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Self-similarity in Fibonacci gratings
Self-similarity in Fibonacci gratings
Fractal signatures appear in the spectrum of Fibonacci gratings due to their quasi-periodic nature, which leads to self-similarity. We demonstrated that the grating structure can be reconstructed using only a small sub-band of information (excluding the central frequency), when combined with sparsity techniques. The figure below compares the reconstruction results with and without our method. This work was conducted at the Indian Institute of Technology, Delhi, working with Dr. Kedar Khare.
Super-resolution using sparsity in Gerchberg-papoulis extrapolation
Super-resolution using sparsity in Gerchberg-papoulis extrapolation
The classical Gerchberg-Papoulis (GP) method was modified by incorporating sparsity. We demonstrated the reconstruction of an object using only a limited portion of its Fourier spectrum, applying total variation as a constraint in the spatial domain. This approach resulted in a notable improvement in resolution beyond the diffraction limit. Additionally, we observed more robust reconstructions from noisy data. The L2-norm reconstruction error was significantly reduced by combining the GP method with sparsity. This work was carried out at the Indian Institute of Technology, Delhi, working with Dr. Kedar Khare.
Resolution enhancement using Fourier ptychographic microscopy
Resolution enhancement using Fourier ptychographic microscopy
A proof of concept for Fourier ptychographic microscopy was successfully implemented. We generated multiple low-resolution images by using different pass-bands in the Fourier space to mimic structured illumination. These images were then combined in the Fourier space through iterative phase retrieval. The figure demonstrates how doubling the Fourier space pass-band results in a twofold improvement in resolution. Additionally, we fabricated an LED array to mount on an inverted light microscope, acquiring images with varying spatial frequency information. This work was part of my final-year undergraduate project, conducted in collaboration with the Tata Institute of Fundamental Research (TIFR), Mumbai.
High-resolution holographic microscope for 3-D imaging of live biological cells
High-resolution holographic microscope for 3-D imaging of live biological cells
The digital holographic microscope (DHM) recovers lost phase information using computational holography. We developed a tool for image segmentation of cervical cancer cell images, and the segmented areas were then combined with phase information to reconstruct a 3D map for measuring surface roughness. This work was conducted at the Indian Institute of Technology, Delhi, working with Dr. Kedar Khare.
Face recognition tool using deep learning
Face recognition tool using deep learning
Face detection and recognition using very few training examples were implemented with deep learning architectures. We employed the MTCNN network for cropping, aligning, and detecting faces, while face recognition was based on the FaceNet network developed by Facebook, utilizing Google’s ImageNet architecture. This work was conducted at the Indian Institute of Technology, Delhi, working with Dr. Brejesh Lall.
Reconstruction from highly irregular samples
Reconstruction from highly irregular samples
We reconstructed an irregularly sampled, band-limited object with a known bandwidth and sub-Nyquist sampling. This was achieved by exploiting the theory of alternating projections onto convex sets (APOCS). The reconstruction was implemented using both Sinc and Bessel basis functions. This work was carried out at the Indian Institute of Technology, Delhi.
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