An <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> adaptive dete

Abstract We consider image deblurring problems in the presence of impulse noise. The key to successful image restoration is the accurate identification of impulse noise locations. Using the maximum a posteriori probability estimation, we first derive an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> TV model for image deblurring with impulse noise. A novel objective function is proposed to implicitly approximate the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math> norm, and an alternating minimization ‘like’ algorithm is developed to solve the resulting surrogate model. The main advantage of our method is that it can adaptively identify and update the impulse locations at each iteration and then restore the image using current estimated noise-free pixels. Theoretically, we establish global convergence to a local minimizer of the nonconvex objective function. Additionally, we propose a strategy for adaptively updating parameters to empirically accelerate the convergence rate and enhance the quality of the restored image. Experimental results demonstrate the superiority of the proposed method in comparison to competing methods, especially in detecting and restoring random valued impulse noise, where it achieves significantly improved performance.