Ultrasound (US) imaging is a widely used medical modality since it is inexpensive non-invasive and portable. However, the quality of US is limited by physical constraints (e.g. thermal noise) and hardware restrictions (e.g. the number of sensors in a US probe). To increase the quality and improve the resolution of US images, I proposed two novel algorithms, namely COherent Denoising for Elastography (CODE), for removing noise of RF data for elastography technique and coherent ultrasound super-resolution to perform a novel super-resolution technique. I first propose CODE to improve the estimation of tissue displacement in ultrasound elastography. Ultrasound elastography computes the mechanical properties of tissues affected by an internal of external force. The radio frequency data acquired from ultrasound is usually corrupted with noise that leads ultrasound elastography techniques for fail. To remove this noise I proposed CODE that despite the local denoising algorithms, keeps the information of the RF data for elastography. I investigate two state-of-the-art elastography methods, GLobal Ultrasound Elastography (GLUE), and; (ii) Dynamic Programming Analytic Minimization elastography, and results shows the improvement of the strain maps on both patient and phantom data. I then introduce a super-resolution technique for improving the quality of ultrasound B-mode images. The resolution of ultrasound images is limited by hardware constraints and physical restrictions. Conventionally, ultrasound machines use interpolation techniques for improving the resolution of the B-mode images. However, I propose a new method for coherent ultrasound super-resolution that overcomes conventional approaches in both qualitative and quantitative measures. In both cases, I proposed a mathematical framework that justified the behavior of the algorithms and tested the methods on both in-vivo, and phantom data, and discussed qualitatively and quantitatively.