Evaluating Effect of Block Size in Compressed Sensing for Grayscale Images

Compressed sensing is an evolving methodology that enables sampling at sub-Nyquist rates and still provides decent signal reconstruction. During the last decade, the reported works have suggested to improve time efficiency by adopting Block based Compressed Sensing (BCS) and reconstruction performance improvement through new algorithms. A trade-off is required between the time efficiency and reconstruction quality. In this paper we have evaluated the significance of block size in BCS to improve reconstruction performance for grayscale images. A parameter variant of BCS [15] based sampling followed by reconstruction through Smoothed Projected Landweber (SPL) technique [16] involving use of Weiner smoothing filter and iterative hard thresholding is applied in this paper. The BCS variant is used to evaluate the effect of block size on image reconstruction quality by carrying out extensive testing on 9200 images acquired from online resources provided by Caltech101 [6], University of Granada [7] and Florida State University [8]. The experimentation showed some consistent results which can improve reconstruction performance in all BCS frameworks including BCS-SPL [17] and its variants [19], [27]. Firstly, the effect of varying block size (4x4, 8x8, 16x16, 32x32 and 64x64) results in changing the Peak Signal to Noise Ratio (PSNR) of reconstructed images from at least 1 dB to a maximum of 16 dB. This challenges the common notion that bigger block sizes always result in better reconstruction performance. Secondly, the variation in reconstruction quality with changing block size is mostly dependent on the image visual contents. Thirdly, images having similar visual contents, irrespective of the size, e.g., those from the same category of Caltech101 [6] gave majority vote for the same Optimum Block Size (OBS). These focused notes may help improve BCS based image capturing at many of the existing applications. For example, experimental results suggest using block size of 8x8 or 16x16 to capture facial identity using BCS. Fourthly, the average processing time taken for BCS and reconstruction through SPL with Lapped transform of Discrete Cosine Transform as the sparifying basis remained 300 milli-seconds for block size of 4x4 to 5 seconds for block size of 64x64. Since the processing time variation remains less than 5 seconds, selecting the OBS may not affect the time constraint in many applications. Analysis reveals that no particular block size is able to provide optimum reconstruction for all images with varying nature of visual contents. Therefore, the selection of block size should be made specific to the particular type of application images depending upon their visual contents