Non-invasively reosolving spatial distribution of tissue metabolites serves as a diagnostic tool to in-vivo metabolism thus making magnetic resonance spectroscopic imaging (MRSI) a very useful application. The tissue concentrations of various metabolites reveal disease state and pseudo-progression of tumors. Also, bio-chemical changes manifest much earlier than structural changes that are achieved using standard magnetic resonance imaging(MRI). However, MRSI has not achieved its potential due to several technical challenges that are specic to it. Several technical advances in the eld of MRI does not translate to MRSI. The specic limitations which make MRSI challenging include long scan times, poor spatial resolution, extremely low signal to noise ratio (SNR). In the last few decades, research in MRSI has focused on advanced data acquisition and reconstruction methods, however they cannot achieve high resolution and feasible scan time. Moreover there are several artifacts that lead to increase of spatial resolution not to mention starved SNR. Existing methods cannot deal with these limitations which considerably impacts applications of MRSI. This thesis work we revisit these problems and introduce data acquisition and reconstruction techniques to address several such challenges. In the first part of the thesis we introduce a variable density spiral acquisition technique which achieves high SNR corresponding to metabolites of interest while reducing truncation artifacts. Along with that we develop a novel compartmentalized reconstruction framework to recover high resolution data from lipid unsuppressed data. Avoiding lipid suppression not only reduces scan time and reliability but also improves SNR which is otherwise reduced even further with existing lipid suppression methods. The proposed algorithm exploits the idea that the lipid and metabolite compartment reside in low-dimensional subspace and we use orthogonality priors to reduce overlap of subspaces. We also look at spectral artifacts like Nyquist ghosting which is a common problem with spectral interleaving. Especially in echo-planar spectroscopic imaging (EPSI), one of the most popular MRSI techniques, maintaining a spatial and spectral resolution requires interleaving. Due to scanner inconsistencies spurious peaks arise which makes quantication inecient. In this thesis a novel structural low-rank prior is used to reduce and denoise spectra and achieve high resolution ESPI data. Finally we look at accelerating multi-dimensional spectroscopic problems. Resolving spectra in two dimensions can help study overlapping spectra and achieve more insight. However with an increased dimension the scan time increases. We developed an algorithm for accelerating this method by recovering data from undersampled measurements. We demonstrate the performance in two applications, 2D infra red spectroscopy and 2D MR spectroscopy . The aim of the thesis is to solve these challenges in MRSI from a signal processing perspective and be able to achieve higher resolution data in practical scan time to ultimately help MRSI reach its potential.