting error, is related to the number of photons collected from the fluorophore and affects the precision in locating the centroids of single molecules (Thompson, Larson, and Webb 2002). Previous work has tried to devise methods to deal with the sample drift problem but unfortunately, these methods either add too much complexity to the experimental setup or are just inefficient in correctly estimating the drift at the single frame level (Wang et al. 2014). As for measurement noise, all current regular image rendering algorithms treat every detection of the fluorophore as a separate event and hence, the localization uncertainty of every detection of the same molecule would give offset coordinates from the other detections leading to a distorted final image. In this thesis, I demonstrate two novel approaches based on statistical concepts to address each of these two problems. The algorithm for solving the sample drift problem is based on Bayesian inference and it showed efficiency in estimating drift at the single-frame level and proved superior and more straightforward than the available methods. The algorithm for addressing the measurement noise problem is based on Gibbs sampling and not only did it enhance resolution, but it also offers for the first time a means to quantify resolution uncertainty as well as uncertainty in cluster size measurement for clustering proteins. Therefore, this work offers a significant advancement in the field of SMLM and more generally, cell biology

Key Information Retrieval in Hyperspectral Imagery through Spatial-Spectral Data Fusion

Hyperspectral (HS) imaging is measuring the radiance of materials within each pixel area at a large number of contiguous spectral wavelength bands. The key spatial information such as small targets and border lines are hard to be precisely detected from HS data due to the technological constraints. Therefore, the need for image processing techniques is an important field of research in HS remote sensing. A novel semisupervised spatial-spectral data fusion method for resolution enhancement of HS images through maximizing the spatial correlation of the endmembers (signature of pure or purest materials in the scene) using a superresolution mapping (SRM) technique is proposed in this paper. The method adopts a linear mixture model and a fully constrained least squares spectral unmixing algorithm to obtain the endmember abundances (fractional images) of HS images. Then, the extracted endmember distribution maps are fused with the spatial information using a spatial-spectral correlation maximizing model and a learning-based SRM technique to exploit the subpixel level data. The obtained results validate the reliability of the technique for key information retrieval. The proposed method is very efficient and is low in terms of computational cost which makes it favorable for real-time applications