Michalina Wanda Pacholska

Biography

I’m quite bad at following a simple path. I studied inter-faculty math and science studies (mostly mathematics, some physics with just a pinch of chemistry and biology) at University of Warsaw. In 2016 I finished Masters with specialisation in topology and set theory. My master thesis was in (mathematical) signal processing, and I’ve been under guidance of Computational Biology Group. Then I have done an internship at Google Mountain View where I worked on C data processing pipeline. Came back to Europe to do PhD in computer science at EPFL, where I tried working on physically based rendering only to go back to settle in LCAV. Signal processing led me to Fourier optics and playing with lasers in the Galata Laboratory, but as cool it sounds, I wandered off towards localisation and SLAM. Oh, and I had a break last year, I went for an internship to DeepMind to fold some proteins.In the free time I draw cows for Helvetic Coding Contest :)

Official source

https://people.epfl.ch/michalina.pacholska

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Lippmann Photography: A Signal Processing Perspective

Gilles Baechler, Arnaud Latty, Michalina Wanda Pacholska, Adam James Scholefield, Martin Vetterli

Lippmann (or interferential) photography is the first and only analog photography method that can capture the full color spectrum of a scene in a single take. This technique, invented more than a hundred years ago, records the colors by creating interference patterns inside the photosensitive plate. Lippmann photography provides a great opportunity to demonstrate several fundamental concepts in signal processing. Conversely, a signal processing perspective enables us to shed new light on the technique. In our previous work (G. Baechler et al., 2021), we analyzed the spectra of historical Lippmann plates using our own mathematical model. In this paper, we provide the derivation of this model and validate it experimentally. We highlight new behaviors whose explanations were ignored by physicists to date. In particular, we show that the spectra generated by Lippmann plates are in fact distorted versions of the original spectra. We also show that these distortions are influenced by the thickness of the plate and the reflection coefficient of the reflective medium used in the capture of the photographs. We verify our model with extensive experiments on our own Lippmann photographs.

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

Sampling Geometry and Colour

Michalina Wanda Pacholska

In this thesis, we take a signal-processing approach to two research areas outside of the core of the signal processing research: geometry reconstruction and light propagation through non-uniform media.In the first area, we consider new sampling schemes inspired by problems of surface recovery and continuous localisation. We analyse sampling at unknown locations and show signal recovery uniqueness under constraints. We also study non-synchronised sampling of vector-valued signals or fields, that arise in the problem of localisation of a smoothly moving device. We provide sufficient conditions for device localisation. To this end, we formulate the problem of rank-one sensing of full-rank matrices and develop sufficient conditions for matrix recovery when some measurements are missing.In the second area, we study Lippmann photography, a century-old colour photography technique. We model recording and viewing of a Lippmann photograph as analysis and synthesis operators and study the invertibility of their composition. We extend our analysis to a potential method of creating digital photographs, namely internal modification of glass with femto-second lasers.

EPFL2021

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Matrix (or operator) recovery from linear measurements is a well-studied problem. However, there are situations where only bilinear or quadratic measurements are available. A bilinear or quadratic problem can easily be transformed into a linear one, but it raises questions when the linearized problem is solvable and what is the cost of linearization. In this work, we study a few specific cases of this general problem and show when the bilinear problem is solvable. Using this result and certain properties of polynomial rings, we present a scenario when the quadratic problem can be linearized at the cost of just a linear number of additional measurements. Finally, we link our results back to two applications that inspired it: Time Encoding Machines and Continuous Localisation.

ArXiv2020