Computational Imaging and Inverse Problems: Making the Invisible Visible

Computational imaging is a rapidly evolving interdisciplinary field awarded of many Nobel prizes. In computationalopticalimaging, digitalprocessing is employed in conjunction with an optical system toformimages. That is, images are computationally formed fromsome indirectmeasurements bysolving an inverse problem. Driven by advances insignal processing techniques and faster computing platforms, this approach continuously yields the development of next-generationimaging systems in consumerelectronics, defenseindustry, space physics, bioimaging and medicine. Theseimaging systemsenablenew forms of visual information, new imaging functionalities, reducedhardware complexity, and cost,as well ashigher resolution, that would be difficult, if not impossible, to achieve using traditional imaging. In this talk, first the fundamentals ofcomputational optical imaging will be describedand a unified treatment of the mathematical principles, inverse problems,and computational methods underlying the development of modernopticalimaging technologies will be provided. Afterwards, an overview of ongoing projects at METU Computational Imaging Lab will be presented with a focus on spectral imaging. In particular, aclass of novel spectral imaging techniques will be describedin detail. All of these involve distributing the imaging task between a novel optical system and a reconstruction algorithm. The optical systems take multiplexed measurementsusing diffractive lenses and coded apertures,andthen these measurements are usedwith areconstruction algorithmto digitally formthe spectral images. Compressive sensing theory, convex optimization, sparsity-and deep learning-basedimage reconstruction approaches are exploited for this purpose. The developed spectral imaging techniques not only enablehighspatial, spectral, and temporal resolutions that are beyond the reach of conventional techniques, but also allow reduced hardware complexityand cost.


On generalized semi-infinite optimization of genetic networks
Weber, Gerhard Wilhelm; Tezel, Aysun (2007-07-01)
Since some years, the emerging area of computational biology is looking for its mathematical foundations. Based on modem contributions given to this area, our paper approaches modeling and prediction of gene-expression patterns by optimization theory, with a special emphasis on generalized semi-infinite optimization. Based on experimental data, nonlinear ordinary differential equations are obtained by the optimization of least-squares errors. The genetic process can be investigated by a time-discretization ...
Mathematical contributions to dynamics and optimization of gene-environment networks
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This article contributes to a further introduction of continuous optimization in the field of computational biology which is one of the most challenging and emerging areas of science, in addition to foundations presented and the state-of-the-art displayed in [C.A. Floudas and P.M. Pardalos, eds., Optimization in Computational Chemistry and Molecular Biology: Local and Global Approaches, Kluwer Academic Publishers, Boston, 2000]. Based on a summary of earlier works by the coauthors and their colleagues, it r...
Computational spectral imaging techniques using diffractive lenses and compressive sensing
Kar, Oğuzhan Fatih; Öktem, Sevinç Figen; Department of Electrical and Electronics Engineering (2019)
Spectral imaging is a fundamental diagnostic technique in physical sciences with application in diverse fields such as physics, chemistry, biology, medicine, astronomy, and remote sensing. In this thesis, we first present a modified version of a high-resolution computational spectral imaging modality and develop a fast sparse recovery method to solve the associated large-scale inverse problems. This technique uses a diffractive lens called photon sieve for dispersing the optical field. We then extend this t...
Computational representation of protein sequences for homology detection and classification
Oğul, Hasan; Mumcuoğlu, Ünal Erkan; Department of Information Systems (2006)
Machine learning techniques have been widely used for classification problems in computational biology. They require that the input must be a collection of fixedlength feature vectors. Since proteins are of varying lengths, there is a need for a means of representing protein sequences by a fixed-number of features. This thesis introduces three novel methods for this purpose: n-peptide compositions with reduced alphabets, pairwise similarity scores by maximal unique matches, and pairwise similarity scores by...
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In line with the advances in high-throughput technologies, multiple omic datasets have accumulated to study biological systems and diseases coherently. No single omics data type is capable of fully representing cellular activity. The complexity of the biological processes arises from the interactions between omic entities such as genes, proteins, and metabolites. Therefore, multi-omic data integration is crucial but challenging. The impact of the molecular alterations in multi-omic data is not local in the ...
Citation Formats
S. F. Öktem, “Computational Imaging and Inverse Problems: Making the Invisible Visible,” Koç Üniversitesi , İstanbul, Türkiye, 2019, p. 15, Accessed: 00, 2021. [Online]. Available: