Seismic data reconstruction on a dense periodic grid from data acquired on a coarse grid allows oil & gas companies to save on operationally challenging and expensive dense seismic data acquisition. Dense seismic data especially at high frequencies is desired for generating highresolution subsurface image for exploration and production decisions. Although, low-rank based data reconstruction methods perform well at lower frequencies and scalable for large data, their performance degrades at higher frequencies due to increase in rank of approximating matrices. One of the contributions of this thesis is a recursively weighted matrix factorization approach to improve the quality of reconstructed data at higher frequencies. Recursively weighted approach exploits the similarity between adjacent frequency slices. Another contribution of this thesis is a computationally efficient recursively weighted framework for large-scale dataset by parallelizing data reconstruction over rows of low-rank factors of each frequency slices. To reduce the cost and turnaround time of seismic data acquisition simultaneous source acquisition is adapted by the oil and gas industry in recent years. Another contribution of this thesis is a low-rank based method for separation and reconstruction of seismic data on a dense periodic grid from large scale seismic data acquired with simultaneous source acquisition. Next part of this thesis focuses on accurate detection of fractures created by hydraulic fracturing in unconventional reservoirs for economical production of oil & gas. Fracturing of rocks during hydraulic fracturing gives rise to microseismic events, which are localized along these fractures. In this work, a sparsity-promoting microseismic source estimation framework is proposed to detect closely spaced microseismic sources along with estimation of their associated source-time functions from noisy microseismic data. Detecting closely spaced microseismic events helps in delineating fractures and source-time functions are useful in estimating fracture's origin in time. Also, source-time functions can be potentially useful for estimating the source-mechanism. This method does not make any prior assumption on number of microseismic sources or shape of their source-time functions. Last part of this thesis focuses on sparsity-promoting photoacoustic imaging to detect photoabsorbers along with estimating the associated source-time functions. Traditional photoacoustic imaging can only estimate the locations of photoacoustic absorbers. Also, traditional methods require dense transducer coverage whereas sparsity-promotion method can work with poor transducer sampling reducing the overall data storage cost.