Image Super-Resolution Through Compressive Sensing-based Recovery Hadi Zanddizari Electrical Engineering University of South Florida Tampa, Florida, USA hadiz@usf.edu Ankita Dey Systems and Computer Engineering Carleton University Ottawa, Canada ankitadey@cmail.carleton.ca Sreeraman Rajan Systems and Computer Engineering Carleton University Ottawa, Canada sreeraman.rajan@carleton.ca Abstract— The primary aim of image super-resolution tech- niques is to produce a high resolution (HR) image from a low resolution (LR) image efficiently. Deep learning algorithms are being extensively used to address the ill-posed problem of single image super-resolution which requires extremely large data-sets and high processing power. When one does not have access to large data-sets or have limited processing power, an alternative technique may be in order. In this study, we have developed a novel positive scale image resizing method inspired by compressive sensing (CS). We have considered the image super-resolution as a CS recovery problem in which a low res- olution image is assumed as a compressed measurement and the required interpolated image is treated as output of the CS-based recovery. In the proposed HR recovery method, a deterministic binary block diagonal measurement matrix, (DBBD), is used as measurement matrix since it maintains the visual similarity between the low and high resolution images. Then along with a sparsification matrix, the sparse representation of HR image is first recovered and subsequently the dense HR image is obtained. The proposed method is applied to medical and non- medical images. The HR images obtained using the traditional proximal, bilinear and bi-cubic interpolation techniques are compared with those obtained using the proposed method. The proposed CS inspired method delivers superior HR images than the traditional techniques. The superiority of the proposed method is attributed to the unique usage of the DBBD matrix and the CS recovery algorithm to obtain a high resolution image without any prior training data-set. Index Terms–Compressive Sensing, Image interpolation, Im- age Super-Resolution, Deterministic sensing matrix, Recovery techniques I. I NTRODUCTION Images with high resolution help in making better di- agnostic decisions from medical images. Often an image with higher resolution (HR) will enable better detection of anomalies such as tumors and cancerous cells than a low resolution (LR) image. The quality and the resolution of an image obtained through various medical imaging systems such as X-rays, magnetic resonance imaging or computer tomography play a crucial role in the diagnosis of a disease. With high resolution images, it is possible to design auto- matic diagnostic tools that could aid medical professionals to make accurate decisions. It also enables doing object detection and image segmentation with higher accuracy [3]. Realizing this, many diagnostic tools based on deep learning models [1], [2] have been proposed lately. All these models, however, require lot of images for training purposes. When only one low resolution image is available, no learning model can be developed. This paper aims to perform super- resolution (SR) from just a single low resolution (LR) image under the assumption that there is no access to any huge dataset. The term SR can be defined as a technique to enhance or increase the resolution of an image. Single image super- resolution (SISR) aims to generate a HR image from a LR one. Traditionally, super-resolution is attempted either using multiple images and solving for a set of linear constraints or by learning relationship between LR and HR image patches from a database (called example-based approach) [4]. Since the mapping between LR image and HR images are not unique, SISR is an ill-posed problem for image recovery [5]. Although multiple HR images were used in [6] to reconstruct the HR image, the reconstructed image was not guaranteed to contain true HR details. Since recovery of HR was based on multiple examples, new learning algorithms such Bayesian approach [7], neighbour embedding method [8], recovery using sparse patches from LR images [9] were introduced. Over the years, interestingly even for SISR problem, deep learning (DL)-based approaches have become the most sought method. Amongst the DL-based approaches, the SR convolu- tional neural network (CNN) has become the benchmark architecture for DL-based SR algorithm [10]. Deep neural network based unsupervised algorithms such as the deep Boltzmann machine [11], variational autoencoder (VAE) [12] and generative adversarial nets (GAN) [13] have also been implemented to handle unlabeled data situations. All these methods claim their superiority in terms of accuracy but do not highlight the shortcomings associated with them. Firstly, DL algorithms need large pre-trained data-sets for efficient mapping (or learning) which may not be available in many problems. Secondly, DL techniques are image specific. Thirdly, the DL networks may have the problem of over-fitting. Particularly for medical images, such erroneous results may lead to wrong diagnosis. Lastly, implementation of DL algorithms are computationally intensive and therefore require computers with huge processing capability. Unfortu- nately, DL methods are of no avail when only one LR image is available and needs to be converted into a SR image. To overcome the aforementioned shortcomings, non- learning based algorithms may be used. Traditional predic- tion models or interpolation techniques such as proximal, bilinear or bicubic interpolation use weighted average neigh- bouring LR pixel intensities to generate a HR image. 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