Using noninvasive medical imaging techniques to observe internal organs can result in more accurate diagnoses, while avoiding uncomfortable, expensive invasive procedures such as biopsies. One such technique, elastography, uses pairs of ultrasonic images (relaxed and compressed) to create an image called a strain diagram or an elastogram. Elastography has been shown to be useful for detecting and characterizing lesions in nonporous tissue, but fails to provide results for porous tissue such as the lung due to the limitations of ultrasound. Fortunately, X-rays are not limited by tissue-air boundaries and thus X-ray computed tomography elastography (CTE) promises to enable diagnosis and monitoring of ailments such as emphysema or interstitial lung disease. This paper presents improvements upon existing elastography techniques and applies them to CT scans of porous material. Specifically, the improvements include (1) pre-correlation edge detection filtering, and (2) the implementation of 2-D techniques. Edge detection, performed with a first derivative filter, is shown to result in a higher correlation between relaxed and compressed images. This is especially true for feature-rich lung images, which consist of many small pockets of air-filled tissue. This paper also shows the benefit of employing 2-D techniques, even to a 1-D problem.