We consider the problem of a holographic associative memory (HAM) which must reconstruct a 2-D optical signal with corrected amplitude errors. The experimental conditions for an associative reconstruction with true brightness tone rendering by a regular HAM based on the ghost-image hologram are determined. More universal all-optical error-correcting (EC) HAMs are also presented and demonstrated. These HAMs perform a reconstruction of the second image of a stored memory that is angularly separated from the readout beam of its partial version. We describe the scheme solution of an ECHAM problem using Denisyuk's hologram, which reconstructs an error-corrected associative response in reflection. Then the original all-optical ECHAM using the so-called quadric hologram (QH) is presented. This term here refers to a thin off-axis nonlinearly recorded hologram used as the matched filter of a regular coherent correlator. When a QH is read out by the partial or distorted version of the stored memory, the complex conjugated associative response is reconstructed at the output plane with an original brightness distribution. A QH-based ECHAM is equivalent in efficiency to nonlinear HAMs based on the resonator architectures using phase-conjugation techniques and external nonlinearities, but it differs from these in arrangement simplicity and implementation flexibility as an EC associative module of the more general neural network architectures.