ICe: interior cevian initialization for enhanced reconstruction methods

Abstract This paper introduces two novel self-induced basis strategies, interior cevian initialization for orthogonal matching pursuit (ICe) and its $$l_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>l</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> -sense optimized version, optimized interior cevian initialization (OICe). These methods address the complexity and convergence issues of the previously proposed self-inspired bases (SIBS) approach. Both algorithms enhance sparse image representation by generating adaptive auxiliary atoms tailored to the image, thereby improving reconstruction quality and computational efficiency. Experimental results show that ICe achieves up to a 35.6% improvement in Normalized Mean Squared Error (NMSE) and a 16.4% increase in Structural Similarity Index (SSIM) compared to conventional OMP. OICe, as the $$l_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>l</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> -sense optimized version of ICe, delivers even greater performance, with improvements of up to 40% in NMSE and 18.5% in SSIM. Additionally, both ICe and OICe significantly reduce bits per pixel (BPP) for image encoding, outperforming SIBS when paired with state-of-the-art dictionaries such as KSVD, MOD, RBDL, and ODL. These results highlight the effectiveness of ICe and OICe in addressing key challenges in sparse representation, offering enhanced accuracy and efficiency across a variety of applications.