Unfortunately, the likelihood is you'll not be able to recover those files once they've been corrupted.
If these files were obtained by the aforementioned recovery software, they may contain the data at the indicated-to-it locations on the disk the file(s) occupied, but that doesn't mean it reconstructed the file(s) identically.
A valid MATLAB Level 5 MAT-file begins with a 128-bye header, of which the first 116-bytes is human-readable text that contains the header information of how/when the file was created. (There's a link to the detailed specification @ <Documentation Link to .mat file format>
Looking at the content of your file, there's no recognizable text at the beginning of the file (nor, in fact, anywhere within it) so there's no chance any of the TMW mex routines are going to work; they'll all fail in it containing a valid haeader.
Whether there's any of the actual data there that could be read or not is uncertain but certainly it would take extensive forensic analysis and intimate knowledge of what the actual content of each was to have any hope at all and I'd venture that the probability of success would still be infinitesimaly small.
