The analysis of retinal vasculature in digital fundus images is important for diagnosing eye-related diseases. However, digital colour fundus images suffer from low and varied contrast, and are also affected by noise, requiring the use of fundus angiogram modality. The fundus Fluorescein Angiogram (FFA) modality gives about 5 times higher contrast and average PSNR of 26.97 dB for the retinal vasculature. However, FFA is an invasive method that requires injecting contrast agents and this can lead to other physiological problems. Here, low varied contrast and noise in fundus images are addressed. Noise reduction has been incorporated in a non-invasive image-enhancement technique named RETICA. RETICA improves the contrast by first normalising the varied contrast of whole image with Retinex algorithm and then enhancing contrast of retinal vasculature using ICA. To reduce noise, the SNR of fundus images is improved by applying a denoising method, linear subspace Time Domain Constraint Estimator (TDCE), prior to RETICA. Two fundus image datasets are used, 35-Fundus image dataset (Average PSNR of 27.57 dB) and the FINDeRS (Fundus Image for Noninvasive Diabetic Retinopathy System) dataset that contained 175 colour fundus images (Average PSNR of 24.34 dB). The PSNR of the FINDeRS images (green band) are first improved by nearly 3 dB using TDCE and after applying RETICA, higher contrast improvement factors have been achieved averaging around 5.56 compared to 5.46 (RETICA only) for the normal fundus images and 5.12 for FFA images of the 35-Fundus dataset. Hence, incorporating the noise reduction TDCE method with RETICA or with image-enhancement techniques can significantly improve the contrast of fundus images comparable if not better than FFA. Image-enhancement techniques with TDCE thus provides a practical non-invasive alternative to the invasive fluorescein angiogram for retinal imaging.